Merge commit for internal changes

55 files changed, 1982 insertions, 755 deletions

diff --git a/tensorflow/contrib/framework/BUILD b/tensorflow/contrib/framework/BUILD
index b13de8e53f..cb4749c88e 100644
--- a/tensorflow/contrib/framework/BUILD
+++ b/tensorflow/contrib/framework/BUILD
@@ -78,17 +78,6 @@ py_test(
 )
 
 cuda_py_test(
-    name = "embedding_ops_test",
-    size = "small",
-    srcs = ["python/ops/embedding_ops_test.py"],
-    additional_deps = [
-        ":framework_py",
-        "//tensorflow/python:framework_test_lib",
-        "//tensorflow/python:platform_test",
-    ],
-)
-
-cuda_py_test(
     name = "sampling_ops_test",
     size = "small",
     srcs = ["python/ops/sampling_ops_test.py"],
diff --git a/tensorflow/contrib/layers/BUILD b/tensorflow/contrib/layers/BUILD
index f4827c0646..bd05720b26 100644
--- a/tensorflow/contrib/layers/BUILD
+++ b/tensorflow/contrib/layers/BUILD
@@ -213,6 +213,19 @@ py_test(
     ],
 )
 
+py_test(
+    name = "embedding_ops_test",
+    size = "small",
+    srcs = ["python/layers/embedding_ops_test.py"],
+    srcs_version = "PY2AND3",
+    deps = [
+        ":layers_py",
+        "//tensorflow:tensorflow_py",
+        "//tensorflow/python:framework_test_lib",
+        "//tensorflow/python:platform_test",
+    ],
+)
+
 filegroup(
     name = "all_files",
     srcs = glob(
diff --git a/tensorflow/contrib/layers/python/layers/__init__.py b/tensorflow/contrib/layers/python/layers/__init__.py
index 239aee7a3d..f1f3b52a50 100644
--- a/tensorflow/contrib/layers/python/layers/__init__.py
+++ b/tensorflow/contrib/layers/python/layers/__init__.py
@@ -19,6 +19,7 @@ from __future__ import division
 from __future__ import print_function
 
 # pylint: disable=wildcard-import
+from tensorflow.contrib.layers.python.layers.embedding_ops import *
 from tensorflow.contrib.layers.python.layers.feature_column import *
 from tensorflow.contrib.layers.python.layers.feature_column_ops import *
 from tensorflow.contrib.layers.python.layers.initializers import *
diff --git a/tensorflow/contrib/layers/python/layers/embedding_ops.py b/tensorflow/contrib/layers/python/layers/embedding_ops.py
new file mode 100644
index 0000000000..4904c16a9c
--- /dev/null
+++ b/tensorflow/contrib/layers/python/layers/embedding_ops.py
@@ -0,0 +1,191 @@
+# pylint: disable=g-bad-file-header
+# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+"""Embedding functions."""
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+from tensorflow.contrib.framework.python.ops import embedding_ops as contrib_embedding_ops
+from tensorflow.contrib.layers.python.ops import sparse_feature_cross_op
+from tensorflow.python.framework import dtypes
+
+from tensorflow.python.framework import ops
+from tensorflow.python.ops import array_ops
+from tensorflow.python.ops import embedding_ops
+from tensorflow.python.ops import math_ops
+from tensorflow.python.ops import sparse_ops
+
+__all__ = ["safe_embedding_lookup_sparse", "hashed_embedding_lookup",
+           "hashed_embedding_lookup_sparse"]
+
+
+# TODO(chapelle): move the safe_embedding_lookup_sparse code here (b/29826543)
+safe_embedding_lookup_sparse = contrib_embedding_ops.safe_embedding_lookup_sparse  # pylint: disable=line-too-long
+
+
+def hashed_embedding_lookup(params, values, dimension, name=None):
+  """Looks up embeddings using parameter hashing for each value in `values`.
+
+  The i-th embedding component of a value v in `values` is found by retrieving
+  the weight whose index is a fingerprint of the pair (v,i).
+  The concept is explored as "feature hashing" for model compression in this
+  paper: http://arxiv.org/pdf/1504.04788.pdf
+
+  Feature hashing has the pleasant effect of allowing us to compute an embedding
+  without needing a pre-determined vocabulary, relieving some amount of process
+  complexity. It also allows for us to maintain embeddings for possibly
+  trillions of features with a fixed amount of memory.
+
+  Note that this is superior to out-of-vocabulary shared "hash buckets" in that
+  the embedding is extremely likely to be unique for each token as opposed to
+  being shared across probably-colliding tokens. The price is that we must
+  compute a hash once for each scalar in the token's embedding as opposed to
+  once per token.
+
+  If `params` is a list, it represents a partition of the embedding parameters.
+  Each tensor in the list should have the same length, except for the first ones
+  which may have an additional element. For instance 10 parameters can be
+  partitioned in 4 tensors with length `[3, 3, 2, 2]`.
+
+  Args:
+    params: A `Tensor` or `list` of `Tensors`.
+      Each tensor must be of rank 1 with fully-defined shape.
+    values: `Tensor` of values to be embedded.
+    dimension: Embedding dimension
+    name: An optional name for this op.
+
+  Returns:
+    A tensor with shape [d0, ..., dn, dimension]
+      with shape(values) = [d0, ..., dn]
+
+  Raises:
+    ValueError: if dimension is not positive or the partition size is invalid.
+  """
+  if not isinstance(params, list):
+    params = [params]
+
+  with ops.op_scope(params + [dimension, values], name,
+                    "hashed_embedding_lookup"):
+    if dimension <= 0:
+      raise ValueError("Dimension should be >0 not %d" % dimension)
+
+    num_partitions = len(params)
+    partition_sizes = []
+    for p in range(num_partitions):
+      shape = params[p].get_shape()
+      shape.assert_has_rank(1)
+      shape.assert_is_fully_defined()
+      partition_sizes.append(shape[0].value)
+    num_params = sum(partition_sizes)  # Total number of parameters.
+
+    # Assert the size of each partition.
+    for p in range(num_partitions):
+      expected_size = (num_params - p - 1) // num_partitions + 1
+      if partition_sizes[p] != expected_size:
+        raise ValueError("Tensor %d in params has size %d, expected %d." %
+                         (p, partition_sizes[p], expected_size))
+
+    # Flatten the values
+    values_shape = array_ops.shape(values)
+    values = array_ops.reshape(values, [-1, 1])
+
+    # With two values v1 and v2 and 3 dimensions, we will cross
+    # [[0, 1, 2], [0, 1, 2]] with [[v1], [v2]].
+    tensors_to_cross = [array_ops.tile(array_ops.expand_dims(
+        math_ops.range(0, dimension), 0), array_ops.shape(values)), values]
+    ids = sparse_feature_cross_op.sparse_feature_cross(
+        tensors_to_cross, hashed_output=True, num_buckets=num_params)
+    ids = sparse_ops.sparse_tensor_to_dense(ids)
+
+    # No need to validate the indices since we have checked the params
+    # dimensions and we know the largest id.
+    result = embedding_ops.embedding_lookup(
+        params, ids, partition_strategy="div", validate_indices=False)
+
+    return array_ops.reshape(result, array_ops.concat(
+        0, [values_shape, [dimension]]))
+
+
+def hashed_embedding_lookup_sparse(params,
+                                   sparse_values,
+                                   dimension,
+                                   combiner="mean",
+                                   default_value=None,
+                                   name=None):
+  """Looks up embeddings of a sparse feature using parameter hashing.
+
+  See `tf.contrib.layers.hashed_embedding_lookup` for embedding with hashing.
+
+  Args:
+    params: A `Tensor` or `list` of `Tensors`.
+      Each tensor must be of rank 1 with fully-defined shape.
+    sparse_values: A 2-D `SparseTensor` containing the values to be embedded.
+      Some rows may be empty.
+    dimension: Embedding dimension
+    combiner: A string specifying how to combine embedding results for each
+        entry. Currently "mean", "sqrtn" and "sum" are supported, with "mean"
+        the default.
+    default_value: The value to use for an entry with no features.
+    name: An optional name for this op.
+
+  Returns:
+     Dense tensor with shape [N, dimension] with N the number of rows in
+       sparse_values.
+
+  Raises:
+    TypeError: If sparse_values is not a SparseTensor.
+    ValueError: If combiner is not one of {"mean", "sqrtn", "sum"}.
+  """
+
+  if not isinstance(params, list):
+    params = [params]
+  if not isinstance(sparse_values, ops.SparseTensor):
+    raise TypeError("sparse_values must be SparseTensor")
+
+  with ops.op_scope(params + [sparse_values], name,
+                    "hashed_sparse_embedding_lookup") as scope:
+    # Fill in the empty rows.
+    if default_value is None:
+      # Random default values to reduce the risk of collision.
+      if sparse_values.dtype == dtypes.string:
+        default_value = "6ZxWzWOHxZ"
+      else:
+        default_value = 1288896567
+    sparse_values, _ = sparse_ops.sparse_fill_empty_rows(
+        sparse_values, default_value)
+
+    segment_ids = sparse_values.indices[:, 0]
+    if segment_ids.dtype != dtypes.int32:
+      segment_ids = math_ops.cast(segment_ids, dtypes.int32)
+
+    values = sparse_values.values
+    values, idx = array_ops.unique(values)
+
+    embeddings = hashed_embedding_lookup(params, values, dimension)
+
+    if combiner == "sum":
+      embeddings = math_ops.sparse_segment_sum(embeddings, idx, segment_ids,
+                                               name=scope)
+    elif combiner == "mean":
+      embeddings = math_ops.sparse_segment_mean(embeddings, idx, segment_ids,
+                                                name=scope)
+    elif combiner == "sqrtn":
+      embeddings = math_ops.sparse_segment_sqrt_n(embeddings, idx, segment_ids,
+                                                  name=scope)
+    else:
+      raise ValueError("Combiner must be one of 'mean', 'sqrtn' or 'sum'.")
+
+    return embeddings
diff --git a/tensorflow/contrib/framework/python/ops/embedding_ops_test.py b/tensorflow/contrib/layers/python/layers/embedding_ops_test.py
index 78d4dabdc4..8d2103207e 100644
--- a/tensorflow/contrib/framework/python/ops/embedding_ops_test.py
+++ b/tensorflow/contrib/layers/python/layers/embedding_ops_test.py
@@ -100,7 +100,7 @@ class SafeEmbeddingLookupSparseTest(tf.test.TestCase):
       sparse_ids, sparse_weights = self._ids_and_weights_2d()
 
       embedding_lookup_result = (
-          tf.contrib.framework.safe_embedding_lookup_sparse(
+          tf.contrib.layers.safe_embedding_lookup_sparse(
               embedding_weights, sparse_ids, sparse_weights).eval())
 
       self.assertAllClose(embedding_lookup_result, [
@@ -114,7 +114,7 @@ class SafeEmbeddingLookupSparseTest(tf.test.TestCase):
       sparse_ids, sparse_weights = self._ids_and_weights_2d()
 
       embedding_lookup_result = (
-          tf.contrib.framework.safe_embedding_lookup_sparse(
+          tf.contrib.layers.safe_embedding_lookup_sparse(
               embedding_weights,
               sparse_ids,
               sparse_weights,
@@ -132,9 +132,9 @@ class SafeEmbeddingLookupSparseTest(tf.test.TestCase):
       sparse_ids, _ = self._ids_and_weights_2d()
 
       embedding_lookup_result = (
-          tf.contrib.framework.safe_embedding_lookup_sparse(embedding_weights,
-                                                            sparse_ids,
-                                                            None).eval())
+          tf.contrib.layers.safe_embedding_lookup_sparse(embedding_weights,
+                                                         sparse_ids,
+                                                         None).eval())
 
       self.assertAllClose(embedding_lookup_result, [
           (embedding_weights[0][0] + embedding_weights[0][1]) / 2.0, [0] * 4,
@@ -148,9 +148,9 @@ class SafeEmbeddingLookupSparseTest(tf.test.TestCase):
       sparse_ids, _ = self._ids_and_weights_2d()
 
       embedding_lookup_result = (
-          tf.contrib.framework.safe_embedding_lookup_sparse(embedding_weights,
-                                                            sparse_ids,
-                                                            None).eval())
+          tf.contrib.layers.safe_embedding_lookup_sparse(embedding_weights,
+                                                         sparse_ids,
+                                                         None).eval())
 
       embedding_weights = list(itertools.chain(*embedding_weights))
       self.assertAllClose(embedding_lookup_result, [
@@ -166,13 +166,13 @@ class SafeEmbeddingLookupSparseTest(tf.test.TestCase):
 
       embedding_weights[1] = embedding_weights[1].astype(np.float64)
       self.assertRaises(ValueError,
-                        tf.contrib.framework.safe_embedding_lookup_sparse,
+                        tf.contrib.layers.safe_embedding_lookup_sparse,
                         embedding_weights, sparse_ids)
       embedding_weights = [
           tf.constant(w, dtype=tf.float64) for w in embedding_weights
       ]
       self.assertRaises(ValueError,
-                        tf.contrib.framework.safe_embedding_lookup_sparse,
+                        tf.contrib.layers.safe_embedding_lookup_sparse,
                         embedding_weights, sparse_ids, sparse_weights)
 
   def test_safe_embedding_lookup_sparse_3d_return_zero_vector(self):
@@ -181,7 +181,7 @@ class SafeEmbeddingLookupSparseTest(tf.test.TestCase):
       sparse_ids, sparse_weights = self._ids_and_weights_3d()
 
       embedding_lookup_result = (
-          tf.contrib.framework.safe_embedding_lookup_sparse(
+          tf.contrib.layers.safe_embedding_lookup_sparse(
               embedding_weights, sparse_ids, sparse_weights).eval())
 
       self.assertAllClose(embedding_lookup_result, [
@@ -195,7 +195,7 @@ class SafeEmbeddingLookupSparseTest(tf.test.TestCase):
       sparse_ids, sparse_weights = self._ids_and_weights_3d()
 
       embedding_lookup_result = (
-          tf.contrib.framework.safe_embedding_lookup_sparse(
+          tf.contrib.layers.safe_embedding_lookup_sparse(
               embedding_weights,
               sparse_ids,
               sparse_weights,
@@ -214,9 +214,9 @@ class SafeEmbeddingLookupSparseTest(tf.test.TestCase):
       sparse_ids, _ = self._ids_and_weights_3d()
 
       embedding_lookup_result = (
-          tf.contrib.framework.safe_embedding_lookup_sparse(embedding_weights,
-                                                            sparse_ids,
-                                                            None).eval())
+          tf.contrib.layers.safe_embedding_lookup_sparse(embedding_weights,
+                                                         sparse_ids,
+                                                         None).eval())
 
       self.assertAllClose(embedding_lookup_result, [
           [(embedding_weights[0][0] + embedding_weights[0][1]) / 2.0, [0] * 4,
@@ -231,9 +231,9 @@ class SafeEmbeddingLookupSparseTest(tf.test.TestCase):
       sparse_ids, _ = self._ids_and_weights_3d()
 
       embedding_lookup_result = (
-          tf.contrib.framework.safe_embedding_lookup_sparse(embedding_weights,
-                                                            sparse_ids,
-                                                            None).eval())
+          tf.contrib.layers.safe_embedding_lookup_sparse(embedding_weights,
+                                                         sparse_ids,
+                                                         None).eval())
 
       embedding_weights = list(itertools.chain(*embedding_weights))
       self.assertAllClose(embedding_lookup_result, [
@@ -251,15 +251,110 @@ class SafeEmbeddingLookupSparseTest(tf.test.TestCase):
 
       embedding_weights[1] = embedding_weights[1].astype(np.float64)
       self.assertRaises(ValueError,
-                        tf.contrib.framework.safe_embedding_lookup_sparse,
+                        tf.contrib.layers.safe_embedding_lookup_sparse,
                         embedding_weights, sparse_ids)
       embedding_weights = [
           tf.constant(w, dtype=tf.float64) for w in embedding_weights
       ]
       self.assertRaises(ValueError,
-                        tf.contrib.framework.safe_embedding_lookup_sparse,
+                        tf.contrib.layers.safe_embedding_lookup_sparse,
                         embedding_weights, sparse_ids, sparse_weights)
 
 
+class HashedEmbeddingLookupTest(tf.test.TestCase):
+
+  def setUp(self):
+    tf.set_random_seed(1)
+
+  def _random_weights(self, size=50, num_shards=1):
+    assert size > 0
+    assert num_shards > 0
+    assert num_shards <= size
+
+    embedding_weights = tf.create_partitioned_variables(
+        shape=[size],
+        slicing=[num_shards],
+        initializer=tf.truncated_normal_initializer(mean=0.0,
+                                                    stddev=1.0,
+                                                    dtype=tf.float32))
+    for w in embedding_weights:
+      w.initializer.run()
+    return embedding_weights
+
+  def test_hashed_embedding_consistency(self):
+    with self.test_session():
+      embedding_weights = self._random_weights()
+      values = tf.constant(["foo", "foo"])
+
+      embedding_lookup_result = tf.contrib.layers.hashed_embedding_lookup(
+          embedding_weights, values, dimension=10).eval()
+
+      self.assertAllEqual(embedding_lookup_result.shape, [2, 10])
+      self.assertAllEqual(embedding_lookup_result[0],
+                          embedding_lookup_result[1])
+
+  def test_hashed_embedding_multiple_partition(self):
+    with self.test_session():
+      embedding_weights = self._random_weights(num_shards=7)
+      values = tf.constant([4, 4, 5])
+
+      embedding_lookup_result = tf.contrib.layers.hashed_embedding_lookup(
+          embedding_weights, values, dimension=5).eval()
+
+      self.assertAllEqual(embedding_lookup_result.shape, [3, 5])
+      self.assertAllEqual(embedding_lookup_result[0],
+                          embedding_lookup_result[1])
+      # Different embedding expected for different value.
+      embedding_diff = np.min((embedding_lookup_result[2] -
+                               embedding_lookup_result[0]) ** 2)
+      self.assertGreater(embedding_diff, 0)
+
+  def test_hashed_embedding_coverage(self):
+    with self.test_session():
+      size = 8
+      embedding_weights = self._random_weights(size=size, num_shards=3)
+      values = tf.constant(["foo"])
+
+      # Large embedding dimension to cover the full range of weights.
+      embedding_lookup_result = tf.contrib.layers.hashed_embedding_lookup(
+          embedding_weights, values, dimension=100).eval()
+
+      self.assertEqual(len(np.unique(embedding_lookup_result[0])), size)
+
+  def test_hashed_embedding_multi_dimension(self):
+    with self.test_session():
+      embedding_weights = self._random_weights()
+      values = tf.constant([["foo", "bar", "bar"], ["bar", "bar", "foo"]])
+
+      embedding_lookup_result = tf.contrib.layers.hashed_embedding_lookup(
+          embedding_weights, values, dimension=10).eval()
+
+      self.assertAllEqual(embedding_lookup_result.shape, [2, 3, 10])
+      self.assertAllEqual(embedding_lookup_result[0][0],
+                          embedding_lookup_result[1][2])
+
+  def test_hashed_embedding_lookup_sparse(self):
+    with self.test_session():
+      embedding_weights = self._random_weights(num_shards=3)
+      sparse_tensor = tf.SparseTensor(values=["foo", "bar", "foo", "bar"],
+                                      indices=[[0, 0], [1, 0], [1, 1], [3, 0]],
+                                      shape=[5, 2])
+
+      embedding_lookup_result = (
+          tf.contrib.layers.hashed_embedding_lookup_sparse(
+              embedding_weights, sparse_tensor, dimension=5, combiner="mean")
+          .eval())
+
+      self.assertAllEqual(embedding_lookup_result.shape, [5, 5])
+      # Same non-zero embedding for the empty rows filled with a default value.
+      self.assertAllEqual(embedding_lookup_result[2],
+                          embedding_lookup_result[4])
+      embedding_norm = np.sum(embedding_lookup_result[2] ** 2)
+      self.assertGreater(embedding_norm, 0)
+
+      self.assertAllEqual(embedding_lookup_result[1],
+                          0.5 * (embedding_lookup_result[0] +
+                                 embedding_lookup_result[3]))
+
 if __name__ == "__main__":
   tf.test.main()
diff --git a/tensorflow/contrib/layers/python/layers/feature_column.py b/tensorflow/contrib/layers/python/layers/feature_column.py
index c05aa6c291..ba19d77355 100644
--- a/tensorflow/contrib/layers/python/layers/feature_column.py
+++ b/tensorflow/contrib/layers/python/layers/feature_column.py
@@ -75,7 +75,7 @@ import abc
 import collections
 import math
 
-from tensorflow.contrib.framework.python.ops import embedding_ops as contrib_embedding_ops
+from tensorflow.contrib.layers.python.layers import embedding_ops
 from tensorflow.contrib.layers.python.ops import bucketization_op
 from tensorflow.contrib.layers.python.ops import sparse_feature_cross_op
 from tensorflow.contrib.lookup import lookup_ops as contrib_lookup_ops
@@ -517,7 +517,7 @@ class _EmbeddingColumn(_FeatureColumn, collections.namedtuple(
 
     # This is effectively the same format as str(self), except with our special
     # treatment.
-    return "_EmbeddingColumn(%s)" % ", ".join(fields_values)
+    return "%s(%s)" % (type(self).__name__, ", ".join(fields_values))
 
   def insert_transformed_feature(self, columns_to_tensors):
     self.sparse_id_column.insert_transformed_feature(columns_to_tensors)
@@ -576,6 +576,105 @@ def embedding_column(sparse_id_column,
   return _EmbeddingColumn(sparse_id_column, dimension, combiner, initializer)
 
 
+class _HashedEmbeddingColumn(collections.namedtuple(
+    "_HashedEmbeddingColumn", ["column_name", "size", "dimension", "combiner",
+                               "initializer"]), _EmbeddingColumn):
+  """See `hashed_embedding_column`."""
+
+  def __new__(cls,
+              column_name,
+              size,
+              dimension,
+              combiner="mean",
+              initializer=None):
+    if initializer is not None and not callable(initializer):
+      raise ValueError("initializer must be callable if specified.")
+    if initializer is None:
+      stddev = 0.1
+      # TODO(b/25671353): Better initial value?
+      initializer = init_ops.truncated_normal_initializer(mean=0.0,
+                                                          stddev=stddev)
+    return super(_HashedEmbeddingColumn, cls).__new__(cls, column_name, size,
+                                                      dimension, combiner,
+                                                      initializer)
+
+  @property
+  def name(self):
+    return self.column_name + "_embedding"
+
+  @property
+  def config(self):
+    return {self.column_name: parsing_ops.VarLenFeature(dtypes.string)}
+
+  def insert_transformed_feature(self, columns_to_tensors):
+    columns_to_tensors[self] = columns_to_tensors[self.column_name]
+
+  def to_dnn_input_layer(self,
+                         input_tensor,
+                         weight_collections=None,
+                         trainable=True):
+    # Same heuristic for the number of shards as _max_size_embedding_partitioner
+    max_shard_bytes = (64 << 20) - 1
+    shards = self.size * 4.0  / max_shard_bytes
+    shards = max(1, int(math.ceil(shards)))
+
+    embeddings = partitioned_variables.create_partitioned_variables(
+        shape=[self.size],
+        slicing=[shards],
+        initializer=self.initializer,
+        dtype=dtypes.float32,
+        collections=_add_variable_collection(weight_collections),
+        name=self.name + "_weights",
+        reuse=False,
+        trainable=trainable)
+
+    return embedding_ops.hashed_embedding_lookup_sparse(
+        embeddings, input_tensor, self.dimension, name=self.name + "_lookup")
+
+
+def hashed_embedding_column(column_name,
+                            size,
+                            dimension,
+                            combiner="mean",
+                            initializer=None):
+  """Creates an embedding column of a sparse feature using parameter hashing.
+
+  The i-th embedding component of a value v is found by retrieving an
+  embedding weight whose index is a fingerprint of the pair (v,i).
+
+  Args:
+    column_name: A string defining sparse column name.
+    size: An integer specifying the number of parameters in the embedding layer.
+    dimension: An integer specifying dimension of the embedding.
+    combiner: A string specifying how to reduce if there are multiple entries
+      in a single row. Currently "mean", "sqrtn" and "sum" are supported. Each
+      of this can be thought as example level normalizations on the column:
+        * "sum": do not normalize features in the column
+        * "mean": do l1 normalization on features in the column
+        * "sqrtn": do l2 normalization on features in the column
+      For more information: `tf.embedding_lookup_sparse`.
+    initializer: A variable initializer function to be used in embedding
+      variable initialization. If not specified, defaults to
+      `tf.truncated_normal_initializer` with mean 0 and standard deviation 0.1.
+
+  Returns:
+    A _HashedEmbeddingColumn.
+
+  Raises:
+    ValueError: if dimension or size is not a positive integer; or if combiner
+      is not supported.
+
+  """
+  if (dimension < 1) or (size < 1):
+    raise ValueError("Dimension and size must be greater than 0.")
+
+  if combiner not in ("mean", "sqrtn", "sum"):
+    raise ValueError("Combiner must be one of 'mean', 'sqrtn' or 'sum'.")
+
+  return _HashedEmbeddingColumn(column_name, size, dimension, combiner,
+                                initializer)
+
+
 class _RealValuedColumn(_FeatureColumn, collections.namedtuple(
     "_RealValuedColumn",
     ["column_name", "dimension", "default_value", "dtype"])):
@@ -1237,7 +1336,7 @@ def _create_embedding_lookup(input_tensor, vocab_size, dimension,
       reuse=False,
       trainable=trainable)
 
-  return contrib_embedding_ops.safe_embedding_lookup_sparse(
+  return embedding_ops.safe_embedding_lookup_sparse(
       embeddings,
       input_tensor,
       default_id=0,
diff --git a/tensorflow/contrib/layers/python/layers/feature_column_ops_test.py b/tensorflow/contrib/layers/python/layers/feature_column_ops_test.py
index 60516ddae5..1d0f45357e 100644
--- a/tensorflow/contrib/layers/python/layers/feature_column_ops_test.py
+++ b/tensorflow/contrib/layers/python/layers/feature_column_ops_test.py
@@ -282,6 +282,27 @@ class InputLayerTest(tf.test.TestCase):
       tf.initialize_all_variables().run()
       self.assertAllEqual(output.eval().shape, [2, 10])
 
+  def testHashedEmbeddingColumn(self):
+    wire_tensor = tf.SparseTensor(values=["omar", "stringer", "marlo", "omar"],
+                                  indices=[[0, 0], [1, 0], [1, 1], [2, 0]],
+                                  shape=[3, 2])
+
+    features = {"wire": wire_tensor}
+    # Big enough hash space so that hopefully there is no collision
+    embedded_sparse = tf.contrib.layers.hashed_embedding_column("wire", 1000, 3)
+    output = tf.contrib.layers.input_from_feature_columns(
+        features, [embedded_sparse], weight_collections=["my_collection"])
+    weights = tf.get_collection("my_collection")
+    grad = tf.gradients(output, weights)
+    with self.test_session():
+      tf.initialize_all_variables().run()
+      gradient_values = []
+      # Collect the gradient from the different partitions (one in this test)
+      for p in range(len(grad)):
+        gradient_values.extend(grad[p].values.eval())
+      gradient_values.sort()
+      self.assertAllEqual(gradient_values, [0.5]*6 + [2]*3)
+
   def testEmbeddingColumnWithInitializer(self):
     hashed_sparse = tf.contrib.layers.sparse_column_with_hash_bucket("wire", 10)
     wire_tensor = tf.SparseTensor(values=["omar", "stringer", "marlo"],
diff --git a/tensorflow/contrib/learn/python/learn/estimators/_sklearn.py b/tensorflow/contrib/learn/python/learn/estimators/_sklearn.py
index 7125d1b82a..15277415a1 100644
--- a/tensorflow/contrib/learn/python/learn/estimators/_sklearn.py
+++ b/tensorflow/contrib/learn/python/learn/estimators/_sklearn.py
@@ -42,7 +42,8 @@ class _BaseEstimator(object):
 
     Args:
       deep: boolean, optional
-        If True, will return the parameters for this estimator and
+
+        If `True`, will return the parameters for this estimator and
         contained subobjects that are estimators.
 
     Returns:
@@ -209,4 +210,3 @@ else:
   log_loss = None
   mean_squared_error = _mean_squared_error
   train_test_split = _train_test_split
-
diff --git a/tensorflow/contrib/learn/python/learn/estimators/base.py b/tensorflow/contrib/learn/python/learn/estimators/base.py
index cca18bd225..3ea4e3673c 100644
--- a/tensorflow/contrib/learn/python/learn/estimators/base.py
+++ b/tensorflow/contrib/learn/python/learn/estimators/base.py
@@ -89,10 +89,14 @@ class TensorFlowEstimator(estimator.Estimator):
         Instead, a customized decay function can be passed that accepts
         global_step as parameter and returns a Tensor.
         e.g. exponential decay function:
+
+        ````python
         def exp_decay(global_step):
             return tf.train.exponential_decay(
                 learning_rate=0.1, global_step,
                 decay_steps=2, decay_rate=0.001)
+        ````
+
       clip_gradients: Clip norm of the gradients to this value to stop
         gradient explosion.
       class_weight: None or list of n_classes floats. Weight associated with
@@ -103,9 +107,10 @@ class TensorFlowEstimator(estimator.Estimator):
       config: RunConfig object that controls the configurations of the
         session, e.g. num_cores, gpu_memory_fraction, etc.
       verbose: Controls the verbosity, possible values:
-        0: the algorithm and debug information is muted.
-        1: trainer prints the progress.
-        2: log device placement is printed.
+
+        * 0: the algorithm and debug information is muted.
+        * 1: trainer prints the progress.
+        * 2: log device placement is printed.
     """
     self.class_weight = class_weight
     self.learning_rate = learning_rate
diff --git a/tensorflow/contrib/learn/python/learn/estimators/dnn.py b/tensorflow/contrib/learn/python/learn/estimators/dnn.py
index 2390909d0c..79b1e7b2ec 100644
--- a/tensorflow/contrib/learn/python/learn/estimators/dnn.py
+++ b/tensorflow/contrib/learn/python/learn/estimators/dnn.py
@@ -69,15 +69,16 @@ class DNNClassifier(dnn_linear_combined.DNNLinearCombinedClassifier):
 
   Input of `fit` and `evaluate` should have following features,
     otherwise there will be a `KeyError`:
-      if `weight_column_name` is not `None`, a feature with
-        `key=weight_column_name` whose value is a `Tensor`.
-      for each `column` in `feature_columns`:
-      - if `column` is a `SparseColumn`, a feature with `key=column.name`
-        whose `value` is a `SparseTensor`.
-      - if `column` is a `RealValuedColumn, a feature with `key=column.name`
-        whose `value` is a `Tensor`.
-      - if `feauture_columns` is `None`, then `input` must contains only real
-        valued `Tensor`.
+
+  * if `weight_column_name` is not `None`, a feature with
+     `key=weight_column_name` whose value is a `Tensor`.
+  * for each `column` in `feature_columns`:
+    - if `column` is a `SparseColumn`, a feature with `key=column.name`
+      whose `value` is a `SparseTensor`.
+    - if `column` is a `RealValuedColumn`, a feature with `key=column.name`
+      whose `value` is a `Tensor`.
+    - if `feature_columns` is `None`, then `input` must contains only real
+      valued `Tensor`.
   """
 
   def __init__(self,
@@ -219,15 +220,16 @@ class DNNRegressor(dnn_linear_combined.DNNLinearCombinedRegressor):
 
   Input of `fit` and `evaluate` should have following features,
     otherwise there will be a `KeyError`:
-      if `weight_column_name` is not `None`, a feature with
-        `key=weight_column_name` whose value is a `Tensor`.
-      for each `column` in `feature_columns`:
-      - if `column` is a `SparseColumn`, a feature with `key=column.name`
-        whose `value` is a `SparseTensor`.
-      - if `column` is a `RealValuedColumn, a feature with `key=column.name`
-        whose `value` is a `Tensor`.
-      - if `feauture_columns` is `None`, then `input` must contains only real
-        valued `Tensor`.
+
+  * if `weight_column_name` is not `None`, a feature with
+    `key=weight_column_name` whose value is a `Tensor`.
+  * for each `column` in `feature_columns`:
+    - if `column` is a `SparseColumn`, a feature with `key=column.name`
+      whose `value` is a `SparseTensor`.
+    - if `column` is a `RealValuedColumn`, a feature with `key=column.name`
+      whose `value` is a `Tensor`.
+    - if `feature_columns` is `None`, then `input` must contains only real
+      valued `Tensor`.
   """
 
   def __init__(self,
diff --git a/tensorflow/contrib/learn/python/learn/estimators/dnn_test.py b/tensorflow/contrib/learn/python/learn/estimators/dnn_test.py
index 5b7329b748..4ceb6a996b 100644
--- a/tensorflow/contrib/learn/python/learn/estimators/dnn_test.py
+++ b/tensorflow/contrib/learn/python/learn/estimators/dnn_test.py
@@ -42,9 +42,23 @@ class DNNClassifierTest(tf.test.TestCase):
 
     classifier.fit(input_fn=_iris_input_fn, steps=1000)
     classifier.evaluate(input_fn=_iris_input_fn, steps=100)
+    self.assertTrue('centered_bias_weight' in classifier.get_variable_names())
     # TODO(ispir): Enable accuracy check after resolving the randomness issue.
     # self.assertGreater(scores['accuracy/mean'], 0.6)
 
+  def testDisableCenteredBias(self):
+    """Tests that we can disable centered bias."""
+    cont_features = [
+        tf.contrib.layers.real_valued_column('feature', dimension=4)]
+
+    classifier = tf.contrib.learn.DNNClassifier(n_classes=3,
+                                                feature_columns=cont_features,
+                                                hidden_units=[3, 3],
+                                                enable_centered_bias=False)
+
+    classifier.fit(input_fn=_iris_input_fn, steps=1000)
+    self.assertFalse('centered_bias_weight' in classifier.get_variable_names())
+
 
 class DNNRegressorTest(tf.test.TestCase):
 
diff --git a/tensorflow/contrib/learn/python/learn/estimators/estimator.py b/tensorflow/contrib/learn/python/learn/estimators/estimator.py
index 87776da30b..3cccf40c58 100644
--- a/tensorflow/contrib/learn/python/learn/estimators/estimator.py
+++ b/tensorflow/contrib/learn/python/learn/estimators/estimator.py
@@ -102,7 +102,8 @@ def _get_arguments(func):
 class BaseEstimator(sklearn.BaseEstimator):
   """Abstract BaseEstimator class to train and evaluate TensorFlow models.
 
-  Concrete implementation of this class should provide following functions:
+  Concrete implementation of this class should provide the following functions:
+
     * _get_train_ops
     * _get_eval_ops
     * _get_predict_ops
@@ -165,12 +166,15 @@ class BaseEstimator(sklearn.BaseEstimator):
       input_fn: Input function. If set, `x`, `y`, and `batch_size` must be
         `None`.
       steps: Number of steps for which to train model. If `None`, train forever.
+        If set, `max_steps` must be `None`.
       batch_size: minibatch size to use on the input, defaults to first
         dimension of `x`. Must be `None` if `input_fn` is provided.
       monitors: List of `BaseMonitor` subclass instances. Used for callbacks
         inside the training loop.
       max_steps: Number of total steps for which to train model. If `None`,
-        train forever. Two calls to `fit(steps=100)` means 200 training
+        train forever. If set, `steps` must be `None`.
+
+        Two calls to `fit(steps=100)` means 200 training
         iterations. On the other hand, two calls to `fit(max_steps=100)` means
         that the second call will not do any iteration since first call did
         all 100 steps.
@@ -180,8 +184,6 @@ class BaseEstimator(sklearn.BaseEstimator):
 
     Raises:
       ValueError: If `x` or `y` are not `None` while `input_fn` is not `None`.
-      ValueError: If at least one of `x` and `y` is provided, and `input_fn` is
-          provided.
       ValueError: If both `steps` and `max_steps` are not `None`.
     """
     if (steps is not None) and (max_steps is not None):
@@ -273,17 +275,19 @@ class BaseEstimator(sklearn.BaseEstimator):
         provided.
       steps: Number of steps for which to evaluate model. If `None`, evaluate
         until running tensors generated by `metrics` raises an exception.
-      metrics: Dict of metric ops to run. If None, the default metric functions
-        are used; if {}, no metrics are used. If model has one output (i.e.,
-        returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-        name of the metric that will show up in the logs / summaries.
-        Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-        - name of the metric and name of `Tensor` in the predictions to run
-        this metric on. Metric ops should support streaming, e.g., returning
+      metrics: Dict of metric ops to run. If `None`, the default metric
+        functions are used; if `{}`, no metrics are used. If model has one
+        output (i.e., returning single predction), keys are `str`, e.g.
+        `'accuracy'` - just a name of the metric that will show up in
+        the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+        `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+        the predictions to run this metric on.
+
+        Metric ops should support streaming, e.g., returning
         update_op and value tensors. See more details in
         ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-      name: Name of the evaluation if user needs to run multiple evaluation on
-        different data sets, such as evaluate on training data vs test data.
+      name: Name of the evaluation if user needs to run multiple evaluations on
+        different data sets, such as on training data vs test data.
 
     Returns:
       Returns `dict` with evaluation results.
@@ -656,20 +660,23 @@ class Estimator(BaseEstimator):
       model_fn: Model function, takes features and targets tensors or dicts of
                 tensors and returns predictions and loss tensors.
                 Supports next three signatures for the function:
-                  * `(features, targets) -> (predictions, loss, train_op)`
-                  * `(features, targets, mode) -> (predictions, loss, train_op)`
-                  * `(features, targets, mode, params) ->
-                      (predictions, loss, train_op)`
-                Where:
-                  * `features` are single `Tensor` or `dict` of `Tensor`s
-                       (depending on data passed to `fit`),
-                  * `targets` are `Tensor` or
-                      `dict` of `Tensor`s (for multi-head model).
-                  * `mode` represents if this training, evaluation or
-                      prediction. See `ModeKeys` for example keys.
-                  * `params` is a `dict` of hyperparameters. Will receive what
-                      is passed to Estimator in `params` parameter. This allows
-                      to configure Estimators from hyper parameter tunning.
+
+          * `(features, targets) -> (predictions, loss, train_op)`
+          * `(features, targets, mode) -> (predictions, loss, train_op)`
+          * `(features, targets, mode, params) -> (predictions, loss, train_op)`
+
+      Where
+
+          * `features` are single `Tensor` or `dict` of `Tensor`s
+                 (depending on data passed to `fit`),
+          * `targets` are `Tensor` or
+                 `dict` of `Tensor`s (for multi-head model).
+          * `mode` represents if this training, evaluation or
+                 prediction. See `ModeKeys` for example keys.
+          * `params` is a `dict` of hyperparameters. Will receive what
+                 is passed to Estimator in `params` parameter. This allows
+                 to configure Estimators from hyper parameter tunning.
+
       model_dir: Directory to save model parameters, graph and etc.
       config: Configuration object.
       params: `dict` of hyper parameters that will be passed into `model_fn`.
diff --git a/tensorflow/contrib/learn/python/learn/estimators/linear.py b/tensorflow/contrib/learn/python/learn/estimators/linear.py
index f4efa38335..98ec0ab000 100644
--- a/tensorflow/contrib/learn/python/learn/estimators/linear.py
+++ b/tensorflow/contrib/learn/python/learn/estimators/linear.py
@@ -78,15 +78,16 @@ class LinearClassifier(dnn_linear_combined.DNNLinearCombinedClassifier):
 
   Input of `fit` and `evaluate` should have following features,
     otherwise there will be a `KeyError`:
-      if `weight_column_name` is not `None`, a feature with
-        `key=weight_column_name` whose value is a `Tensor`.
-      for each `column` in `feature_columns`:
-      - if `column` is a `SparseColumn`, a feature with `key=column.name`
-        whose `value` is a `SparseTensor`.
-      - if `column` is a `RealValuedColumn, a feature with `key=column.name`
-        whose `value` is a `Tensor`.
-      - if `feauture_columns` is `None`, then `input` must contains only real
-        valued `Tensor`.
+
+  * if `weight_column_name` is not `None`, a feature with
+    `key=weight_column_name` whose value is a `Tensor`.
+  * for each `column` in `feature_columns`:
+    - if `column` is a `SparseColumn`, a feature with `key=column.name`
+      whose `value` is a `SparseTensor`.
+    - if `column` is a `RealValuedColumn`, a feature with `key=column.name`
+      whose `value` is a `Tensor`.
+    - if `feature_columns` is `None`, then `input` must contains only real
+      valued `Tensor`.
   """
 
   def __init__(self,
@@ -229,15 +230,16 @@ class LinearRegressor(dnn_linear_combined.DNNLinearCombinedRegressor):
 
   Input of `fit` and `evaluate` should have following features,
     otherwise there will be a KeyError:
-      if `weight_column_name` is not `None`:
-        key=weight_column_name, value=a `Tensor`
-      for column in `feature_columns`:
-      - if isinstance(column, `SparseColumn`):
-          key=column.name, value=a `SparseTensor`
-      - if isinstance(column, `RealValuedColumn`):
-          key=column.name, value=a `Tensor`
-      - if `feauture_columns` is `None`:
-          input must contains only real valued `Tensor`.
+
+  * if `weight_column_name` is not `None`:
+    key=weight_column_name, value=a `Tensor`
+  * for column in `feature_columns`:
+    - if isinstance(column, `SparseColumn`):
+        key=column.name, value=a `SparseTensor`
+    - if isinstance(column, `RealValuedColumn`):
+        key=column.name, value=a `Tensor`
+    - if `feature_columns` is `None`:
+        input must contains only real valued `Tensor`.
   """
 
   def __init__(self,
diff --git a/tensorflow/contrib/learn/python/learn/estimators/linear_test.py b/tensorflow/contrib/learn/python/learn/estimators/linear_test.py
index 57a36b9f7a..445a1e9ee1 100644
--- a/tensorflow/contrib/learn/python/learn/estimators/linear_test.py
+++ b/tensorflow/contrib/learn/python/learn/estimators/linear_test.py
@@ -47,6 +47,26 @@ class LinearClassifierTest(tf.test.TestCase):
     loss2 = classifier.evaluate(input_fn=input_fn, steps=1)['loss']
     self.assertLess(loss2, loss1)
     self.assertLess(loss2, 0.01)
+    self.assertTrue('centered_bias_weight' in classifier.get_variable_names())
+
+  def testDisableCenteredBias(self):
+    """Tests that we can disable centered bias."""
+
+    def input_fn():
+      return {
+          'age': tf.constant([1]),
+          'language': tf.SparseTensor(values=['english'],
+                                      indices=[[0, 0]],
+                                      shape=[1, 1])
+      }, tf.constant([[1]])
+
+    language = tf.contrib.layers.sparse_column_with_hash_bucket('language', 100)
+    age = tf.contrib.layers.real_valued_column('age')
+
+    classifier = tf.contrib.learn.LinearClassifier(
+        feature_columns=[age, language], enable_centered_bias=False)
+    classifier.fit(input_fn=input_fn, steps=100)
+    self.assertFalse('centered_bias_weight' in classifier.get_variable_names())
 
   def testTrainOptimizerWithL1Reg(self):
     """Tests l1 regularized model has higher loss."""
diff --git a/tensorflow/contrib/learn/python/learn/estimators/rnn.py b/tensorflow/contrib/learn/python/learn/estimators/rnn.py
index da5b66f1f4..4082693fbf 100644
--- a/tensorflow/contrib/learn/python/learn/estimators/rnn.py
+++ b/tensorflow/contrib/learn/python/learn/estimators/rnn.py
@@ -81,10 +81,14 @@ class TensorFlowRNNClassifier(TensorFlowEstimator, _sklearn.ClassifierMixin):
         used. Instead, a customized decay function can be passed that accepts
         global_step as parameter and returns a Tensor.
         e.g. exponential decay function:
+
+        ````python
         def exp_decay(global_step):
             return tf.train.exponential_decay(
                 learning_rate=0.1, global_step,
                 decay_steps=2, decay_rate=0.001)
+        ````
+
       class_weight: None or list of n_classes floats. Weight associated with
         classes for loss computation. If not given, all classes are
         supposed to have weight one.
@@ -186,18 +190,23 @@ class TensorFlowRNNRegressor(TensorFlowEstimator, _sklearn.RegressorMixin):
         used. Instead, a customized decay function can be passed that accepts
         global_step as parameter and returns a Tensor.
         e.g. exponential decay function:
+
+        ````python
         def exp_decay(global_step):
             return tf.train.exponential_decay(
                 learning_rate=0.1, global_step,
                 decay_steps=2, decay_rate=0.001)
+        ````
+
       continue_training: when continue_training is True, once initialized
         model will be continuely trained on every call of fit.
       config: RunConfig object that controls the configurations of the
         session, e.g. num_cores, gpu_memory_fraction, etc.
       verbose: Controls the verbosity, possible values:
-        0: the algorithm and debug information is muted.
-        1: trainer prints the progress.
-        2: log device placement is printed.
+
+        * 0: the algorithm and debug information is muted.
+        * 1: trainer prints the progress.
+        * 2: log device placement is printed.
     """
     self.rnn_size = rnn_size
     self.cell_type = cell_type
diff --git a/tensorflow/contrib/learn/python/learn/io/graph_io.py b/tensorflow/contrib/learn/python/learn/io/graph_io.py
index 05c044504b..eee1b88353 100644
--- a/tensorflow/contrib/learn/python/learn/io/graph_io.py
+++ b/tensorflow/contrib/learn/python/learn/io/graph_io.py
@@ -216,7 +216,7 @@ def read_keyed_batch_features(
     file_pattern, batch_size, features, reader,
     randomize_input=True, num_epochs=None,
     queue_capacity=10000, reader_num_threads=1,
-    parser_num_threads=1, read_batch_size=1, name=None):
+    parser_num_threads=1, name=None):
   """Adds operations to read, queue, batch and parse `Example` protos.
 
   Given file pattern (or list of files), will setup a queue for file names,
@@ -245,8 +245,6 @@ def read_keyed_batch_features(
     queue_capacity: Capacity for input queue.
     reader_num_threads: The number of threads to read examples.
     parser_num_threads: The number of threads to parse examples.
-    read_batch_size: An int or scalar `Tensor` specifying the number of
-      records to read at once
     name: Name of resulting op.
 
   Returns:
@@ -260,7 +258,7 @@ def read_keyed_batch_features(
     keys, examples = read_keyed_batch_examples(
         file_pattern, batch_size, reader, randomize_input=randomize_input,
         num_epochs=num_epochs, queue_capacity=queue_capacity,
-        num_threads=reader_num_threads, read_batch_size=read_batch_size,
+        num_threads=reader_num_threads, read_batch_size=batch_size,
         name=scope)
 
     if parser_num_threads == 1:
@@ -286,8 +284,7 @@ def read_keyed_batch_features(
 def read_batch_features(file_pattern, batch_size, features, reader,
                         randomize_input=True, num_epochs=None,
                         queue_capacity=10000, reader_num_threads=1,
-                        parser_num_threads=1, read_batch_size=1,
-                        name=None):
+                        parser_num_threads=1, name=None):
   """Adds operations to read, queue, batch and parse `Example` protos.
 
   Given file pattern (or list of files), will setup a queue for file names,
@@ -316,7 +313,6 @@ def read_batch_features(file_pattern, batch_size, features, reader,
     queue_capacity: Capacity for input queue.
     reader_num_threads: The number of threads to read examples.
     parser_num_threads: The number of threads to parse examples.
-    read_batch_size: An int or scalar `Tensor` specifying the number of
       records to read at once
     name: Name of resulting op.
 
@@ -331,8 +327,7 @@ def read_batch_features(file_pattern, batch_size, features, reader,
       file_pattern, batch_size, features, reader,
       randomize_input=randomize_input, num_epochs=num_epochs,
       queue_capacity=queue_capacity, reader_num_threads=reader_num_threads,
-      parser_num_threads=parser_num_threads, read_batch_size=read_batch_size,
-      name=name)
+      parser_num_threads=parser_num_threads, name=name)
   return features
 
 
diff --git a/tensorflow/contrib/linear_optimizer/kernels/BUILD b/tensorflow/contrib/linear_optimizer/kernels/BUILD
index 1f68065c60..0fb037f5de 100644
--- a/tensorflow/contrib/linear_optimizer/kernels/BUILD
+++ b/tensorflow/contrib/linear_optimizer/kernels/BUILD
@@ -58,6 +58,7 @@ tf_cc_test(
     linkstatic = tf_kernel_tests_linkstatic(),  # Required for benchmarking
     deps = [
         "//tensorflow/contrib/linear_optimizer:sdca_op_kernels",
+        "//tensorflow/contrib/linear_optimizer:sdca_ops_op_lib",
         "//tensorflow/core:all_kernels",
         "//tensorflow/core:core_cpu",
         "//tensorflow/core:framework",
diff --git a/tensorflow/contrib/linear_optimizer/kernels/sdca_ops_test.cc b/tensorflow/contrib/linear_optimizer/kernels/sdca_ops_test.cc
index ae50553a60..d776170367 100644
--- a/tensorflow/contrib/linear_optimizer/kernels/sdca_ops_test.cc
+++ b/tensorflow/contrib/linear_optimizer/kernels/sdca_ops_test.cc
@@ -51,12 +51,14 @@ std::vector<Node*> VarVector(Graph* const g, const int nodes,
   return result;
 }
 
-Node* Zeros(Graph* const g, const int n) {
-  Tensor data(DT_FLOAT, TensorShape({n}));
+Node* Zeros(Graph* const g, const TensorShape& shape) {
+  Tensor data(DT_FLOAT, shape);
   data.flat<float>().setZero();
   return test::graph::Constant(g, data);
 }
 
+Node* Zeros(Graph* const g, const int n) { return Zeros(g, TensorShape({n})); }
+
 Node* Ones(Graph* const g, const int n) {
   Tensor data(DT_FLOAT, TensorShape({n}));
   test::FillFn<float>(&data, [](const int i) { return 1.0f; });
@@ -166,28 +168,25 @@ void GetGraphs(const int32 num_examples, const int32 sparse_feature_groups,
 
     Node* const weights = Ones(g, num_examples);
     Node* const labels = RandomZeroOrOne(g, num_examples);
-    Node* const ids = StringIota(g, num_examples);
+    Node* const example_state_data = Zeros(g, TensorShape({num_examples, 4}));
 
     Node* sdca = nullptr;
-    TF_CHECK_OK(
-        NodeBuilder(g->NewName("sdca"), "SdcaSolver")
-            .Attr("loss_type", "logistic_loss")
-            .Attr("num_sparse_features", sparse_feature_groups)
-            .Attr("num_dense_features", dense_feature_groups)
-            .Attr("l1", 0.0)
-            .Attr("l2", 1.0)
-            .Attr("num_inner_iterations", 2)
-            .Attr("container", strings::StrCat(strings::Hex(random::New64())))
-            .Attr("solver_uuid", strings::StrCat(strings::Hex(random::New64())))
-            .Input(sparse_indices)
-            .Input(sparse_values)
-            .Input(dense_features)
-            .Input(weights)
-            .Input(labels)
-            .Input(ids)
-            .Input(sparse_weights)
-            .Input(dense_weights)
-            .Finalize(g, &sdca));
+    TF_CHECK_OK(NodeBuilder(g->NewName("sdca"), "SdcaSolver")
+                    .Attr("loss_type", "logistic_loss")
+                    .Attr("num_sparse_features", sparse_feature_groups)
+                    .Attr("num_dense_features", dense_feature_groups)
+                    .Attr("l1", 0.0)
+                    .Attr("l2", 1.0)
+                    .Attr("num_inner_iterations", 2)
+                    .Input(sparse_indices)
+                    .Input(sparse_values)
+                    .Input(dense_features)
+                    .Input(weights)
+                    .Input(labels)
+                    .Input(sparse_weights)
+                    .Input(dense_weights)
+                    .Input(example_state_data)
+                    .Finalize(g, &sdca));
 
     *train_g = g;
   }
@@ -202,14 +201,22 @@ void BM_SDCA(const int iters, const int num_examples) {
             &train);
   testing::StartTiming();
   test::Benchmark("cpu", train, GetOptions(), init).Run(iters);
-  // TODO(sibyl-toe9oF2e):  Each all to Run() currently creates a container which
-  // gets deleted as the context gets deleted.  It would be nicer to
-  // explicitly clean up the container ourselves at this point (after calling
-  // testing::StopTiming).
+}
+
+void BM_SDCA_LARGE_SPARSE(const int iters, const int num_examples) {
+  testing::StopTiming();
+  Graph* init = nullptr;
+  Graph* train = nullptr;
+  GetGraphs(num_examples, 65 /* sparse feature groups */,
+            1e6 /* sparse features per group */, 0 /* dense features */, &init,
+            &train);
+  testing::StartTiming();
+  test::Benchmark("cpu", train, GetOptions(), init).Run(iters);
 }
 
 }  // namespace
 
 BENCHMARK(BM_SDCA)->Arg(128)->Arg(256)->Arg(512)->Arg(1024);
+BENCHMARK(BM_SDCA_LARGE_SPARSE)->Arg(128)->Arg(256)->Arg(512)->Arg(1024);
 
 }  // namespace tensorflow
diff --git a/tensorflow/contrib/quantization/kernels/BUILD b/tensorflow/contrib/quantization/kernels/BUILD
index 5ee3911116..5dbcf6bb9c 100644
--- a/tensorflow/contrib/quantization/kernels/BUILD
+++ b/tensorflow/contrib/quantization/kernels/BUILD
@@ -137,11 +137,15 @@ tf_cc_test(
         "//tensorflow/contrib/quantization:cc_array_ops",
         "//tensorflow/contrib/quantization:cc_math_ops",
         "//tensorflow/contrib/quantization:cc_nn_ops",
+        "//tensorflow/core:core_cpu",
+        "//tensorflow/core:core_cpu_internal",
         "//tensorflow/core:framework",
+        "//tensorflow/core:lib",
         "//tensorflow/core:protos_all_cc",
         "//tensorflow/core:test",
         "//tensorflow/core:test_main",
         "//tensorflow/core:testlib",
+        "//third_party/eigen3",
     ],
 )
 
diff --git a/tensorflow/contrib/quantization/kernels/quantization_utils.h b/tensorflow/contrib/quantization/kernels/quantization_utils.h
index 36e63f8de7..676ae6bbc4 100644
--- a/tensorflow/contrib/quantization/kernels/quantization_utils.h
+++ b/tensorflow/contrib/quantization/kernels/quantization_utils.h
@@ -16,12 +16,15 @@ limitations under the License.
 #ifndef THIRD_PARTY_TENSORFLOW_CONTRIB_QUANTIZATION_KERNELS_QUANTIZATION_UTILS_H_
 #define THIRD_PARTY_TENSORFLOW_CONTRIB_QUANTIZATION_KERNELS_QUANTIZATION_UTILS_H_
 
+#define EIGEN_USE_THREADS
+
 // This is a set of functions that standardizes how quantized values are
 // interpreted as float numbers.
 // All of the current implementations are for reference and have not been
 // optimized. They should be implementable using fixed point representations
 // to avoid a dependency on floating-point hardware.
 
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
 #include "tensorflow/core/framework/tensor.h"
 
 namespace tensorflow {
@@ -104,6 +107,74 @@ void QuantizationRangeForMultiplication(float min_a, float max_a, float min_b,
   *max_c = c_float_for_one_quant_level * c_highest;
 }
 
+// input_array is an eigen Tensor.  q2f is a QuantizedToFloatStruct.
+// This evaluates to an eigen tensor expression, to be used like:
+// auto tensor = DEQUANTIZE_WITH_EIGEN(input_tensor, q2f);
+#define DEQUANTIZE_WITH_EIGEN(input_array, q2f)                       \
+  (q2f.range_min +                                                    \
+   (((input_array.template cast<float>() - q2f.lowest_quantized())) * \
+    q2f.range_scale));
+
+// input_array is an eigen Tensor.  f2q is a FloatToQuantizedStruct.
+// OutputType is the type of output (e.g. quint8).
+// This evaluates to an eigen tensor expression, to be used like:
+// auto tensor = QUANTIZE_WITH_EIGEN(input_tensor, f2q, T);
+#define QUANTIZE_WITH_EIGEN(input_array, f2q, OutputType) \
+  ((input_array * f2q.range_scale).round() -              \
+   (f2q.range_min_scaled - f2q.lowest_quantized()))       \
+      .cwiseMax(f2q.lowest_quantized())                   \
+      .cwiseMin(f2q.highest_quantized())                  \
+      .template cast<int32>()                             \
+      .template cast<OutputType>()
+
+// For use with DEQUANTIZE_WITH_EIGEN.
+template <typename T>
+struct QuantizedToFloatStruct {
+  static constexpr int number_of_bits = sizeof(T) * 8;
+  static constexpr int64 number_of_steps = static_cast<int64>(1)
+                                           << number_of_bits;
+
+  static float lowest_quantized() {
+    return static_cast<float>(Eigen::NumTraits<T>::lowest());
+  }
+
+  QuantizedToFloatStruct(float range_min, float range_max)
+      : range_min(range_min),
+        range_scale((range_max - range_min) / (number_of_steps - 1.0)) {}
+
+  const float range_min;
+  const float range_scale;
+};
+
+// For use with QUANTIZE_WITH_EIGEN.
+template <typename T>
+struct FloatToQuantizedStruct {
+  static constexpr int number_of_bits = sizeof(T) * 8;
+  static constexpr int64 number_of_steps = static_cast<int64>(1)
+                                           << number_of_bits;
+  static constexpr double range_adjust =
+      (number_of_steps / (number_of_steps - 1.0));
+
+  static float lowest_quantized() {
+    return static_cast<float>(Eigen::NumTraits<T>::lowest());
+  }
+  static double lowest_quantized_double() {
+    return static_cast<double>(Eigen::NumTraits<T>::lowest());
+  }
+  static float highest_quantized() {
+    return static_cast<float>(Eigen::NumTraits<T>::highest());
+  }
+
+  FloatToQuantizedStruct(float range_min, float range_max)
+      : range_min(range_min),
+        range_scale((number_of_steps - 1.0) / (range_max - range_min)),
+        range_min_scaled(round(range_min * range_scale)) {}
+
+  const float range_min;
+  const float range_scale;
+  const float range_min_scaled;
+};
+
 template <class T1, class T2>
 inline T2 RequantizeInNewRange(T1 input, float min_input, float max_input,
                                float min_new, float max_new) {
@@ -130,19 +201,22 @@ inline void RequantizeManyInNewRange<qint32, quint8>(
     qint32* input, size_t count, float min_input, float max_input,
     float min_output, float max_output, quint8* output) {
   // Initially we calculate all the constants we need once, before we go into
-  // the inner loop.
+  // the inner loop.  If this is updated, also update the Eigen version.
   const int fp_shift = 16;
   const float input_range = max_input - min_input;
   const float output_range = max_output - min_output;
-  const float recip_output_range = (255.0 / output_range);
+  const float recip_output_range =
+      output_range == 0.0 ? 0.0 : (255.0 / output_range);
   const int64 recip_output_range_fp =
       static_cast<int64>(recip_output_range * (1 << fp_shift));
   const int64 range_scale_fp =
       static_cast<int64>(255.0 * (1 << fp_shift) * input_range / output_range);
   const int64 input_offset_fp =
       (min_input * recip_output_range_fp) + (range_scale_fp >> 1);
-  const int64 output_offset_fp = round((min_output * 255.0) / output_range);
+  const int64 output_offset_fp =
+      output_range == 0.0 ? 0.0 : round((min_output * 255.0) / output_range);
   const int64 rounding_delta = 1 << (fp_shift - 1);
+
   // Inside this loop we just do minimal adds, multiplies, and shifts, in a way
   // that could be easily adapted for a SIMD implementation. It should also be
   // possible to perform all the calculations in 32-bit rather than 64, but
@@ -162,6 +236,77 @@ inline void RequantizeManyInNewRange<qint32, quint8>(
   }
 }
 
+template <int shift>
+struct int64_right_shift_op {
+  EIGEN_EMPTY_STRUCT_CTOR(int64_right_shift_op)
+  EIGEN_DEVICE_FUNC
+  EIGEN_STRONG_INLINE const int64 operator()(const int64& a) const {
+    return a >> shift;
+  }
+};
+
+// See RequantizeManyInNewRange() for a non-eigen reference implementation.
+template <class T1, class T2>
+inline void RequantizeManyInNewRangeUsingEigen(
+    const Eigen::ThreadPoolDevice& device, const Tensor& input, float min_input,
+    float max_input, float min_output, float max_output, Tensor* output) {
+  auto input_array = input.flat<T1>();
+  QuantizedToFloatStruct<T1> q2f(min_input, max_input);
+  auto input_float = DEQUANTIZE_WITH_EIGEN(input_array, q2f);
+  FloatToQuantizedStruct<T2> f2q(min_output, max_output);
+  auto input_requantized = QUANTIZE_WITH_EIGEN(input_float, f2q, T2);
+
+  output->flat<T2>().device(device) = input_requantized;
+}
+
+#if 0
+// See RequantizeManyInNewRange() for a non-eigen reference implementation.
+//
+// Because converting 32-bit accumulated results down to eight bit is a common
+// case, we have a specialized code path to handle it as efficiently as
+// possible using only fixed-point math for the inner loop.
+//
+// See #ifdefed out test in quantization_utils_test.cc
+// (RequantizeManyInNewRange32To8BitUsingEigen).
+template <>
+inline void RequantizeManyInNewRangeUsingEigen<qint32, quint8>(
+    const Eigen::ThreadPoolDevice& device, const Tensor& input, float min_input,
+    float max_input, float min_output, float max_output, Tensor* output) {
+  // Initially we calculate all the constants we need once, before we go into
+  // the inner loop.  If this is updated, also update the non-Eigen version.
+  const int fp_shift = 16;
+  const float input_range = max_input - min_input;
+  const float output_range = max_output - min_output;
+  const float recip_output_range =
+      output_range == 0.0 ? 0.0 : (255.0 / output_range);
+  const int64 recip_output_range_fp =
+      static_cast<int64>(recip_output_range * (1 << fp_shift));
+  const int64 range_scale_fp =
+      static_cast<int64>(255.0 * (1 << fp_shift) * input_range / output_range);
+  const int64 input_offset_fp =
+      (min_input * recip_output_range_fp) + (range_scale_fp >> 1);
+  const int64 output_offset_fp =
+      output_range == 0.0 ? 0.0 : round((min_output * 255.0) / output_range);
+  const int64 rounding_delta = 1 << (fp_shift - 1);
+
+  // Inside this eigen expression we just do minimal adds, multiplies, and
+  // shifts. It should be possible to perform all the calculations in 32-bit
+  // rather than 64, but that's not been implemented yet.
+  auto input_array = input.flat<qint32>();
+  auto fp_value = ((input_array.template cast<int64>() * range_scale_fp)
+                       .unaryExpr(int64_right_shift_op<32>())) +
+                  input_offset_fp;
+  auto round_intermediate = (fp_value + rounding_delta * fp_value.sign())
+                                .unaryExpr(int64_right_shift_op<fp_shift>());
+  auto input_requantized = (round_intermediate - output_offset_fp)
+                               .cwiseMax(0LL)
+                               .cwiseMin(255LL)
+                               .template cast<int32>()
+                               .template cast<quint8>();
+  output->flat<quint8>().device(device) = input_requantized;
+}
+#endif
+
 // REQUIRES: 'result->NumElements() == input.NumElements()'
 template <class T>
 void FloatTensorToQuantizedInPlace(const Tensor& input, float min, float max,
diff --git a/tensorflow/contrib/quantization/kernels/quantization_utils_test.cc b/tensorflow/contrib/quantization/kernels/quantization_utils_test.cc
index 4cb34838a2..ca8965426d 100644
--- a/tensorflow/contrib/quantization/kernels/quantization_utils_test.cc
+++ b/tensorflow/contrib/quantization/kernels/quantization_utils_test.cc
@@ -13,17 +13,145 @@ See the License for the specific language governing permissions and
 limitations under the License.
 ==============================================================================*/
 
+#define EIGEN_USE_THREADS
+
 #include <limits>
 
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
 #include "tensorflow/contrib/quantization/kernels/quantization_utils.h"
+#include "tensorflow/core/common_runtime/eigen_thread_pool.h"
 #include "tensorflow/core/framework/allocator.h"
 #include "tensorflow/core/framework/tensor_testutil.h"
 #include "tensorflow/core/framework/types.h"
+#include "tensorflow/core/lib/core/threadpool.h"
+#include "tensorflow/core/lib/random/simple_philox.h"
 #include "tensorflow/core/platform/test.h"
 
 namespace tensorflow {
 
-TEST(QuantizationUtils, FloatToQuantized) {
+class QuantizationUtilsTest : public ::testing::Test {
+ protected:
+  // If eigen_device is NULL, then the reference implementation is tested.
+  void TestRequantizeManyInNewRange32To8Bit(
+      Eigen::ThreadPoolDevice* eigen_device) {
+    // These are the float values we're going to test the conversions on.
+    const size_t values_count = 6;
+    const float values[values_count] = {0.0f,  0.45f,  1.0f,
+                                        -1.0f, 127.0f, 255.0f};
+    // These are the input and output ranges we'll test.
+    const size_t ranges_count = 6;
+    const float ranges[ranges_count][4] = {
+        {0.0f, 255.0f, 0.0f, 255.0f},    //
+        {0.0f, 1.0f, 0.0f, 1.0f},        //
+        {-1.0f, 1.0f, -1.0f, 1.0f},      //
+        {-1.0f, 1.0f, -255.0f, 255.0f},  //
+        {3.0f, 3.0f, 0.0f, 255.0f},      // input min == max
+        {0.0f, 255.0f, 5.0f, 5.0f},      // output min == max
+    };
+    for (size_t range_index = 0; range_index < ranges_count; ++range_index) {
+      const float input_min = ranges[range_index][0];
+      const float input_max = ranges[range_index][1];
+      const float output_min = ranges[range_index][2];
+      const float output_max = ranges[range_index][3];
+      std::vector<qint32> values_quantized;
+      std::vector<quint8> expected_values;
+      for (size_t value_index = 0; value_index < values_count; ++value_index) {
+        const float value_float = values[value_index];
+        values_quantized.push_back(
+            FloatToQuantized<qint32>(value_float, input_min, input_max));
+        expected_values.push_back(FloatToQuantized<quint8>(
+            QuantizedToFloat(values_quantized[value_index], input_min,
+                             input_max),
+            output_min, output_max));
+      }
+
+      Tensor i_tensor =
+          tensorflow::test::AsTensor(gtl::ArraySlice<qint32>(values_quantized));
+      Tensor o_tensor(DT_QUINT8, TensorShape{values_count});
+      auto output_values = o_tensor.flat<quint8>();
+
+      if (eigen_device == nullptr) {
+        auto input_array = i_tensor.flat<qint32>();
+        RequantizeManyInNewRange(input_array.data(), input_array.size(),
+                                 input_min, input_max, output_min, output_max,
+                                 output_values.data());
+      } else {
+        RequantizeManyInNewRangeUsingEigen<qint32, quint8>(
+            *eigen_device, i_tensor, input_min, input_max, output_min,
+            output_max, &o_tensor);
+      }
+
+      for (size_t value_index = 0; value_index < values_count; ++value_index) {
+        // Here we convert the quantized input value to what we expect
+        // to get in the output range.
+        ASSERT_EQ(expected_values[value_index], output_values(value_index))
+            << "values_quantized[" << value_index
+            << "]=" << values_quantized[value_index] << ", values["
+            << value_index << "]=" << values[value_index]
+            << ", input_min=" << input_min << ", input_max=" << input_max
+            << ", output_min=" << output_min << ", output_max=" << output_max
+            << ", value_index=" << value_index;
+      }
+    }
+  }
+
+  template <typename InputType, typename OutputType>
+  void TestRequantizeManyInNewRangeEigenVsNonEigen() {
+    thread::ThreadPool threadpool(Env::Default(), "test", 2 /* num_threads */);
+    EigenThreadPoolWrapper wrapper(&threadpool);
+    Eigen::ThreadPoolDevice eigen_device(&wrapper, 2 /* num_threads */);
+
+    const size_t ranges_count = 6;
+    const float ranges[ranges_count][4] = {
+        {0.0f, 255.0f, 0.0f, 255.0f},    //
+        {0.0f, 1.0f, 0.0f, 1.0f},        //
+        {-1.0f, 1.0f, -1.0f, 1.0f},      //
+        {-1.0f, 1.0f, -255.0f, 255.0f},  //
+        {3.0f, 3.0f, 0.0f, 255.0f},      // input min == max
+        {0.0f, 255.0f, 5.0f, 5.0f},      // output min == max
+    };
+
+    // Random values.
+    for (size_t range_index = 0; range_index < ranges_count; ++range_index) {
+      const float input_min = ranges[range_index][0];
+      const float input_max = ranges[range_index][1];
+      const float output_min = ranges[range_index][2];
+      const float output_max = ranges[range_index][3];
+      const int values_count = 10000;
+      random::PhiloxRandom philox(testing::RandomSeed(), 17);
+      random::SimplePhilox rnd(&philox);
+      std::vector<InputType> values_quantized;
+      for (int i = 0; i < values_count; ++i) {
+        float v = (rnd.RandFloat() * (input_max - input_min)) + input_min;
+        values_quantized.push_back(
+            FloatToQuantized<InputType>(v, input_min, input_max));
+      }
+
+      Tensor i_tensor = tensorflow::test::AsTensor(
+          gtl::ArraySlice<InputType>(values_quantized));
+      const auto i_array = i_tensor.flat<InputType>();
+      Tensor o_tensor_eigen(DataTypeToEnum<OutputType>::v(),
+                            TensorShape{values_count});
+      auto output_values_eigen = o_tensor_eigen.flat<OutputType>();
+      Tensor o_tensor_ref(DataTypeToEnum<OutputType>::v(),
+                          TensorShape{values_count});
+      auto output_values_ref = o_tensor_ref.flat<OutputType>();
+
+      RequantizeManyInNewRange(i_array.data(), i_array.size(), input_min,
+                               input_max, output_min, output_max,
+                               output_values_ref.data());
+      RequantizeManyInNewRangeUsingEigen<InputType, OutputType>(
+          eigen_device, i_tensor, input_min, input_max, output_min, output_max,
+          &o_tensor_eigen);
+
+      for (int i = 0; i < values_quantized.size(); ++i) {
+        EXPECT_EQ(output_values_eigen(i), output_values_ref(i)) << i;
+      }
+    }
+  }
+};
+
+TEST_F(QuantizationUtilsTest, FloatToQuantized) {
   EXPECT_EQ(quint8(0), FloatToQuantized<quint8>(0.0f, 0.0f, 1.0f));
   EXPECT_EQ(quint8(0), FloatToQuantized<quint8>(0.0f, 0.0f, 2.0f));
   EXPECT_EQ(quint8(128), FloatToQuantized<quint8>(0.5f, 0.0f, 1.0f));
@@ -47,7 +175,7 @@ TEST(QuantizationUtils, FloatToQuantized) {
             FloatToQuantized<qint32>(128.0f, -128.0f, 128.0f));
 }
 
-TEST(QuantizationUtils, QuantizedToFloat) {
+TEST_F(QuantizationUtilsTest, QuantizedToFloat) {
   EXPECT_LT(fabsf(0.0f - QuantizedToFloat<quint8>(0, 0.0f, 1.0f)), 1 / 255.0f);
   EXPECT_LT(fabsf(0.0f - QuantizedToFloat<quint8>(0, 0.0f, 2.0f)), 1 / 255.0f);
   EXPECT_LT(fabsf(0.5f - QuantizedToFloat<quint8>(127, 0.0f, 1.0f)),
@@ -78,7 +206,7 @@ TEST(QuantizationUtils, QuantizedToFloat) {
       1e-5f);
 }
 
-TEST(QuantizationUtils, AvoidBias) {
+TEST_F(QuantizationUtilsTest, AvoidBias) {
   for (int i = 0; i < 256; ++i) {
     const float as_float = QuantizedToFloat<quint8>(i, 0.0f, 2.0f);
     const int back_to_int = FloatToQuantized<quint8>(as_float, 0.0f, 2.0f);
@@ -86,7 +214,7 @@ TEST(QuantizationUtils, AvoidBias) {
   }
 }
 
-TEST(QuantizationUtils, RequantizeInNewRange) {
+TEST_F(QuantizationUtilsTest, RequantizeInNewRange) {
   // These are the float values we're going to test the conversions on.
   const size_t values_count = 6;
   const float values[values_count] = {0.0f, 0.5f, 1.0f, -1.0f, 127.0f, 255.0f};
@@ -122,7 +250,7 @@ TEST(QuantizationUtils, RequantizeInNewRange) {
   }
 }
 
-TEST(QuantizationUtils, RequantizeInNewRangeRealData) {
+TEST_F(QuantizationUtilsTest, RequantizeInNewRangeRealData) {
   const float value_as_float = -0.290169f;
   const float input_min = -0.739539f;
   const float input_max = 0.641057f;
@@ -138,7 +266,7 @@ TEST(QuantizationUtils, RequantizeInNewRangeRealData) {
   EXPECT_LT(std::abs(value_as_qint32 - actual_output), 10);
 }
 
-TEST(QuantizationUtils, RequantizeInNewRange32To8Bit) {
+TEST_F(QuantizationUtilsTest, RequantizeInNewRange32To8Bit) {
   // These are the float values we're going to test the conversions on.
   const size_t values_count = 6;
   const float values[values_count] = {0.0f, 0.45f, 1.0f, -1.0f, 127.0f, 255.0f};
@@ -174,51 +302,29 @@ TEST(QuantizationUtils, RequantizeInNewRange32To8Bit) {
   }
 }
 
-TEST(QuantizationUtils, RequantizeManyInNewRange32To8Bit) {
-  // These are the float values we're going to test the conversions on.
-  const size_t values_count = 6;
-  const float values[values_count] = {0.0f, 0.45f, 1.0f, -1.0f, 127.0f, 255.0f};
-  // These are the input and output ranges we'll test.
-  const size_t ranges_count = 4;
-  const float ranges[ranges_count][4] = {
-      {0.0f, 255.0f, 0.0f, 255.0f},
-      {0.0f, 1.0f, 0.0f, 1.0f},
-      {-1.0f, 1.0f, -1.0f, 1.0f},
-      {-1.0f, 1.0f, -255.0f, 255.0f},
-  };
-  for (size_t range_index = 0; range_index < ranges_count; ++range_index) {
-    const float input_min = ranges[range_index][0];
-    const float input_max = ranges[range_index][1];
-    const float output_min = ranges[range_index][2];
-    const float output_max = ranges[range_index][3];
-    qint32 values_quantized[values_count];
-    quint8 expected_values[values_count];
-    for (size_t value_index = 0; value_index < values_count; ++value_index) {
-      const float value_float = values[value_index];
-      values_quantized[value_index] =
-          FloatToQuantized<qint32>(value_float, input_min, input_max);
-      expected_values[value_index] = FloatToQuantized<quint8>(
-          QuantizedToFloat(values_quantized[value_index], input_min, input_max),
-          output_min, output_max);
-    }
-    quint8 output_values[values_count];
-    RequantizeManyInNewRange<qint32, quint8>(values_quantized, values_count,
-                                             input_min, input_max, output_min,
-                                             output_max, output_values);
-    for (size_t value_index = 0; value_index < values_count; ++value_index) {
-      // Here we convert the quantized input value to what we expect
-      // to get in the output range.
-      EXPECT_EQ(expected_values[value_index], output_values[value_index])
-          << "values_quantized[" << value_index
-          << "]=" << values_quantized[value_index] << ", values[" << value_index
-          << "]=" << values[value_index] << ", input_min=" << input_min
-          << ", input_max=" << input_max << ", output_min=" << output_min
-          << ", output_max=" << output_max << ", value_index=" << value_index;
-    }
-  }
+TEST_F(QuantizationUtilsTest, RequantizeManyInNewRange32To8Bit) {
+  TestRequantizeManyInNewRange32To8Bit(nullptr /* eigen_device */);
+}
+
+#if 0
+TEST_F(QuantizationUtilsTest, RequantizeManyInNewRange32To8BitUsingEigen) {
+  thread::ThreadPool threadpool(Env::Default(), "test", 2 /* num_threads */);
+  EigenThreadPoolWrapper wrapper(&threadpool);
+  Eigen::ThreadPoolDevice eigen_device(&wrapper, 2 /* num_threads */);
+  TestRequantizeManyInNewRange32To8Bit(&eigen_device);
+}
+#endif
+
+TEST_F(QuantizationUtilsTest, RequantizeManyInNewRange32To8BitEigenVsNonEigen) {
+  TestRequantizeManyInNewRangeEigenVsNonEigen<qint32, quint8>();
+}
+
+TEST_F(QuantizationUtilsTest,
+       RequantizeManyInNewRange32To8BitSignedEigenVsNonEigen) {
+  TestRequantizeManyInNewRangeEigenVsNonEigen<qint32, qint8>();
 }
 
-TEST(QuantizationUtils, FloatTensorToQuantized) {
+TEST_F(QuantizationUtilsTest, FloatTensorToQuantized) {
   const int input_width = 3;
   const int input_height = 3;
   const float input_min = 0.0f;
@@ -232,7 +338,7 @@ TEST(QuantizationUtils, FloatTensorToQuantized) {
   test::ExpectTensorEqual<quint8>(expected, output);
 }
 
-TEST(QuantizationUtils, QuantizedTensorToFloat) {
+TEST_F(QuantizationUtilsTest, QuantizedTensorToFloat) {
   const int input_width = 3;
   const int input_height = 3;
   const float input_min = -128.0f;
diff --git a/tensorflow/contrib/quantization/kernels/quantize_down_and_shrink_range.cc b/tensorflow/contrib/quantization/kernels/quantize_down_and_shrink_range.cc
index dde31ea5c5..5a109d9f76 100644
--- a/tensorflow/contrib/quantization/kernels/quantize_down_and_shrink_range.cc
+++ b/tensorflow/contrib/quantization/kernels/quantize_down_and_shrink_range.cc
@@ -15,8 +15,11 @@ limitations under the License.
 
 // See docs in ../ops/array_ops.cc.
 
+#define EIGEN_USE_THREADS
+
 #include <math.h>
 
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
 #include "tensorflow/contrib/quantization/kernels/quantization_utils.h"
 #include "tensorflow/core/framework/op.h"
 #include "tensorflow/core/framework/op_kernel.h"
@@ -26,6 +29,8 @@ limitations under the License.
 
 namespace tensorflow {
 
+typedef Eigen::ThreadPoolDevice CPUDevice;
+
 template <class T1, class T2>
 class QuantizeDownAndShrinkRangeOp : public OpKernel {
  public:
@@ -62,10 +67,22 @@ class QuantizeDownAndShrinkRangeOp : public OpKernel {
                                         input_max_float));
     const float actual_max_float = QuantizedToFloat(
         actual_max_quantized, input_min_float, input_max_float);
+
+#if 0
+    // This is the reference, non-eigen implementation:
     auto output_array = output->flat<T2>();
     RequantizeManyInNewRange(input_array.data(), input_array.size(),
                              input_min_float, input_max_float, actual_min_float,
                              actual_max_float, output_array.data());
+
+#endif
+
+    if (input_array.size() > 0) {
+      RequantizeManyInNewRangeUsingEigen<T1, T2>(
+          ctx->eigen_device<CPUDevice>(), input, input_min_float,
+          input_max_float, actual_min_float, actual_max_float, output);
+    }
+
     output_min->flat<float>().setConstant(actual_min_float);
     output_max->flat<float>().setConstant(actual_max_float);
   }
diff --git a/tensorflow/contrib/quantization/kernels/quantized_batch_norm_op.cc b/tensorflow/contrib/quantization/kernels/quantized_batch_norm_op.cc
index 77dcd98860..2a684824d3 100644
--- a/tensorflow/contrib/quantization/kernels/quantized_batch_norm_op.cc
+++ b/tensorflow/contrib/quantization/kernels/quantized_batch_norm_op.cc
@@ -13,6 +13,8 @@ See the License for the specific language governing permissions and
 limitations under the License.
 ==============================================================================*/
 
+#define EIGEN_USE_THREADS
+
 #include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
 #include "tensorflow/contrib/quantization/kernels/quantization_utils.h"
 #include "tensorflow/core/framework/numeric_op.h"
diff --git a/tensorflow/contrib/quantization/kernels/quantized_concat_op.cc b/tensorflow/contrib/quantization/kernels/quantized_concat_op.cc
index a029422b7f..e91e82a4a7 100644
--- a/tensorflow/contrib/quantization/kernels/quantized_concat_op.cc
+++ b/tensorflow/contrib/quantization/kernels/quantized_concat_op.cc
@@ -13,6 +13,8 @@ See the License for the specific language governing permissions and
 limitations under the License.
 ==============================================================================*/
 
+#define EIGEN_USE_THREADS
+
 #include <vector>
 
 #include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
diff --git a/tensorflow/contrib/quantization/tools/quantize_graph_test.py b/tensorflow/contrib/quantization/tools/quantize_graph_test.py
index 72c2b09346..428fafcccb 100644
--- a/tensorflow/contrib/quantization/tools/quantize_graph_test.py
+++ b/tensorflow/contrib/quantization/tools/quantize_graph_test.py
@@ -142,9 +142,9 @@ def are_tensors_near(a, b, tolerance):
     return True
   else:
     print("Tensors have {0} different values ({1}%), with mean difference"
-          " {2} and mean absolute difference {3}").format(
+          " {2} and mean absolute difference {3}".format(
               how_many_different, proportion_different * 100, mean_difference,
-              mean_abs_difference)
+              mean_abs_difference))
     return False
 
 
diff --git a/tensorflow/core/kernels/BUILD b/tensorflow/core/kernels/BUILD
index b0d0648fe8..5cf48bfab5 100644
--- a/tensorflow/core/kernels/BUILD
+++ b/tensorflow/core/kernels/BUILD
@@ -952,6 +952,7 @@ tf_cc_tests(
         ":io",
         ":ops_testutil",
         ":ops_util",
+        "//tensorflow/cc:cc_ops",
         "//tensorflow/core:core_cpu",
         "//tensorflow/core:core_cpu_internal",
         "//tensorflow/core:framework",
diff --git a/tensorflow/core/kernels/crop_and_resize_op.cc b/tensorflow/core/kernels/crop_and_resize_op.cc
index 4e50a04190..caf73420ba 100644
--- a/tensorflow/core/kernels/crop_and_resize_op.cc
+++ b/tensorflow/core/kernels/crop_and_resize_op.cc
@@ -42,6 +42,10 @@ static inline void ParseAndCheckBoxSizes(OpKernelContext* context,
                                          const Tensor& boxes,
                                          const Tensor& box_ind,
                                          int* num_boxes) {
+  if (boxes.NumElements() == 0 && box_ind.NumElements() == 0) {
+    *num_boxes = 0;
+    return;
+  }
   // The shape of 'boxes' is [num_boxes, 4].
   OP_REQUIRES(context, boxes.dims() == 2,
               errors::InvalidArgument("boxes must be 2-D",
@@ -132,9 +136,13 @@ class CropAndResizeOp : public OpKernel {
 
     CheckValidBoxInd<Device>(context, box_ind_data, batch);
 
-    functor::CropAndResize<Device, T>()(context->eigen_device<Device>(),
-                                        image_data, boxes_data, box_ind_data,
-                                        extrapolation_value_, crops_data);
+    bool status = functor::CropAndResize<Device, T>()(
+        context->eigen_device<Device>(), image_data, boxes_data, box_ind_data,
+        extrapolation_value_, crops_data);
+    if (!status) {
+      context->SetStatus(
+          errors::Internal("Failed launch CropAndResizeKernel."));
+    }
   }
 
  private:
@@ -145,11 +153,12 @@ class CropAndResizeOp : public OpKernel {
 namespace functor {
 template <typename T>
 struct CropAndResize<CPUDevice, T> {
-  void operator()(const CPUDevice& d, typename TTypes<T, 4>::ConstTensor image,
+  bool operator()(const CPUDevice& d, typename TTypes<T, 4>::ConstTensor image,
                   typename TTypes<float, 2>::ConstTensor boxes,
                   typename TTypes<int32, 1>::ConstTensor box_ind,
                   float extrapolation_value,
                   typename TTypes<float, 4>::Tensor crops) {
+    const int batch = image.dimension(0);
     const int image_height = image.dimension(1);
     const int image_width = image.dimension(2);
 
@@ -163,7 +172,11 @@ struct CropAndResize<CPUDevice, T> {
       const float x1 = boxes(b, 1);
       const float y2 = boxes(b, 2);
       const float x2 = boxes(b, 3);
+
       const int32 b_in = box_ind(b);
+      if (b_in < 0 || b_in >= batch) {
+        continue;
+      }
 
       const float height_scale =
           (crop_height > 1) ? (y2 - y1) * (image_height - 1) / (crop_height - 1)
@@ -217,6 +230,7 @@ struct CropAndResize<CPUDevice, T> {
         }
       }
     }
+    return true;
   }
 };
 }  // namespace functor
@@ -235,6 +249,7 @@ class CropAndResizeGradImageOp : public OpKernel {
   void Compute(OpKernelContext* context) override {
     // The shape of 'grads' is [num_boxes, crop_height, crop_width, depth].
     const Tensor& grads = context->input(0);
+
     OP_REQUIRES(context, grads.dims() == 4,
                 errors::InvalidArgument("grads image must be 4-D",
                                         grads.shape().DebugString()));
@@ -294,9 +309,13 @@ class CropAndResizeGradImageOp : public OpKernel {
 
     CheckValidBoxInd<Device>(context, box_ind_data, batch);
 
-    functor::CropAndResizeBackpropImage<Device, T>()(
+    bool status = functor::CropAndResizeBackpropImage<Device, T>()(
         context->eigen_device<Device>(), grads_data, boxes_data, box_ind_data,
         output_data);
+    if (!status) {
+      context->SetStatus(
+          errors::Internal("Failed launch CropAndResizeBackpropImageKernel."));
+    }
   }
 };
 
@@ -304,11 +323,12 @@ class CropAndResizeGradImageOp : public OpKernel {
 namespace functor {
 template <typename T>
 struct CropAndResizeBackpropImage<CPUDevice, T> {
-  void operator()(const CPUDevice& d,
+  bool operator()(const CPUDevice& d,
                   typename TTypes<float, 4>::ConstTensor grads,
                   typename TTypes<float, 2>::ConstTensor boxes,
                   typename TTypes<int32, 1>::ConstTensor box_ind,
                   typename TTypes<T, 4>::Tensor grads_image) {
+    const int batch = grads_image.dimension(0);
     const int image_height = grads_image.dimension(1);
     const int image_width = grads_image.dimension(2);
 
@@ -324,7 +344,11 @@ struct CropAndResizeBackpropImage<CPUDevice, T> {
       const float x1 = boxes(b, 1);
       const float y2 = boxes(b, 2);
       const float x2 = boxes(b, 3);
+
       const int32 b_in = box_ind(b);
+      if (b_in < 0 || b_in >= batch) {
+        continue;
+      }
 
       const float height_scale =
           (crop_height > 1) ? (y2 - y1) * (image_height - 1) / (crop_height - 1)
@@ -370,6 +394,7 @@ struct CropAndResizeBackpropImage<CPUDevice, T> {
         }
       }
     }
+    return true;
   }
 };
 }  // namespace functor
@@ -388,6 +413,7 @@ class CropAndResizeGradBoxesOp : public OpKernel {
   void Compute(OpKernelContext* context) override {
     // The shape of 'grads' is [num_boxes, crop_height, crop_width, depth].
     const Tensor& grads = context->input(0);
+
     OP_REQUIRES(context, grads.dims() == 4,
                 errors::InvalidArgument("grads image must be 4-D",
                                         grads.shape().DebugString()));
@@ -441,9 +467,13 @@ class CropAndResizeGradBoxesOp : public OpKernel {
 
     CheckValidBoxInd<Device>(context, box_ind_data, batch);
 
-    functor::CropAndResizeBackpropBoxes<Device, T>()(
+    bool status = functor::CropAndResizeBackpropBoxes<Device, T>()(
         context->eigen_device<Device>(), grads_data, image_data, boxes_data,
         box_ind_data, output_data);
+    if (!status) {
+      context->SetStatus(
+          errors::Internal("Failed launch CropAndResizeBackpropBoxesKernel."));
+    }
   }
 };
 
@@ -451,12 +481,13 @@ class CropAndResizeGradBoxesOp : public OpKernel {
 namespace functor {
 template <typename T>
 struct CropAndResizeBackpropBoxes<CPUDevice, T> {
-  void operator()(const CPUDevice& d,
+  bool operator()(const CPUDevice& d,
                   typename TTypes<float, 4>::ConstTensor grads,
                   typename TTypes<T, 4>::ConstTensor image,
                   typename TTypes<float, 2>::ConstTensor boxes,
                   typename TTypes<int32, 1>::ConstTensor box_ind,
                   typename TTypes<float, 2>::Tensor grads_boxes) {
+    const int batch = image.dimension(0);
     const int image_height = image.dimension(1);
     const int image_width = image.dimension(2);
 
@@ -472,7 +503,11 @@ struct CropAndResizeBackpropBoxes<CPUDevice, T> {
       const float x1 = boxes(b, 1);
       const float y2 = boxes(b, 2);
       const float x2 = boxes(b, 3);
+
       const int32 b_in = box_ind(b);
+      if (b_in < 0 || b_in >= batch) {
+        continue;
+      }
 
       const float height_ratio =
           (crop_height > 1)
@@ -547,6 +582,7 @@ struct CropAndResizeBackpropBoxes<CPUDevice, T> {
         }
       }
     }
+    return true;
   }
 };
 }  // namespace functor
@@ -563,37 +599,25 @@ inline void CheckValidBoxInd<CPUDevice>(
   }
 }
 
-#define REGISTER_KERNEL(T)                              \
-  REGISTER_KERNEL_BUILDER(Name("CropAndResize")         \
-                              .Device(DEVICE_CPU)       \
-                              .TypeConstraint<T>("T")   \
-                              .HostMemory("crop_size"), \
-                          CropAndResizeOp<CPUDevice, T>);
-
-TF_CALL_REAL_NUMBER_TYPES(REGISTER_KERNEL);
-
-#undef REGISTER_KERNEL
-
-#define REGISTER_KERNEL(T)                               \
-  REGISTER_KERNEL_BUILDER(Name("CropAndResizeGradImage") \
-                              .Device(DEVICE_CPU)        \
-                              .TypeConstraint<T>("T")    \
-                              .HostMemory("image_size"), \
-                          CropAndResizeGradImageOp<CPUDevice, T>);
-
-TF_CALL_half(REGISTER_KERNEL);
-TF_CALL_float(REGISTER_KERNEL);
-TF_CALL_double(REGISTER_KERNEL);
-
-#undef REGISTER_KERNEL
-
-#define REGISTER_KERNEL(T)                               \
-  REGISTER_KERNEL_BUILDER(Name("CropAndResizeGradBoxes") \
-                              .Device(DEVICE_CPU)        \
-                              .TypeConstraint<T>("T"),   \
+#define REGISTER_KERNEL(T)                                         \
+  REGISTER_KERNEL_BUILDER(Name("CropAndResize")                    \
+                              .Device(DEVICE_CPU)                  \
+                              .TypeConstraint<T>("T")              \
+                              .HostMemory("crop_size"),            \
+                          CropAndResizeOp<CPUDevice, T>);          \
+                                                                   \
+  REGISTER_KERNEL_BUILDER(Name("CropAndResizeGradImage")           \
+                              .Device(DEVICE_CPU)                  \
+                              .TypeConstraint<T>("T")              \
+                              .HostMemory("image_size"),           \
+                          CropAndResizeGradImageOp<CPUDevice, T>); \
+                                                                   \
+  REGISTER_KERNEL_BUILDER(Name("CropAndResizeGradBoxes")           \
+                              .Device(DEVICE_CPU)                  \
+                              .TypeConstraint<T>("T"),             \
                           CropAndResizeGradBoxesOp<CPUDevice, T>);
 
-TF_CALL_REAL_NUMBER_TYPES(REGISTER_KERNEL);
+TF_CALL_float(REGISTER_KERNEL);
 
 #undef REGISTER_KERNEL
 
@@ -613,6 +637,10 @@ template <>
 inline void CheckValidBoxInd<GPUDevice>(
     OpKernelContext* context, typename TTypes<int32, 1>::ConstTensor box_ind,
     int batch) {
+  const int num_boxes = box_ind.dimension(0);
+  if (num_boxes == 0) {
+    return;
+  }
   Tensor isvalid_tensor;
   OP_REQUIRES_OK(context,
                  context->allocate_temp(DataTypeToEnum<bool>::value,
@@ -657,7 +685,7 @@ inline void CheckValidBoxInd<GPUDevice>(
                               .TypeConstraint<T>("T"),             \
                           CropAndResizeGradBoxesOp<GPUDevice, T>);
 
-TF_CALL_GPU_NUMBER_TYPES_NO_HALF(REGISTER_KERNEL);
+TF_CALL_float(REGISTER_KERNEL);
 
 #undef REGISTER_KERNEL
 
diff --git a/tensorflow/core/kernels/crop_and_resize_op.h b/tensorflow/core/kernels/crop_and_resize_op.h
index 9278893704..22df1bdd56 100644
--- a/tensorflow/core/kernels/crop_and_resize_op.h
+++ b/tensorflow/core/kernels/crop_and_resize_op.h
@@ -26,7 +26,7 @@ namespace functor {
 template <typename Device, typename T>
 struct CropAndResize {
   // We assume that the tensor sizes are correct.
-  void operator()(const Device& d, typename TTypes<T, 4>::ConstTensor image,
+  bool operator()(const Device& d, typename TTypes<T, 4>::ConstTensor image,
                   typename TTypes<float, 2>::ConstTensor boxes,
                   typename TTypes<int32, 1>::ConstTensor box_ind,
                   float extrapolation_value,
@@ -36,7 +36,7 @@ struct CropAndResize {
 template <typename Device, typename T>
 struct CropAndResizeBackpropImage {
   // We assume that the tensor sizes are correct.
-  void operator()(const Device& d, typename TTypes<float, 4>::ConstTensor grads,
+  bool operator()(const Device& d, typename TTypes<float, 4>::ConstTensor grads,
                   typename TTypes<float, 2>::ConstTensor boxes,
                   typename TTypes<int32, 1>::ConstTensor box_ind,
                   typename TTypes<T, 4>::Tensor grads_image);
@@ -45,7 +45,7 @@ struct CropAndResizeBackpropImage {
 template <typename Device, typename T>
 struct CropAndResizeBackpropBoxes {
   // We assume that the tensor sizes are correct.
-  void operator()(const Device& d, typename TTypes<float, 4>::ConstTensor grads,
+  bool operator()(const Device& d, typename TTypes<float, 4>::ConstTensor grads,
                   typename TTypes<T, 4>::ConstTensor image,
                   typename TTypes<float, 2>::ConstTensor boxes,
                   typename TTypes<int32, 1>::ConstTensor box_ind,
diff --git a/tensorflow/core/kernels/crop_and_resize_op_gpu.cu.cc b/tensorflow/core/kernels/crop_and_resize_op_gpu.cu.cc
index 3759a8cb4c..75146b28e6 100644
--- a/tensorflow/core/kernels/crop_and_resize_op_gpu.cu.cc
+++ b/tensorflow/core/kernels/crop_and_resize_op_gpu.cu.cc
@@ -33,27 +33,30 @@ typedef Eigen::GpuDevice GPUDevice;
 namespace {
 
 template <typename T>
-__global__ void CropAndResizeKernel(const int32 nthreads, const T* image_ptr,
-                                    const float* boxes_ptr,
-                                    const int32* box_ind_ptr, int num_boxes,
-                                    int image_height, int image_width,
-                                    int crop_height, int crop_width, int depth,
-                                    float extrapolation_value,
-                                    float* crops_ptr) {
+__global__ void CropAndResizeKernel(
+    const int32 nthreads, const T* image_ptr, const float* boxes_ptr,
+    const int32* box_ind_ptr, int num_boxes, int batch, int image_height,
+    int image_width, int crop_height, int crop_width, int depth,
+    float extrapolation_value, float* crops_ptr) {
   CUDA_1D_KERNEL_LOOP(out_idx, nthreads) {
     // out_idx = d + depth * (w + crop_width * (h + crop_height * b))
-    const int d = out_idx % depth;
-    const int out_idx2 = out_idx / depth;
-    const int x = out_idx2 % crop_width;
-    const int out_idx3 = out_idx2 / crop_width;
-    const int y = out_idx3 % crop_height;
-    const int b = out_idx3 / crop_height;
+    int idx = out_idx;
+    const int d = idx % depth;
+    idx /= depth;
+    const int x = idx % crop_width;
+    idx /= crop_width;
+    const int y = idx % crop_height;
+    const int b = idx / crop_height;
 
     const float y1 = boxes_ptr[b * 4];
     const float x1 = boxes_ptr[b * 4 + 1];
     const float y2 = boxes_ptr[b * 4 + 2];
     const float x2 = boxes_ptr[b * 4 + 3];
+
     const int32 b_in = box_ind_ptr[b];
+    if (b_in < 0 || b_in >= batch) {
+      continue;
+    }
 
     const float height_scale =
         (crop_height > 1) ? (y2 - y1) * (image_height - 1) / (crop_height - 1)
@@ -66,7 +69,7 @@ __global__ void CropAndResizeKernel(const int32 nthreads, const T* image_ptr,
                            : 0.5 * (y1 + y2) * (image_height - 1);
     if (in_y < 0 || in_y > image_height - 1) {
       crops_ptr[out_idx] = extrapolation_value;
-      return;
+      continue;
     }
 
     const float in_x = (crop_width > 1)
@@ -74,7 +77,7 @@ __global__ void CropAndResizeKernel(const int32 nthreads, const T* image_ptr,
                            : 0.5 * (x1 + x2) * (image_width - 1);
     if (in_x < 0 || in_x > image_width - 1) {
       crops_ptr[out_idx] = extrapolation_value;
-      return;
+      continue;
     }
 
     const int top_y_index = floorf(in_y);
@@ -114,22 +117,28 @@ __global__ void CropAndResizeKernel(const int32 nthreads, const T* image_ptr,
 template <typename T>
 __global__ void CropAndResizeBackpropImageKernel(
     const int32 nthreads, const float* grads_ptr, const float* boxes_ptr,
-    const int32* box_ind_ptr, int num_boxes, int image_height, int image_width,
-    int crop_height, int crop_width, int depth, T* grads_image_ptr) {
+    const int32* box_ind_ptr, int num_boxes, int batch, int image_height,
+    int image_width, int crop_height, int crop_width, int depth,
+    T* grads_image_ptr) {
   CUDA_1D_KERNEL_LOOP(out_idx, nthreads) {
     // out_idx = d + depth * (w + crop_width * (h + crop_height * b))
-    const int d = out_idx % depth;
-    const int out_idx2 = out_idx / depth;
-    const int x = out_idx2 % crop_width;
-    const int out_idx3 = out_idx2 / crop_width;
-    const int y = out_idx3 % crop_height;
-    const int b = out_idx3 / crop_height;
+    int idx = out_idx;
+    const int d = idx % depth;
+    idx /= depth;
+    const int x = idx % crop_width;
+    idx /= crop_width;
+    const int y = idx % crop_height;
+    const int b = idx / crop_height;
 
     const float y1 = boxes_ptr[b * 4];
     const float x1 = boxes_ptr[b * 4 + 1];
     const float y2 = boxes_ptr[b * 4 + 2];
     const float x2 = boxes_ptr[b * 4 + 3];
+
     const int32 b_in = box_ind_ptr[b];
+    if (b_in < 0 || b_in >= batch) {
+      continue;
+    }
 
     const float height_scale =
         (crop_height > 1) ? (y2 - y1) * (image_height - 1) / (crop_height - 1)
@@ -141,14 +150,14 @@ __global__ void CropAndResizeBackpropImageKernel(
                            ? y1 * (image_height - 1) + y * height_scale
                            : 0.5 * (y1 + y2) * (image_height - 1);
     if (in_y < 0 || in_y > image_height - 1) {
-      return;
+      continue;
     }
 
     const float in_x = (crop_width > 1)
                            ? x1 * (image_width - 1) + x * width_scale
                            : 0.5 * (x1 + x2) * (image_width - 1);
     if (in_x < 0 || in_x > image_width - 1) {
-      return;
+      continue;
     }
 
     const int top_y_index = floorf(in_y);
@@ -192,23 +201,28 @@ __global__ void CropAndResizeBackpropImageKernel(
 template <typename T>
 __global__ void CropAndResizeBackpropBoxesKernel(
     const int32 nthreads, const float* grads_ptr, const T* image_ptr,
-    const float* boxes_ptr, const int32* box_ind_ptr, int num_boxes,
+    const float* boxes_ptr, const int32* box_ind_ptr, int num_boxes, int batch,
     int image_height, int image_width, int crop_height, int crop_width,
     int depth, float* grads_boxes_ptr) {
   CUDA_1D_KERNEL_LOOP(out_idx, nthreads) {
     // out_idx = d + depth * (w + crop_width * (h + crop_height * b))
-    const int d = out_idx % depth;
-    const int out_idx2 = out_idx / depth;
-    const int x = out_idx2 % crop_width;
-    const int out_idx3 = out_idx2 / crop_width;
-    const int y = out_idx3 % crop_height;
-    const int b = out_idx3 / crop_height;
+    int idx = out_idx;
+    const int d = idx % depth;
+    idx /= depth;
+    const int x = idx % crop_width;
+    idx /= crop_width;
+    const int y = idx % crop_height;
+    const int b = idx / crop_height;
 
     const float y1 = boxes_ptr[b * 4];
     const float x1 = boxes_ptr[b * 4 + 1];
     const float y2 = boxes_ptr[b * 4 + 2];
     const float x2 = boxes_ptr[b * 4 + 3];
+
     const int32 b_in = box_ind_ptr[b];
+    if (b_in < 0 || b_in >= batch) {
+      continue;
+    }
 
     const float height_ratio =
         (crop_height > 1)
@@ -226,14 +240,14 @@ __global__ void CropAndResizeBackpropBoxesKernel(
                            ? y1 * (image_height - 1) + y * height_scale
                            : 0.5 * (y1 + y2) * (image_height - 1);
     if (in_y < 0 || in_y > image_height - 1) {
-      return;
+      continue;
     }
 
     const float in_x = (crop_width > 1)
                            ? x1 * (image_width - 1) + x * width_scale
                            : 0.5 * (x1 + x2) * (image_width - 1);
     if (in_x < 0 || in_x > image_width - 1) {
-      return;
+      continue;
     }
 
     const int top_y_index = floorf(in_y);
@@ -306,11 +320,12 @@ namespace functor {
 
 template <typename T>
 struct CropAndResize<GPUDevice, T> {
-  void operator()(const GPUDevice& d, typename TTypes<T, 4>::ConstTensor image,
+  bool operator()(const GPUDevice& d, typename TTypes<T, 4>::ConstTensor image,
                   typename TTypes<float, 2>::ConstTensor boxes,
                   typename TTypes<int32, 1>::ConstTensor box_ind,
                   float extrapolation_value,
                   typename TTypes<float, 4>::Tensor crops) {
+    const int batch = image.dimension(0);
     const int image_height = image.dimension(1);
     const int image_width = image.dimension(2);
 
@@ -320,19 +335,22 @@ struct CropAndResize<GPUDevice, T> {
     const int depth = crops.dimension(3);
 
     const int total_count = num_boxes * crop_height * crop_width * depth;
-    CudaLaunchConfig config = GetCudaLaunchConfig(total_count, d);
 
-    CropAndResizeKernel<<<config.block_count, config.thread_per_block, 0,
-                          d.stream()>>>(
-        config.virtual_thread_count, image.data(), boxes.data(), box_ind.data(),
-        num_boxes, image_height, image_width, crop_height, crop_width, depth,
-        extrapolation_value, crops.data());
+    if (total_count > 0) {
+      CudaLaunchConfig config = GetCudaLaunchConfig(total_count, d);
+      CropAndResizeKernel<<<config.block_count, config.thread_per_block, 0,
+                            d.stream()>>>(
+          config.virtual_thread_count, image.data(), boxes.data(),
+          box_ind.data(), num_boxes, batch, image_height, image_width,
+          crop_height, crop_width, depth, extrapolation_value, crops.data());
+    }
+    return d.ok();
   }
 };
 
 template <typename T>
 struct CropAndResizeBackpropImage<GPUDevice, T> {
-  void operator()(const GPUDevice& d,
+  bool operator()(const GPUDevice& d,
                   typename TTypes<float, 4>::ConstTensor grads,
                   typename TTypes<float, 2>::ConstTensor boxes,
                   typename TTypes<int32, 1>::ConstTensor box_ind,
@@ -351,29 +369,35 @@ struct CropAndResizeBackpropImage<GPUDevice, T> {
 
     // Initialize grads_image with all zeros.
     total_count = batch * image_height * image_width * depth;
-    config = GetCudaLaunchConfig(total_count, d);
-    SetZero<<<config.block_count, config.thread_per_block, 0, d.stream()>>>(
-        total_count, grads_image.data());
+    if (total_count > 0) {
+      config = GetCudaLaunchConfig(total_count, d);
+      SetZero<<<config.block_count, config.thread_per_block, 0, d.stream()>>>(
+          config.virtual_thread_count, grads_image.data());
+    }
 
     // Accumulate.
     total_count = num_boxes * crop_height * crop_width * depth;
-    config = GetCudaLaunchConfig(total_count, d);
-    CropAndResizeBackpropImageKernel<<<
-        config.block_count, config.thread_per_block, 0, d.stream()>>>(
-        config.virtual_thread_count, grads.data(), boxes.data(), box_ind.data(),
-        num_boxes, image_height, image_width, crop_height, crop_width, depth,
-        grads_image.data());
+    if (total_count > 0) {
+      config = GetCudaLaunchConfig(total_count, d);
+      CropAndResizeBackpropImageKernel<<<
+          config.block_count, config.thread_per_block, 0, d.stream()>>>(
+          config.virtual_thread_count, grads.data(), boxes.data(),
+          box_ind.data(), num_boxes, batch, image_height, image_width,
+          crop_height, crop_width, depth, grads_image.data());
+    }
+    return d.ok();
   }
 };
 
 template <typename T>
 struct CropAndResizeBackpropBoxes<GPUDevice, T> {
-  void operator()(const GPUDevice& d,
+  bool operator()(const GPUDevice& d,
                   typename TTypes<float, 4>::ConstTensor grads,
                   typename TTypes<T, 4>::ConstTensor image,
                   typename TTypes<float, 2>::ConstTensor boxes,
                   typename TTypes<int32, 1>::ConstTensor box_ind,
                   typename TTypes<float, 2>::Tensor grads_boxes) {
+    const int batch = image.dimension(0);
     const int image_height = image.dimension(1);
     const int image_width = image.dimension(2);
 
@@ -387,18 +411,23 @@ struct CropAndResizeBackpropBoxes<GPUDevice, T> {
 
     // Initialize grads_boxes with all zeros.
     total_count = num_boxes * 4;
-    config = GetCudaLaunchConfig(total_count, d);
-    SetZero<<<config.block_count, config.thread_per_block, 0, d.stream()>>>(
-        total_count, grads_boxes.data());
+    if (total_count > 0) {
+      config = GetCudaLaunchConfig(total_count, d);
+      SetZero<<<config.block_count, config.thread_per_block, 0, d.stream()>>>(
+          config.virtual_thread_count, grads_boxes.data());
+    }
 
     // Accumulate.
     total_count = num_boxes * crop_height * crop_width * depth;
-    config = GetCudaLaunchConfig(total_count, d);
-    CropAndResizeBackpropBoxesKernel<<<
-        config.block_count, config.thread_per_block, 0, d.stream()>>>(
-        config.virtual_thread_count, grads.data(), image.data(), boxes.data(),
-        box_ind.data(), num_boxes, image_height, image_width, crop_height,
-        crop_width, depth, grads_boxes.data());
+    if (total_count > 0) {
+      config = GetCudaLaunchConfig(total_count, d);
+      CropAndResizeBackpropBoxesKernel<<<
+          config.block_count, config.thread_per_block, 0, d.stream()>>>(
+          config.virtual_thread_count, grads.data(), image.data(), boxes.data(),
+          box_ind.data(), num_boxes, batch, image_height, image_width,
+          crop_height, crop_width, depth, grads_boxes.data());
+    }
+    return d.ok();
   }
 };
 
@@ -407,7 +436,7 @@ struct CropAndResizeBackpropBoxes<GPUDevice, T> {
   template struct CropAndResizeBackpropImage<GPUDevice, T>; \
   template struct CropAndResizeBackpropBoxes<GPUDevice, T>;
 
-TF_CALL_GPU_NUMBER_TYPES_NO_HALF(DEFINE_GPU_SPECS);
+TF_CALL_float(DEFINE_GPU_SPECS);
 
 #undef DEFINE_GPU_SPECS
 
diff --git a/tensorflow/core/kernels/crop_and_resize_op_test.cc b/tensorflow/core/kernels/crop_and_resize_op_test.cc
index 38f3c1adb2..68e077e44d 100644
--- a/tensorflow/core/kernels/crop_and_resize_op_test.cc
+++ b/tensorflow/core/kernels/crop_and_resize_op_test.cc
@@ -189,6 +189,24 @@ TEST_F(CropAndResizeOpTest, TestCropAndResize2x2To3x3Extrapolated) {
   test::ExpectTensorEqual<float>(expected, *GetOutput(0));
 }
 
+TEST_F(CropAndResizeOpTest, TestCropAndResize2x2To3x3NoCrop) {
+  MakeOp(0);
+  // Input:
+  //  1, 2
+  //  3, 4
+  AddInputFromArray<float>(TensorShape({1, 2, 2, 1}), {1, 2, 3, 4});
+  AddInputFromArray<float>(TensorShape({0, 4}), {});
+  AddInputFromArray<int32>(TensorShape({0}), {});
+  AddInputFromArray<int32>(TensorShape({2}), {3, 3});
+  TF_ASSERT_OK(RunOpKernel());
+
+  Tensor expected(allocator(), DT_FLOAT, TensorShape({0, 3, 3, 1}));
+  // clang-format off
+  test::FillValues<float>(&expected, {});
+  // clang-format on
+  test::ExpectTensorEqual<float>(expected, *GetOutput(0));
+}
+
 TEST_F(CropAndResizeOpTest, TestInvalidInputShape) {
   MakeOp(0);
   AddInputFromArray<float>(TensorShape({2, 2, 1}), {1, 2, 3, 4});
@@ -201,6 +219,19 @@ TEST_F(CropAndResizeOpTest, TestInvalidInputShape) {
       << s;
 }
 
+TEST_F(CropAndResizeOpTest, TestInvalidBoxIndexShape) {
+  MakeOp(0);
+  AddInputFromArray<float>(TensorShape({1, 2, 2, 1}), {1, 2, 3, 4});
+  AddInputFromArray<float>(TensorShape({1, 4}), {0, 0, 1, 1});
+  AddInputFromArray<int32>(TensorShape({2}), {0, 0});
+  AddInputFromArray<int32>(TensorShape({2}), {4, 4});
+  Status s = RunOpKernel();
+  ASSERT_FALSE(s.ok());
+  EXPECT_TRUE(
+      StringPiece(s.ToString()).contains("box_ind has incompatible shape"))
+      << s;
+}
+
 TEST_F(CropAndResizeOpTest, TestInvalidBoxIndex) {
   MakeOp(0);
   AddInputFromArray<float>(TensorShape({1, 2, 2, 1}), {1, 2, 3, 4});
diff --git a/tensorflow/core/kernels/save_op_test.cc b/tensorflow/core/kernels/save_op_test.cc
index 7fae556690..ba4d0f879d 100644
--- a/tensorflow/core/kernels/save_op_test.cc
+++ b/tensorflow/core/kernels/save_op_test.cc
@@ -16,6 +16,9 @@ limitations under the License.
 #include <functional>
 #include <memory>
 
+#include "tensorflow/cc/ops/const_op.h"
+#include "tensorflow/cc/ops/io_ops.h"
+#include "tensorflow/core/common_runtime/kernel_benchmark_testlib.h"
 #include "tensorflow/core/framework/allocator.h"
 #include "tensorflow/core/framework/fake_input.h"
 #include "tensorflow/core/framework/graph.pb.h"
@@ -24,12 +27,15 @@ limitations under the License.
 #include "tensorflow/core/framework/tensor.h"
 #include "tensorflow/core/framework/types.h"
 #include "tensorflow/core/framework/types.pb.h"
+#include "tensorflow/core/graph/graph_def_builder.h"
 #include "tensorflow/core/kernels/ops_testutil.h"
 #include "tensorflow/core/kernels/ops_util.h"
 #include "tensorflow/core/lib/io/path.h"
 #include "tensorflow/core/lib/strings/strcat.h"
 #include "tensorflow/core/platform/test.h"
+#include "tensorflow/core/platform/test_benchmark.h"
 #include "tensorflow/core/platform/types.h"
+#include "tensorflow/core/protobuf/config.pb.h"
 #include "tensorflow/core/util/tensor_slice_reader.h"
 
 namespace tensorflow {
@@ -366,7 +372,6 @@ TEST_F(SaveOpTest, Simple) {
       EXPECT_EQ(200 + i, data[i].imag());
     }
   }
-
   {
     // The 2-d half tensor
     TensorShape shape;
@@ -652,5 +657,40 @@ TEST_F(SaveOpSlices2Test, TwoSlices) {
   }
 }
 
+// Benchmark-related code below.
+
+static void BM_LargeTensorWrite(int iters, int num_elements) {
+  testing::StopTiming();
+
+  // 4 * num_elements bytes total , since sizeof(float) == 4.
+  Tensor tensor(DT_FLOAT, TensorShape({num_elements}));
+  tensor.flat<float>().setZero();
+
+  // Builds the graph.
+  const string temp_filename =
+      io::JoinPath(testing::TmpDir(), "benchmark_checkpoint");
+  GraphDefBuilder b(GraphDefBuilder::kFailImmediately);
+  Node* filename = ops::Const(test::AsScalar<string>(temp_filename), b.opts());
+  Node* tensor_names =
+      ops::Const(test::AsTensor<string>({"my_tensor"}), b.opts());
+  Node* tensors = ops::Const(tensor, b.opts());
+  ops::Save(filename, tensor_names, {tensors}, b.opts());
+
+  // Disables optimizations.
+  SessionOptions session_options;
+  session_options.config.mutable_graph_options()
+      ->mutable_optimizer_options()
+      ->set_opt_level(tensorflow::OptimizerOptions_Level_L0);
+
+  Graph* g = new Graph(OpRegistry::Global());
+  TF_CHECK_OK(b.ToGraph(g));
+  VLOG(1) << "Save op's output path: " << temp_filename;
+  VLOG(1) << "# nodes in Graph: " << g->num_nodes();
+
+  testing::StartTiming();
+  test::Benchmark("cpu", g, &session_options).Run(iters);
+}
+BENCHMARK(BM_LargeTensorWrite)->Arg((1 << 30) / 4 /* 1GB float tensor */);
+
 }  // namespace
 }  // namespace tensorflow
diff --git a/tensorflow/core/ops/math_ops.cc b/tensorflow/core/ops/math_ops.cc
index 51377b6cf0..0f9ee4942a 100644
--- a/tensorflow/core/ops/math_ops.cc
+++ b/tensorflow/core/ops/math_ops.cc
@@ -47,6 +47,74 @@ Add all input tensors element wise.
 inputs: Must all be the same size and shape.
 )doc");
 
+namespace {
+
+// Shape inference function for binary operators that broadcast their inputs.
+Status BroadcastBinaryOpShapeFn(InferenceContext* c) {
+  const Shape* shape_x = c->input(0);
+  const Shape* shape_y = c->input(1);
+  if (!c->RankKnown(shape_x) || !c->RankKnown(shape_y)) {
+    c->set_output(0, c->CreateUnknownShape());
+    return Status::OK();
+  }
+  const int32 rank_x = c->Rank(shape_x);
+  const int32 rank_y = c->Rank(shape_y);
+  const int32 rank_out = std::max(rank_x, rank_y);
+
+  // To compute the broadcast dimensions, we zip together shape_x and shape_y
+  // and
+  // pad with 1 to make them the same length.
+  std::vector<const Dimension*> dims;
+  const Dimension* dim_one = rank_x == rank_y ? nullptr : c->CreateDim(1);
+  for (int i = 0; i < rank_out; ++i) {
+    const auto* dim_x = i < (rank_out - rank_x)
+                            ? dim_one
+                            : c->Dim(shape_x, i - (rank_out - rank_x));
+    const auto* dim_y = i < (rank_out - rank_y)
+                            ? dim_one
+                            : c->Dim(shape_y, i - (rank_out - rank_y));
+    if (!c->ValueKnown(dim_x) || !c->ValueKnown(dim_y)) {
+      // One or both dimensions is unknown.
+      //
+      // - If either dimension is greater than 1, we assume that the program is
+      // correct, and the other dimension will be broadcast to match it.
+      // TODO(cwhipkey): For shape inference, if we eliminate the shape checks
+      // in C++ op code, we must still assert that the unknown dim is either 1
+      // or the same as the known dim.
+      // - If either dimension is 1, the other dimension is the output.
+      if (c->Value(dim_x) > 1) {
+        dims.push_back(dim_x);
+      } else if (c->Value(dim_y) > 1) {
+        dims.push_back(dim_y);
+      } else if (c->Value(dim_x) == 1) {
+        dims.push_back(dim_y);
+      } else if (c->Value(dim_y) == 1) {
+        dims.push_back(dim_x);
+      } else {
+        dims.push_back(c->CreateUnknownDim());
+      }
+    } else if (c->Value(dim_x) == 1 || c->Value(dim_y) == 1) {
+      if (c->Value(dim_x) == 1 && dim_y != dim_one) {
+        // We will broadcast dim_x to dim_y.
+        dims.push_back(dim_y);
+      } else {
+        DCHECK_EQ(c->Value(dim_y), 1);
+        // We will broadcast dim_y to dim_x.
+        dims.push_back(dim_x);
+      }
+    } else {
+      const Dimension* dim;
+      TF_RETURN_IF_ERROR(c->Merge(dim_x, dim_y, &dim));
+      dims.push_back(dim);
+    }
+  }
+
+  c->set_output(0, c->CreateShape(dims));
+  return Status::OK();
+}
+
+}  // namespace
+
 // --------------------------------------------------------------------------
 
 REGISTER_OP("BatchMatMul")
@@ -373,6 +441,7 @@ REGISTER_OP("Add")
     .Attr(
         "T: {half, float, double, uint8, int8, int16, int32, int64, complex64, "
         "complex128, string}")
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Returns x + y element-wise.
 
@@ -381,6 +450,7 @@ Returns x + y element-wise.
 
 REGISTER_OP("Sub")
     .BINARY_FEWER()
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Returns x - y element-wise.
 )doc");
@@ -388,12 +458,14 @@ Returns x - y element-wise.
 REGISTER_OP("Mul")
     .BINARY_MORE()
     .SetIsCommutative()
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Returns x * y element-wise.
 )doc");
 
 REGISTER_OP("Div")
     .BINARY_MORE()
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Returns x / y element-wise.
 )doc");
@@ -401,6 +473,7 @@ Returns x / y element-wise.
 REGISTER_OP("SquaredDifference")
     .BINARY_FEWER()
     .SetIsCommutative()
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Returns (x - y)(x - y) element-wise.
 )doc");
@@ -414,6 +487,7 @@ REGISTER_OP("Maximum")
     .Output("z: T")
     .Attr("T: {half, float, double, int32, int64}")
     .SetIsCommutative()
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Returns the max of x and y (i.e. x > y ? x : y) element-wise, broadcasts.
 )doc");
@@ -424,6 +498,7 @@ REGISTER_OP("Minimum")
     .Output("z: T")
     .Attr("T: {half, float, double, int32, int64}")
     .SetIsCommutative()
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Returns the min of x and y (i.e. x < y ? x : y) element-wise, broadcasts.
 )doc");
@@ -433,6 +508,7 @@ REGISTER_OP("Mod")
     .Input("y: T")
     .Output("z: T")
     .Attr("T: {int32, int64, float, double}")
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Returns element-wise remainder of division.
 )doc");
@@ -442,6 +518,7 @@ REGISTER_OP("Pow")
     .Input("y: T")
     .Output("z: T")
     .Attr("T: {half, float, double, int32, int64, complex64, complex128}")
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Computes the power of one value to another.
 
@@ -460,6 +537,7 @@ REGISTER_OP("Igammac")
     .Input("x: T")
     .Output("z: T")
     .Attr("T: {float, double}")
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Compute the upper regularized incomplete Gamma function `Q(a, x)`.
 
@@ -483,6 +561,7 @@ REGISTER_OP("Igamma")
     .Input("x: T")
     .Output("z: T")
     .Attr("T: {float, double}")
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Compute the lower regularized incomplete Gamma function `Q(a, x)`.
 
@@ -506,6 +585,7 @@ REGISTER_OP("Zeta")
     .Input("q: T")
     .Output("z: T")
     .Attr("T: {float, double}")
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Compute the Hurwitz zeta function \\(\zeta(x, q)\\).
 
@@ -521,6 +601,7 @@ REGISTER_OP("Polygamma")
     .Input("x: T")
     .Output("z: T")
     .Attr("T: {float, double}")
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Compute the polygamma function \\(\psi^{(n)}(x)\\).
 
@@ -536,8 +617,12 @@ where \\(\psi(x)\\) is the digamma function.
 
 // Declares cwise binary comparison operations signature: 't, 't -> bool,
 // where 't has a natural total order.
-#define COMPARISON() \
-  Input("x: T").Input("y: T").Output("z: bool").Attr("T: realnumbertype")
+#define COMPARISON()             \
+  Input("x: T")                  \
+      .Input("y: T")             \
+      .Output("z: bool")         \
+      .Attr("T: realnumbertype") \
+      .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
 
 REGISTER_OP("Less")
     .COMPARISON()
@@ -567,10 +652,16 @@ Returns the truth value of (x >= y) element-wise.
 
 // --------------------------------------------------------------------------
 
-#define EQUALITY_COMPARISON()                                                  \
-  Input("x: T").Input("y: T").Output("z: bool").SetIsCommutative().Attr(       \
-      "T: {half, float, double, uint8, int8, int16, int32, int64, complex64, " \
-      "quint8, qint8, qint32, string, bool, complex128}")
+#define EQUALITY_COMPARISON()                                           \
+  Input("x: T")                                                         \
+      .Input("y: T")                                                    \
+      .Output("z: bool")                                                \
+      .SetIsCommutative()                                               \
+      .Attr(                                                            \
+          "T: {half, float, double, uint8, int8, int16, int32, int64, " \
+          "complex64, "                                                 \
+          "quint8, qint8, qint32, string, bool, complex128}")           \
+      .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
 
 REGISTER_OP("Equal")
     .EQUALITY_COMPARISON()
@@ -596,8 +687,12 @@ REGISTER_OP("LogicalNot")
 Returns the truth value of NOT x element-wise.
 )doc");
 
-#define BINARY_LOGICAL() \
-  Input("x: bool").Input("y: bool").Output("z: bool").SetIsCommutative()
+#define BINARY_LOGICAL()  \
+  Input("x: bool")        \
+      .Input("y: bool")   \
+      .Output("z: bool")  \
+      .SetIsCommutative() \
+      .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
 
 REGISTER_OP("LogicalAnd")
     .BINARY_LOGICAL()
@@ -1271,6 +1366,7 @@ REGISTER_OP("Complex")
     .Output("out: Tout")
     .Attr("T: {float, double} = DT_FLOAT")
     .Attr("Tout: {complex64, complex128} = DT_COMPLEX64")
+    .SetShapeFn(OpShapeInferenceFn(BroadcastBinaryOpShapeFn))
     .Doc(R"doc(
 Converts two real numbers to a complex number.
 
diff --git a/tensorflow/core/ops/math_ops_test.cc b/tensorflow/core/ops/math_ops_test.cc
index c75b0310a2..0aee63ce1d 100644
--- a/tensorflow/core/ops/math_ops_test.cc
+++ b/tensorflow/core/ops/math_ops_test.cc
@@ -121,4 +121,52 @@ TEST(MathOpsTest, Segment) {
   }
 }
 
+TEST(MathOpsTest, BroadcastBinaryOps) {
+  for (const auto* op : {"Add",        "Complex",
+                         "Div",        "Equal",
+                         "Greater",    "GreaterEqual",
+                         "Igamma",     "Igammac",
+                         "Zeta",       "Polygamma",
+                         "Less",       "LessEqual",
+                         "LogicalAnd", "LogicalOr",
+                         "Maximum",    "Minimum",
+                         "Mod",        "Mul",
+                         "NotEqual",   "Pow",
+                         "Sub",        "SquaredDifference"}) {
+    INFER_OK(op, "?;?", "?");
+    INFER_OK(op, "[1,2];?", "?");
+    INFER_OK(op, "?;[1,2]", "?");
+
+    INFER_OK(op, "[?];[1]", "[d0_0]");
+    INFER_OK(op, "[1];[?]", "[d1_0]");
+    INFER_OK(op, "[?];[2]", "[d1_0]");
+    INFER_OK(op, "[2];[?]", "[d0_0]");
+    INFER_OK(op, "[?];[?]", "[?]");
+    INFER_OK(op, "[];[?]", "[d1_0]");
+    INFER_OK(op, "[?];[]", "[d0_0]");
+
+    INFER_OK(op, "[1];[1]", "[d0_0|d1_0]");
+    INFER_OK(op, "[];[1]", "[d1_0]");
+    INFER_OK(op, "[1];[]", "[d0_0]");
+
+    INFER_OK(op, "[2];[2]", "[d0_0|d1_0]");
+    INFER_OK(op, "[];[2]", "[d1_0]");
+    INFER_OK(op, "[1];[2]", "[d1_0]");
+    INFER_OK(op, "[2];[1]", "[d0_0]");
+    INFER_OK(op, "[2];[]", "[d0_0]");
+
+    INFER_OK(op, "[0];[0]", "[d0_0|d1_0]");
+    INFER_OK(op, "[];[0]", "[d1_0]");
+    INFER_OK(op, "[1];[0]", "[d1_0]");
+    INFER_OK(op, "[0];[1]", "[d0_0]");
+    INFER_OK(op, "[0];[]", "[d0_0]");
+
+    // Multiple dimension cases (same test cases, switching x and y).
+    INFER_OK(op, "[?,1,2,3,4,5];[3,1,?]",
+             "[d0_0,d0_1,d0_2,d0_3|d1_0,d0_4,d0_5]");
+    INFER_OK(op, "[3,1,?];[?,1,2,3,4,5]",
+             "[d1_0,d1_1,d1_2,d1_3|d0_0,d1_4,d1_5]");
+  }
+}
+
 }  // end namespace tensorflow
diff --git a/tensorflow/g3doc/api_docs/python/contrib.learn.md b/tensorflow/g3doc/api_docs/python/contrib.learn.md
index 48fe1087db..b573b02bd7 100644
--- a/tensorflow/g3doc/api_docs/python/contrib.learn.md
+++ b/tensorflow/g3doc/api_docs/python/contrib.learn.md
@@ -15,7 +15,8 @@ Train and evaluate TensorFlow models.
 
 Abstract BaseEstimator class to train and evaluate TensorFlow models.
 
-Concrete implementation of this class should provide following functions:
+Concrete implementation of this class should provide the following functions:
+
   * _get_train_ops
   * _get_eval_ops
   * _get_predict_ops
@@ -65,17 +66,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -108,12 +112,15 @@ Trains a model given training data `x` predictions and `y` targets.
 *  <b>`input_fn`</b>: Input function. If set, `x`, `y`, and `batch_size` must be
     `None`.
 *  <b>`steps`</b>: Number of steps for which to train model. If `None`, train forever.
+    If set, `max_steps` must be `None`.
 *  <b>`batch_size`</b>: minibatch size to use on the input, defaults to first
     dimension of `x`. Must be `None` if `input_fn` is provided.
 *  <b>`monitors`</b>: List of `BaseMonitor` subclass instances. Used for callbacks
     inside the training loop.
 *  <b>`max_steps`</b>: Number of total steps for which to train model. If `None`,
-    train forever. Two calls to `fit(steps=100)` means 200 training
+    train forever. If set, `steps` must be `None`.
+
+    Two calls to `fit(steps=100)` means 200 training
     iterations. On the other hand, two calls to `fit(max_steps=100)` means
     that the second call will not do any iteration since first call did
     all 100 steps.
@@ -126,8 +133,6 @@ Trains a model given training data `x` predictions and `y` targets.
 
 
 *  <b>`ValueError`</b>: If `x` or `y` are not `None` while `input_fn` is not `None`.
-*  <b>`ValueError`</b>: If at least one of `x` and `y` is provided, and `input_fn` is
-      provided.
 *  <b>`ValueError`</b>: If both `steps` and `max_steps` are not `None`.
 
 
@@ -141,7 +146,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -296,20 +302,24 @@ Constructs an Estimator instance.
 *  <b>`model_fn`</b>: Model function, takes features and targets tensors or dicts of
             tensors and returns predictions and loss tensors.
             Supports next three signatures for the function:
-              * `(features, targets) -> (predictions, loss, train_op)`
-              * `(features, targets, mode) -> (predictions, loss, train_op)`
-              * `(features, targets, mode, params) ->
-                  (predictions, loss, train_op)`
-*  <b>`Where`</b>: 
-              * `features` are single `Tensor` or `dict` of `Tensor`s
-                   (depending on data passed to `fit`),
-              * `targets` are `Tensor` or
-                  `dict` of `Tensor`s (for multi-head model).
-              * `mode` represents if this training, evaluation or
-                  prediction. See `ModeKeys` for example keys.
-              * `params` is a `dict` of hyperparameters. Will receive what
-                  is passed to Estimator in `params` parameter. This allows
-                  to configure Estimators from hyper parameter tunning.
+
+      * `(features, targets) -> (predictions, loss, train_op)`
+      * `(features, targets, mode) -> (predictions, loss, train_op)`
+      * `(features, targets, mode, params) -> (predictions, loss, train_op)`
+
+  Where
+
+      * `features` are single `Tensor` or `dict` of `Tensor`s
+             (depending on data passed to `fit`),
+      * `targets` are `Tensor` or
+             `dict` of `Tensor`s (for multi-head model).
+      * `mode` represents if this training, evaluation or
+             prediction. See `ModeKeys` for example keys.
+      * `params` is a `dict` of hyperparameters. Will receive what
+             is passed to Estimator in `params` parameter. This allows
+             to configure Estimators from hyper parameter tunning.
+
+
 *  <b>`model_dir`</b>: Directory to save model parameters, graph and etc.
 *  <b>`config`</b>: Configuration object.
 *  <b>`params`</b>: `dict` of hyper parameters that will be passed into `model_fn`.
@@ -352,17 +362,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -395,12 +408,15 @@ Trains a model given training data `x` predictions and `y` targets.
 *  <b>`input_fn`</b>: Input function. If set, `x`, `y`, and `batch_size` must be
     `None`.
 *  <b>`steps`</b>: Number of steps for which to train model. If `None`, train forever.
+    If set, `max_steps` must be `None`.
 *  <b>`batch_size`</b>: minibatch size to use on the input, defaults to first
     dimension of `x`. Must be `None` if `input_fn` is provided.
 *  <b>`monitors`</b>: List of `BaseMonitor` subclass instances. Used for callbacks
     inside the training loop.
 *  <b>`max_steps`</b>: Number of total steps for which to train model. If `None`,
-    train forever. Two calls to `fit(steps=100)` means 200 training
+    train forever. If set, `steps` must be `None`.
+
+    Two calls to `fit(steps=100)` means 200 training
     iterations. On the other hand, two calls to `fit(max_steps=100)` means
     that the second call will not do any iteration since first call did
     all 100 steps.
@@ -413,8 +429,6 @@ Trains a model given training data `x` predictions and `y` targets.
 
 
 *  <b>`ValueError`</b>: If `x` or `y` are not `None` while `input_fn` is not `None`.
-*  <b>`ValueError`</b>: If at least one of `x` and `y` is provided, and `input_fn` is
-      provided.
 *  <b>`ValueError`</b>: If both `steps` and `max_steps` are not `None`.
 
 
@@ -428,7 +442,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -642,17 +657,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -683,7 +701,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -889,15 +908,16 @@ estimator.predict(x=x)
 
 Input of `fit` and `evaluate` should have following features,
   otherwise there will be a `KeyError`:
-    if `weight_column_name` is not `None`, a feature with
-      `key=weight_column_name` whose value is a `Tensor`.
-    for each `column` in `feature_columns`:
-    - if `column` is a `SparseColumn`, a feature with `key=column.name`
-      whose `value` is a `SparseTensor`.
-    - if `column` is a `RealValuedColumn, a feature with `key=column.name`
-      whose `value` is a `Tensor`.
-    - if `feauture_columns` is `None`, then `input` must contains only real
-      valued `Tensor`.
+
+* if `weight_column_name` is not `None`, a feature with
+   `key=weight_column_name` whose value is a `Tensor`.
+* for each `column` in `feature_columns`:
+  - if `column` is a `SparseColumn`, a feature with `key=column.name`
+    whose `value` is a `SparseTensor`.
+  - if `column` is a `RealValuedColumn`, a feature with `key=column.name`
+    whose `value` is a `Tensor`.
+  - if `feature_columns` is `None`, then `input` must contains only real
+    valued `Tensor`.
 - - -
 
 #### `tf.contrib.learn.DNNClassifier.__init__(hidden_units, feature_columns=None, model_dir=None, n_classes=2, weight_column_name=None, optimizer=None, activation_fn=relu, dropout=None, gradient_clip_norm=None, enable_centered_bias=True, config=None)` {#DNNClassifier.__init__}
@@ -990,17 +1010,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -1033,12 +1056,15 @@ Trains a model given training data `x` predictions and `y` targets.
 *  <b>`input_fn`</b>: Input function. If set, `x`, `y`, and `batch_size` must be
     `None`.
 *  <b>`steps`</b>: Number of steps for which to train model. If `None`, train forever.
+    If set, `max_steps` must be `None`.
 *  <b>`batch_size`</b>: minibatch size to use on the input, defaults to first
     dimension of `x`. Must be `None` if `input_fn` is provided.
 *  <b>`monitors`</b>: List of `BaseMonitor` subclass instances. Used for callbacks
     inside the training loop.
 *  <b>`max_steps`</b>: Number of total steps for which to train model. If `None`,
-    train forever. Two calls to `fit(steps=100)` means 200 training
+    train forever. If set, `steps` must be `None`.
+
+    Two calls to `fit(steps=100)` means 200 training
     iterations. On the other hand, two calls to `fit(max_steps=100)` means
     that the second call will not do any iteration since first call did
     all 100 steps.
@@ -1051,8 +1077,6 @@ Trains a model given training data `x` predictions and `y` targets.
 
 
 *  <b>`ValueError`</b>: If `x` or `y` are not `None` while `input_fn` is not `None`.
-*  <b>`ValueError`</b>: If at least one of `x` and `y` is provided, and `input_fn` is
-      provided.
 *  <b>`ValueError`</b>: If both `steps` and `max_steps` are not `None`.
 
 
@@ -1066,7 +1090,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -1282,15 +1307,16 @@ estimator.predict(x=x)
 
 Input of `fit` and `evaluate` should have following features,
   otherwise there will be a `KeyError`:
-    if `weight_column_name` is not `None`, a feature with
-      `key=weight_column_name` whose value is a `Tensor`.
-    for each `column` in `feature_columns`:
-    - if `column` is a `SparseColumn`, a feature with `key=column.name`
-      whose `value` is a `SparseTensor`.
-    - if `column` is a `RealValuedColumn, a feature with `key=column.name`
-      whose `value` is a `Tensor`.
-    - if `feauture_columns` is `None`, then `input` must contains only real
-      valued `Tensor`.
+
+* if `weight_column_name` is not `None`, a feature with
+  `key=weight_column_name` whose value is a `Tensor`.
+* for each `column` in `feature_columns`:
+  - if `column` is a `SparseColumn`, a feature with `key=column.name`
+    whose `value` is a `SparseTensor`.
+  - if `column` is a `RealValuedColumn`, a feature with `key=column.name`
+    whose `value` is a `Tensor`.
+  - if `feature_columns` is `None`, then `input` must contains only real
+    valued `Tensor`.
 - - -
 
 #### `tf.contrib.learn.DNNRegressor.__init__(hidden_units, feature_columns=None, model_dir=None, weight_column_name=None, optimizer=None, activation_fn=relu, dropout=None, gradient_clip_norm=None, enable_centered_bias=True, config=None)` {#DNNRegressor.__init__}
@@ -1381,17 +1407,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -1424,12 +1453,15 @@ Trains a model given training data `x` predictions and `y` targets.
 *  <b>`input_fn`</b>: Input function. If set, `x`, `y`, and `batch_size` must be
     `None`.
 *  <b>`steps`</b>: Number of steps for which to train model. If `None`, train forever.
+    If set, `max_steps` must be `None`.
 *  <b>`batch_size`</b>: minibatch size to use on the input, defaults to first
     dimension of `x`. Must be `None` if `input_fn` is provided.
 *  <b>`monitors`</b>: List of `BaseMonitor` subclass instances. Used for callbacks
     inside the training loop.
 *  <b>`max_steps`</b>: Number of total steps for which to train model. If `None`,
-    train forever. Two calls to `fit(steps=100)` means 200 training
+    train forever. If set, `steps` must be `None`.
+
+    Two calls to `fit(steps=100)` means 200 training
     iterations. On the other hand, two calls to `fit(max_steps=100)` means
     that the second call will not do any iteration since first call did
     all 100 steps.
@@ -1442,8 +1474,6 @@ Trains a model given training data `x` predictions and `y` targets.
 
 
 *  <b>`ValueError`</b>: If `x` or `y` are not `None` while `input_fn` is not `None`.
-*  <b>`ValueError`</b>: If at least one of `x` and `y` is provided, and `input_fn` is
-      provided.
 *  <b>`ValueError`</b>: If both `steps` and `max_steps` are not `None`.
 
 
@@ -1457,7 +1487,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -1673,17 +1704,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -1714,7 +1748,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -1938,17 +1973,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -1979,7 +2017,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -2164,10 +2203,15 @@ Initializes a TensorFlowEstimator instance.
     Instead, a customized decay function can be passed that accepts
     global_step as parameter and returns a Tensor.
     e.g. exponential decay function:
+
+    ````python
     def exp_decay(global_step):
         return tf.train.exponential_decay(
             learning_rate=0.1, global_step,
             decay_steps=2, decay_rate=0.001)
+    ````
+
+
 *  <b>`clip_gradients`</b>: Clip norm of the gradients to this value to stop
     gradient explosion.
 *  <b>`class_weight`</b>: None or list of n_classes floats. Weight associated with
@@ -2178,9 +2222,10 @@ Initializes a TensorFlowEstimator instance.
 *  <b>`config`</b>: RunConfig object that controls the configurations of the
     session, e.g. num_cores, gpu_memory_fraction, etc.
 *  <b>`verbose`</b>: Controls the verbosity, possible values:
-    0: the algorithm and debug information is muted.
-    1: trainer prints the progress.
-    2: log device placement is printed.
+
+    * 0: the algorithm and debug information is muted.
+    * 1: trainer prints the progress.
+    * 2: log device placement is printed.
 
 
 - - -
@@ -2234,7 +2279,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -2485,15 +2531,16 @@ estimator.predict(x=x)
 
 Input of `fit` and `evaluate` should have following features,
   otherwise there will be a `KeyError`:
-    if `weight_column_name` is not `None`, a feature with
-      `key=weight_column_name` whose value is a `Tensor`.
-    for each `column` in `feature_columns`:
-    - if `column` is a `SparseColumn`, a feature with `key=column.name`
-      whose `value` is a `SparseTensor`.
-    - if `column` is a `RealValuedColumn, a feature with `key=column.name`
-      whose `value` is a `Tensor`.
-    - if `feauture_columns` is `None`, then `input` must contains only real
-      valued `Tensor`.
+
+* if `weight_column_name` is not `None`, a feature with
+  `key=weight_column_name` whose value is a `Tensor`.
+* for each `column` in `feature_columns`:
+  - if `column` is a `SparseColumn`, a feature with `key=column.name`
+    whose `value` is a `SparseTensor`.
+  - if `column` is a `RealValuedColumn`, a feature with `key=column.name`
+    whose `value` is a `Tensor`.
+  - if `feature_columns` is `None`, then `input` must contains only real
+    valued `Tensor`.
 - - -
 
 #### `tf.contrib.learn.LinearClassifier.__init__(feature_columns=None, model_dir=None, n_classes=2, weight_column_name=None, optimizer=None, gradient_clip_norm=None, enable_centered_bias=True, config=None)` {#LinearClassifier.__init__}
@@ -2579,17 +2626,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -2622,12 +2672,15 @@ Trains a model given training data `x` predictions and `y` targets.
 *  <b>`input_fn`</b>: Input function. If set, `x`, `y`, and `batch_size` must be
     `None`.
 *  <b>`steps`</b>: Number of steps for which to train model. If `None`, train forever.
+    If set, `max_steps` must be `None`.
 *  <b>`batch_size`</b>: minibatch size to use on the input, defaults to first
     dimension of `x`. Must be `None` if `input_fn` is provided.
 *  <b>`monitors`</b>: List of `BaseMonitor` subclass instances. Used for callbacks
     inside the training loop.
 *  <b>`max_steps`</b>: Number of total steps for which to train model. If `None`,
-    train forever. Two calls to `fit(steps=100)` means 200 training
+    train forever. If set, `steps` must be `None`.
+
+    Two calls to `fit(steps=100)` means 200 training
     iterations. On the other hand, two calls to `fit(max_steps=100)` means
     that the second call will not do any iteration since first call did
     all 100 steps.
@@ -2640,8 +2693,6 @@ Trains a model given training data `x` predictions and `y` targets.
 
 
 *  <b>`ValueError`</b>: If `x` or `y` are not `None` while `input_fn` is not `None`.
-*  <b>`ValueError`</b>: If at least one of `x` and `y` is provided, and `input_fn` is
-      provided.
 *  <b>`ValueError`</b>: If both `steps` and `max_steps` are not `None`.
 
 
@@ -2655,7 +2706,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -2860,15 +2912,16 @@ estimator.predict(x=x)
 
 Input of `fit` and `evaluate` should have following features,
   otherwise there will be a KeyError:
-    if `weight_column_name` is not `None`:
-      key=weight_column_name, value=a `Tensor`
-    for column in `feature_columns`:
-    - if isinstance(column, `SparseColumn`):
-        key=column.name, value=a `SparseTensor`
-    - if isinstance(column, `RealValuedColumn`):
-        key=column.name, value=a `Tensor`
-    - if `feauture_columns` is `None`:
-        input must contains only real valued `Tensor`.
+
+* if `weight_column_name` is not `None`:
+  key=weight_column_name, value=a `Tensor`
+* for column in `feature_columns`:
+  - if isinstance(column, `SparseColumn`):
+      key=column.name, value=a `SparseTensor`
+  - if isinstance(column, `RealValuedColumn`):
+      key=column.name, value=a `Tensor`
+  - if `feature_columns` is `None`:
+      input must contains only real valued `Tensor`.
 - - -
 
 #### `tf.contrib.learn.LinearRegressor.__init__(feature_columns=None, model_dir=None, weight_column_name=None, optimizer=None, gradient_clip_norm=None, enable_centered_bias=True, target_dimension=1, config=None)` {#LinearRegressor.__init__}
@@ -2953,17 +3006,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -2996,12 +3052,15 @@ Trains a model given training data `x` predictions and `y` targets.
 *  <b>`input_fn`</b>: Input function. If set, `x`, `y`, and `batch_size` must be
     `None`.
 *  <b>`steps`</b>: Number of steps for which to train model. If `None`, train forever.
+    If set, `max_steps` must be `None`.
 *  <b>`batch_size`</b>: minibatch size to use on the input, defaults to first
     dimension of `x`. Must be `None` if `input_fn` is provided.
 *  <b>`monitors`</b>: List of `BaseMonitor` subclass instances. Used for callbacks
     inside the training loop.
 *  <b>`max_steps`</b>: Number of total steps for which to train model. If `None`,
-    train forever. Two calls to `fit(steps=100)` means 200 training
+    train forever. If set, `steps` must be `None`.
+
+    Two calls to `fit(steps=100)` means 200 training
     iterations. On the other hand, two calls to `fit(max_steps=100)` means
     that the second call will not do any iteration since first call did
     all 100 steps.
@@ -3014,8 +3073,6 @@ Trains a model given training data `x` predictions and `y` targets.
 
 
 *  <b>`ValueError`</b>: If `x` or `y` are not `None` while `input_fn` is not `None`.
-*  <b>`ValueError`</b>: If at least one of `x` and `y` is provided, and `input_fn` is
-      provided.
 *  <b>`ValueError`</b>: If both `steps` and `max_steps` are not `None`.
 
 
@@ -3029,7 +3086,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -3245,17 +3303,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -3286,7 +3347,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -3510,17 +3572,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -3551,7 +3616,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -3750,10 +3816,15 @@ Initializes a TensorFlowRNNClassifier instance.
     used. Instead, a customized decay function can be passed that accepts
     global_step as parameter and returns a Tensor.
     e.g. exponential decay function:
+
+    ````python
     def exp_decay(global_step):
         return tf.train.exponential_decay(
             learning_rate=0.1, global_step,
             decay_steps=2, decay_rate=0.001)
+    ````
+
+
 *  <b>`class_weight`</b>: None or list of n_classes floats. Weight associated with
     classes for loss computation. If not given, all classes are
     supposed to have weight one.
@@ -3821,7 +3892,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -4065,18 +4137,24 @@ Initializes a TensorFlowRNNRegressor instance.
     used. Instead, a customized decay function can be passed that accepts
     global_step as parameter and returns a Tensor.
     e.g. exponential decay function:
+
+    ````python
     def exp_decay(global_step):
         return tf.train.exponential_decay(
             learning_rate=0.1, global_step,
             decay_steps=2, decay_rate=0.001)
+    ````
+
+
 *  <b>`continue_training`</b>: when continue_training is True, once initialized
     model will be continuely trained on every call of fit.
 *  <b>`config`</b>: RunConfig object that controls the configurations of the
     session, e.g. num_cores, gpu_memory_fraction, etc.
 *  <b>`verbose`</b>: Controls the verbosity, possible values:
-    0: the algorithm and debug information is muted.
-    1: trainer prints the progress.
-    2: log device placement is printed.
+
+    * 0: the algorithm and debug information is muted.
+    * 1: trainer prints the progress.
+    * 2: log device placement is printed.
 
 
 - - -
@@ -4137,7 +4215,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
@@ -4407,17 +4486,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -4448,7 +4530,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard0/tf.contrib.learn.LinearRegressor.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard0/tf.contrib.learn.LinearRegressor.md
index f18bc58148..ef0b2ac911 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard0/tf.contrib.learn.LinearRegressor.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard0/tf.contrib.learn.LinearRegressor.md
@@ -29,15 +29,16 @@ estimator.predict(x=x)
 
 Input of `fit` and `evaluate` should have following features,
   otherwise there will be a KeyError:
-    if `weight_column_name` is not `None`:
-      key=weight_column_name, value=a `Tensor`
-    for column in `feature_columns`:
-    - if isinstance(column, `SparseColumn`):
-        key=column.name, value=a `SparseTensor`
-    - if isinstance(column, `RealValuedColumn`):
-        key=column.name, value=a `Tensor`
-    - if `feauture_columns` is `None`:
-        input must contains only real valued `Tensor`.
+
+* if `weight_column_name` is not `None`:
+  key=weight_column_name, value=a `Tensor`
+* for column in `feature_columns`:
+  - if isinstance(column, `SparseColumn`):
+      key=column.name, value=a `SparseTensor`
+  - if isinstance(column, `RealValuedColumn`):
+      key=column.name, value=a `Tensor`
+  - if `feature_columns` is `None`:
+      input must contains only real valued `Tensor`.
 - - -
 
 #### `tf.contrib.learn.LinearRegressor.__init__(feature_columns=None, model_dir=None, weight_column_name=None, optimizer=None, gradient_clip_norm=None, enable_centered_bias=True, target_dimension=1, config=None)` {#LinearRegressor.__init__}
@@ -122,17 +123,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -165,12 +169,15 @@ Trains a model given training data `x` predictions and `y` targets.
 *  <b>`input_fn`</b>: Input function. If set, `x`, `y`, and `batch_size` must be
     `None`.
 *  <b>`steps`</b>: Number of steps for which to train model. If `None`, train forever.
+    If set, `max_steps` must be `None`.
 *  <b>`batch_size`</b>: minibatch size to use on the input, defaults to first
     dimension of `x`. Must be `None` if `input_fn` is provided.
 *  <b>`monitors`</b>: List of `BaseMonitor` subclass instances. Used for callbacks
     inside the training loop.
 *  <b>`max_steps`</b>: Number of total steps for which to train model. If `None`,
-    train forever. Two calls to `fit(steps=100)` means 200 training
+    train forever. If set, `steps` must be `None`.
+
+    Two calls to `fit(steps=100)` means 200 training
     iterations. On the other hand, two calls to `fit(max_steps=100)` means
     that the second call will not do any iteration since first call did
     all 100 steps.
@@ -183,8 +190,6 @@ Trains a model given training data `x` predictions and `y` targets.
 
 
 *  <b>`ValueError`</b>: If `x` or `y` are not `None` while `input_fn` is not `None`.
-*  <b>`ValueError`</b>: If at least one of `x` and `y` is provided, and `input_fn` is
-      provided.
 *  <b>`ValueError`</b>: If both `steps` and `max_steps` are not `None`.
 
 
@@ -198,7 +203,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard1/tf.contrib.learn.LinearClassifier.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard1/tf.contrib.learn.LinearClassifier.md
index b713b3e540..ad35103946 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard1/tf.contrib.learn.LinearClassifier.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard1/tf.contrib.learn.LinearClassifier.md
@@ -46,15 +46,16 @@ estimator.predict(x=x)
 
 Input of `fit` and `evaluate` should have following features,
   otherwise there will be a `KeyError`:
-    if `weight_column_name` is not `None`, a feature with
-      `key=weight_column_name` whose value is a `Tensor`.
-    for each `column` in `feature_columns`:
-    - if `column` is a `SparseColumn`, a feature with `key=column.name`
-      whose `value` is a `SparseTensor`.
-    - if `column` is a `RealValuedColumn, a feature with `key=column.name`
-      whose `value` is a `Tensor`.
-    - if `feauture_columns` is `None`, then `input` must contains only real
-      valued `Tensor`.
+
+* if `weight_column_name` is not `None`, a feature with
+  `key=weight_column_name` whose value is a `Tensor`.
+* for each `column` in `feature_columns`:
+  - if `column` is a `SparseColumn`, a feature with `key=column.name`
+    whose `value` is a `SparseTensor`.
+  - if `column` is a `RealValuedColumn`, a feature with `key=column.name`
+    whose `value` is a `Tensor`.
+  - if `feature_columns` is `None`, then `input` must contains only real
+    valued `Tensor`.
 - - -
 
 #### `tf.contrib.learn.LinearClassifier.__init__(feature_columns=None, model_dir=None, n_classes=2, weight_column_name=None, optimizer=None, gradient_clip_norm=None, enable_centered_bias=True, config=None)` {#LinearClassifier.__init__}
@@ -140,17 +141,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -183,12 +187,15 @@ Trains a model given training data `x` predictions and `y` targets.
 *  <b>`input_fn`</b>: Input function. If set, `x`, `y`, and `batch_size` must be
     `None`.
 *  <b>`steps`</b>: Number of steps for which to train model. If `None`, train forever.
+    If set, `max_steps` must be `None`.
 *  <b>`batch_size`</b>: minibatch size to use on the input, defaults to first
     dimension of `x`. Must be `None` if `input_fn` is provided.
 *  <b>`monitors`</b>: List of `BaseMonitor` subclass instances. Used for callbacks
     inside the training loop.
 *  <b>`max_steps`</b>: Number of total steps for which to train model. If `None`,
-    train forever. Two calls to `fit(steps=100)` means 200 training
+    train forever. If set, `steps` must be `None`.
+
+    Two calls to `fit(steps=100)` means 200 training
     iterations. On the other hand, two calls to `fit(max_steps=100)` means
     that the second call will not do any iteration since first call did
     all 100 steps.
@@ -201,8 +208,6 @@ Trains a model given training data `x` predictions and `y` targets.
 
 
 *  <b>`ValueError`</b>: If `x` or `y` are not `None` while `input_fn` is not `None`.
-*  <b>`ValueError`</b>: If at least one of `x` and `y` is provided, and `input_fn` is
-      provided.
 *  <b>`ValueError`</b>: If both `steps` and `max_steps` are not `None`.
 
 
@@ -216,7 +221,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard2/tf.contrib.learn.BaseEstimator.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard2/tf.contrib.learn.BaseEstimator.md
index b7dc1ae13a..1e20e716f7 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard2/tf.contrib.learn.BaseEstimator.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard2/tf.contrib.learn.BaseEstimator.md
@@ -1,6 +1,7 @@
 Abstract BaseEstimator class to train and evaluate TensorFlow models.
 
-Concrete implementation of this class should provide following functions:
+Concrete implementation of this class should provide the following functions:
+
   * _get_train_ops
   * _get_eval_ops
   * _get_predict_ops
@@ -50,17 +51,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -93,12 +97,15 @@ Trains a model given training data `x` predictions and `y` targets.
 *  <b>`input_fn`</b>: Input function. If set, `x`, `y`, and `batch_size` must be
     `None`.
 *  <b>`steps`</b>: Number of steps for which to train model. If `None`, train forever.
+    If set, `max_steps` must be `None`.
 *  <b>`batch_size`</b>: minibatch size to use on the input, defaults to first
     dimension of `x`. Must be `None` if `input_fn` is provided.
 *  <b>`monitors`</b>: List of `BaseMonitor` subclass instances. Used for callbacks
     inside the training loop.
 *  <b>`max_steps`</b>: Number of total steps for which to train model. If `None`,
-    train forever. Two calls to `fit(steps=100)` means 200 training
+    train forever. If set, `steps` must be `None`.
+
+    Two calls to `fit(steps=100)` means 200 training
     iterations. On the other hand, two calls to `fit(max_steps=100)` means
     that the second call will not do any iteration since first call did
     all 100 steps.
@@ -111,8 +118,6 @@ Trains a model given training data `x` predictions and `y` targets.
 
 
 *  <b>`ValueError`</b>: If `x` or `y` are not `None` while `input_fn` is not `None`.
-*  <b>`ValueError`</b>: If at least one of `x` and `y` is provided, and `input_fn` is
-      provided.
 *  <b>`ValueError`</b>: If both `steps` and `max_steps` are not `None`.
 
 
@@ -126,7 +131,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard2/tf.contrib.learn.TensorFlowDNNRegressor.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard2/tf.contrib.learn.TensorFlowDNNRegressor.md
index 62e711269f..bdd7af5190 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard2/tf.contrib.learn.TensorFlowDNNRegressor.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard2/tf.contrib.learn.TensorFlowDNNRegressor.md
@@ -58,17 +58,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -99,7 +102,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard3/tf.contrib.learn.Estimator.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard3/tf.contrib.learn.Estimator.md
index 23ee632fc7..9341a349b2 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard3/tf.contrib.learn.Estimator.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard3/tf.contrib.learn.Estimator.md
@@ -11,20 +11,24 @@ Constructs an Estimator instance.
 *  <b>`model_fn`</b>: Model function, takes features and targets tensors or dicts of
             tensors and returns predictions and loss tensors.
             Supports next three signatures for the function:
-              * `(features, targets) -> (predictions, loss, train_op)`
-              * `(features, targets, mode) -> (predictions, loss, train_op)`
-              * `(features, targets, mode, params) ->
-                  (predictions, loss, train_op)`
-*  <b>`Where`</b>: 
-              * `features` are single `Tensor` or `dict` of `Tensor`s
-                   (depending on data passed to `fit`),
-              * `targets` are `Tensor` or
-                  `dict` of `Tensor`s (for multi-head model).
-              * `mode` represents if this training, evaluation or
-                  prediction. See `ModeKeys` for example keys.
-              * `params` is a `dict` of hyperparameters. Will receive what
-                  is passed to Estimator in `params` parameter. This allows
-                  to configure Estimators from hyper parameter tunning.
+
+      * `(features, targets) -> (predictions, loss, train_op)`
+      * `(features, targets, mode) -> (predictions, loss, train_op)`
+      * `(features, targets, mode, params) -> (predictions, loss, train_op)`
+
+  Where
+
+      * `features` are single `Tensor` or `dict` of `Tensor`s
+             (depending on data passed to `fit`),
+      * `targets` are `Tensor` or
+             `dict` of `Tensor`s (for multi-head model).
+      * `mode` represents if this training, evaluation or
+             prediction. See `ModeKeys` for example keys.
+      * `params` is a `dict` of hyperparameters. Will receive what
+             is passed to Estimator in `params` parameter. This allows
+             to configure Estimators from hyper parameter tunning.
+
+
 *  <b>`model_dir`</b>: Directory to save model parameters, graph and etc.
 *  <b>`config`</b>: Configuration object.
 *  <b>`params`</b>: `dict` of hyper parameters that will be passed into `model_fn`.
@@ -67,17 +71,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -110,12 +117,15 @@ Trains a model given training data `x` predictions and `y` targets.
 *  <b>`input_fn`</b>: Input function. If set, `x`, `y`, and `batch_size` must be
     `None`.
 *  <b>`steps`</b>: Number of steps for which to train model. If `None`, train forever.
+    If set, `max_steps` must be `None`.
 *  <b>`batch_size`</b>: minibatch size to use on the input, defaults to first
     dimension of `x`. Must be `None` if `input_fn` is provided.
 *  <b>`monitors`</b>: List of `BaseMonitor` subclass instances. Used for callbacks
     inside the training loop.
 *  <b>`max_steps`</b>: Number of total steps for which to train model. If `None`,
-    train forever. Two calls to `fit(steps=100)` means 200 training
+    train forever. If set, `steps` must be `None`.
+
+    Two calls to `fit(steps=100)` means 200 training
     iterations. On the other hand, two calls to `fit(max_steps=100)` means
     that the second call will not do any iteration since first call did
     all 100 steps.
@@ -128,8 +138,6 @@ Trains a model given training data `x` predictions and `y` targets.
 
 
 *  <b>`ValueError`</b>: If `x` or `y` are not `None` while `input_fn` is not `None`.
-*  <b>`ValueError`</b>: If at least one of `x` and `y` is provided, and `input_fn` is
-      provided.
 *  <b>`ValueError`</b>: If both `steps` and `max_steps` are not `None`.
 
 
@@ -143,7 +151,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.DNNClassifier.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.DNNClassifier.md
index 038d895909..035c173e27 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.DNNClassifier.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.DNNClassifier.md
@@ -40,15 +40,16 @@ estimator.predict(x=x)
 
 Input of `fit` and `evaluate` should have following features,
   otherwise there will be a `KeyError`:
-    if `weight_column_name` is not `None`, a feature with
-      `key=weight_column_name` whose value is a `Tensor`.
-    for each `column` in `feature_columns`:
-    - if `column` is a `SparseColumn`, a feature with `key=column.name`
-      whose `value` is a `SparseTensor`.
-    - if `column` is a `RealValuedColumn, a feature with `key=column.name`
-      whose `value` is a `Tensor`.
-    - if `feauture_columns` is `None`, then `input` must contains only real
-      valued `Tensor`.
+
+* if `weight_column_name` is not `None`, a feature with
+   `key=weight_column_name` whose value is a `Tensor`.
+* for each `column` in `feature_columns`:
+  - if `column` is a `SparseColumn`, a feature with `key=column.name`
+    whose `value` is a `SparseTensor`.
+  - if `column` is a `RealValuedColumn`, a feature with `key=column.name`
+    whose `value` is a `Tensor`.
+  - if `feature_columns` is `None`, then `input` must contains only real
+    valued `Tensor`.
 - - -
 
 #### `tf.contrib.learn.DNNClassifier.__init__(hidden_units, feature_columns=None, model_dir=None, n_classes=2, weight_column_name=None, optimizer=None, activation_fn=relu, dropout=None, gradient_clip_norm=None, enable_centered_bias=True, config=None)` {#DNNClassifier.__init__}
@@ -141,17 +142,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -184,12 +188,15 @@ Trains a model given training data `x` predictions and `y` targets.
 *  <b>`input_fn`</b>: Input function. If set, `x`, `y`, and `batch_size` must be
     `None`.
 *  <b>`steps`</b>: Number of steps for which to train model. If `None`, train forever.
+    If set, `max_steps` must be `None`.
 *  <b>`batch_size`</b>: minibatch size to use on the input, defaults to first
     dimension of `x`. Must be `None` if `input_fn` is provided.
 *  <b>`monitors`</b>: List of `BaseMonitor` subclass instances. Used for callbacks
     inside the training loop.
 *  <b>`max_steps`</b>: Number of total steps for which to train model. If `None`,
-    train forever. Two calls to `fit(steps=100)` means 200 training
+    train forever. If set, `steps` must be `None`.
+
+    Two calls to `fit(steps=100)` means 200 training
     iterations. On the other hand, two calls to `fit(max_steps=100)` means
     that the second call will not do any iteration since first call did
     all 100 steps.
@@ -202,8 +209,6 @@ Trains a model given training data `x` predictions and `y` targets.
 
 
 *  <b>`ValueError`</b>: If `x` or `y` are not `None` while `input_fn` is not `None`.
-*  <b>`ValueError`</b>: If at least one of `x` and `y` is provided, and `input_fn` is
-      provided.
 *  <b>`ValueError`</b>: If both `steps` and `max_steps` are not `None`.
 
 
@@ -217,7 +222,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.TensorFlowEstimator.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.TensorFlowEstimator.md
index 6d38364147..f1d3f9dee1 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.TensorFlowEstimator.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.TensorFlowEstimator.md
@@ -19,10 +19,15 @@ Initializes a TensorFlowEstimator instance.
     Instead, a customized decay function can be passed that accepts
     global_step as parameter and returns a Tensor.
     e.g. exponential decay function:
+
+    ````python
     def exp_decay(global_step):
         return tf.train.exponential_decay(
             learning_rate=0.1, global_step,
             decay_steps=2, decay_rate=0.001)
+    ````
+
+
 *  <b>`clip_gradients`</b>: Clip norm of the gradients to this value to stop
     gradient explosion.
 *  <b>`class_weight`</b>: None or list of n_classes floats. Weight associated with
@@ -33,9 +38,10 @@ Initializes a TensorFlowEstimator instance.
 *  <b>`config`</b>: RunConfig object that controls the configurations of the
     session, e.g. num_cores, gpu_memory_fraction, etc.
 *  <b>`verbose`</b>: Controls the verbosity, possible values:
-    0: the algorithm and debug information is muted.
-    1: trainer prints the progress.
-    2: log device placement is printed.
+
+    * 0: the algorithm and debug information is muted.
+    * 1: trainer prints the progress.
+    * 2: log device placement is printed.
 
 
 - - -
@@ -89,7 +95,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.TensorFlowLinearClassifier.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.TensorFlowLinearClassifier.md
index fc2ea1f247..5a61e00629 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.TensorFlowLinearClassifier.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.TensorFlowLinearClassifier.md
@@ -58,17 +58,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -99,7 +102,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.TensorFlowRNNRegressor.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.TensorFlowRNNRegressor.md
index 0a6694151f..2ca01c154e 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.TensorFlowRNNRegressor.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard4/tf.contrib.learn.TensorFlowRNNRegressor.md
@@ -32,18 +32,24 @@ Initializes a TensorFlowRNNRegressor instance.
     used. Instead, a customized decay function can be passed that accepts
     global_step as parameter and returns a Tensor.
     e.g. exponential decay function:
+
+    ````python
     def exp_decay(global_step):
         return tf.train.exponential_decay(
             learning_rate=0.1, global_step,
             decay_steps=2, decay_rate=0.001)
+    ````
+
+
 *  <b>`continue_training`</b>: when continue_training is True, once initialized
     model will be continuely trained on every call of fit.
 *  <b>`config`</b>: RunConfig object that controls the configurations of the
     session, e.g. num_cores, gpu_memory_fraction, etc.
 *  <b>`verbose`</b>: Controls the verbosity, possible values:
-    0: the algorithm and debug information is muted.
-    1: trainer prints the progress.
-    2: log device placement is printed.
+
+    * 0: the algorithm and debug information is muted.
+    * 1: trainer prints the progress.
+    * 2: log device placement is printed.
 
 
 - - -
@@ -104,7 +110,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard5/tf.contrib.learn.TensorFlowDNNClassifier.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard5/tf.contrib.learn.TensorFlowDNNClassifier.md
index aa3c622a1a..9f977f2d2d 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard5/tf.contrib.learn.TensorFlowDNNClassifier.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard5/tf.contrib.learn.TensorFlowDNNClassifier.md
@@ -58,17 +58,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -99,7 +102,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard7/tf.contrib.learn.TensorFlowClassifier.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard7/tf.contrib.learn.TensorFlowClassifier.md
index f9b6c72293..0b18ffa933 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard7/tf.contrib.learn.TensorFlowClassifier.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard7/tf.contrib.learn.TensorFlowClassifier.md
@@ -58,17 +58,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -99,7 +102,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard8/tf.contrib.learn.TensorFlowRegressor.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard8/tf.contrib.learn.TensorFlowRegressor.md
index 7dc7a3c12e..998e068383 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard8/tf.contrib.learn.TensorFlowRegressor.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard8/tf.contrib.learn.TensorFlowRegressor.md
@@ -58,17 +58,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -99,7 +102,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.learn.DNNRegressor.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.learn.DNNRegressor.md
index 8b25a23ded..740a20fa1c 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.learn.DNNRegressor.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.learn.DNNRegressor.md
@@ -40,15 +40,16 @@ estimator.predict(x=x)
 
 Input of `fit` and `evaluate` should have following features,
   otherwise there will be a `KeyError`:
-    if `weight_column_name` is not `None`, a feature with
-      `key=weight_column_name` whose value is a `Tensor`.
-    for each `column` in `feature_columns`:
-    - if `column` is a `SparseColumn`, a feature with `key=column.name`
-      whose `value` is a `SparseTensor`.
-    - if `column` is a `RealValuedColumn, a feature with `key=column.name`
-      whose `value` is a `Tensor`.
-    - if `feauture_columns` is `None`, then `input` must contains only real
-      valued `Tensor`.
+
+* if `weight_column_name` is not `None`, a feature with
+  `key=weight_column_name` whose value is a `Tensor`.
+* for each `column` in `feature_columns`:
+  - if `column` is a `SparseColumn`, a feature with `key=column.name`
+    whose `value` is a `SparseTensor`.
+  - if `column` is a `RealValuedColumn`, a feature with `key=column.name`
+    whose `value` is a `Tensor`.
+  - if `feature_columns` is `None`, then `input` must contains only real
+    valued `Tensor`.
 - - -
 
 #### `tf.contrib.learn.DNNRegressor.__init__(hidden_units, feature_columns=None, model_dir=None, weight_column_name=None, optimizer=None, activation_fn=relu, dropout=None, gradient_clip_norm=None, enable_centered_bias=True, config=None)` {#DNNRegressor.__init__}
@@ -139,17 +140,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -182,12 +186,15 @@ Trains a model given training data `x` predictions and `y` targets.
 *  <b>`input_fn`</b>: Input function. If set, `x`, `y`, and `batch_size` must be
     `None`.
 *  <b>`steps`</b>: Number of steps for which to train model. If `None`, train forever.
+    If set, `max_steps` must be `None`.
 *  <b>`batch_size`</b>: minibatch size to use on the input, defaults to first
     dimension of `x`. Must be `None` if `input_fn` is provided.
 *  <b>`monitors`</b>: List of `BaseMonitor` subclass instances. Used for callbacks
     inside the training loop.
 *  <b>`max_steps`</b>: Number of total steps for which to train model. If `None`,
-    train forever. Two calls to `fit(steps=100)` means 200 training
+    train forever. If set, `steps` must be `None`.
+
+    Two calls to `fit(steps=100)` means 200 training
     iterations. On the other hand, two calls to `fit(max_steps=100)` means
     that the second call will not do any iteration since first call did
     all 100 steps.
@@ -200,8 +207,6 @@ Trains a model given training data `x` predictions and `y` targets.
 
 
 *  <b>`ValueError`</b>: If `x` or `y` are not `None` while `input_fn` is not `None`.
-*  <b>`ValueError`</b>: If at least one of `x` and `y` is provided, and `input_fn` is
-      provided.
 *  <b>`ValueError`</b>: If both `steps` and `max_steps` are not `None`.
 
 
@@ -215,7 +220,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.learn.TensorFlowLinearRegressor.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.learn.TensorFlowLinearRegressor.md
index ec81239ade..60d6cb7b2f 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.learn.TensorFlowLinearRegressor.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.learn.TensorFlowLinearRegressor.md
@@ -58,17 +58,20 @@ for which this evaluation was performed.
     provided.
 *  <b>`steps`</b>: Number of steps for which to evaluate model. If `None`, evaluate
     until running tensors generated by `metrics` raises an exception.
-*  <b>`metrics`</b>: Dict of metric ops to run. If None, the default metric functions
-    are used; if {}, no metrics are used. If model has one output (i.e.,
-    returning single predction), keys are `str`, e.g. `'accuracy'` - just a
-    name of the metric that will show up in the logs / summaries.
-    Otherwise, keys are tuple of two `str`, e.g. `('accuracy', 'classes')`
-    - name of the metric and name of `Tensor` in the predictions to run
-    this metric on. Metric ops should support streaming, e.g., returning
+*  <b>`metrics`</b>: Dict of metric ops to run. If `None`, the default metric
+    functions are used; if `{}`, no metrics are used. If model has one
+    output (i.e., returning single predction), keys are `str`, e.g.
+    `'accuracy'` - just a name of the metric that will show up in
+    the logs / summaries. Otherwise, keys are tuple of two `str`, e.g.
+    `('accuracy', 'classes')`- name of the metric and name of `Tensor` in
+    the predictions to run this metric on.
+
+    Metric ops should support streaming, e.g., returning
     update_op and value tensors. See more details in
     ../../../../metrics/python/metrics/ops/streaming_metrics.py.
-*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluation on
-    different data sets, such as evaluate on training data vs test data.
+
+*  <b>`name`</b>: Name of the evaluation if user needs to run multiple evaluations on
+    different data sets, such as on training data vs test data.
 
 ##### Returns:
 
@@ -99,7 +102,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.learn.TensorFlowRNNClassifier.md b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.learn.TensorFlowRNNClassifier.md
index 8ec358a6c8..6f81b4ef2c 100644
--- a/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.learn.TensorFlowRNNClassifier.md
+++ b/tensorflow/g3doc/api_docs/python/functions_and_classes/shard9/tf.contrib.learn.TensorFlowRNNClassifier.md
@@ -33,10 +33,15 @@ Initializes a TensorFlowRNNClassifier instance.
     used. Instead, a customized decay function can be passed that accepts
     global_step as parameter and returns a Tensor.
     e.g. exponential decay function:
+
+    ````python
     def exp_decay(global_step):
         return tf.train.exponential_decay(
             learning_rate=0.1, global_step,
             decay_steps=2, decay_rate=0.001)
+    ````
+
+
 *  <b>`class_weight`</b>: None or list of n_classes floats. Weight associated with
     classes for loss computation. If not given, all classes are
     supposed to have weight one.
@@ -104,7 +109,8 @@ Get parameters for this estimator.
 
 
 *  <b>`deep`</b>: boolean, optional
-    If True, will return the parameters for this estimator and
+
+    If `True`, will return the parameters for this estimator and
     contained subobjects that are estimators.
 
 ##### Returns:
diff --git a/tensorflow/python/ops/embedding_ops.py b/tensorflow/python/ops/embedding_ops.py
index 06be27633b..c948eeb6ff 100644
--- a/tensorflow/python/ops/embedding_ops.py
+++ b/tensorflow/python/ops/embedding_ops.py
@@ -73,11 +73,11 @@ def embedding_lookup(params, ids, partition_strategy="mod", name=None,
   Raises:
     ValueError: If `params` is empty.
   """
+  if params is None or params == []:  # pylint: disable=g-explicit-bool-comparison
+    raise ValueError("Need at least one param")
   if not isinstance(params, list):
     params = [params]
   with ops.op_scope(params + [ids], name, "embedding_lookup") as name:
-    if not params:
-      raise ValueError("Need at least one param")
     np = len(params)  # Number of partitions
     params = ops.convert_n_to_tensor_or_indexed_slices(params, name="params")
     if np == 1:
diff --git a/tensorflow/python/ops/image_grad_test.py b/tensorflow/python/ops/image_grad_test.py
index dab9619424..ccbae0f157 100644
--- a/tensorflow/python/ops/image_grad_test.py
+++ b/tensorflow/python/ops/image_grad_test.py
@@ -253,54 +253,53 @@ class CropAndResizeOpTest(tf.test.TestCase):
     radius = 2 * delta
     low, high = -0.5, 1.5  # Also covers the case of extrapolation.
 
-    for image_height in range(1, 5):
-      for image_width in range(1, 3):
-        for crop_height in range(1, 3):
-          for crop_width in range(2, 4):
-            for depth in range(1, 3):
-              for num_boxes in range(1, 3):
-
-                batch = num_boxes
-                image_shape = [batch, image_height, image_width, depth]
-                crop_size = [crop_height, crop_width]
-                crops_shape = [num_boxes, crop_height, crop_width, depth]
-                boxes_shape = [num_boxes, 4]
-
-                image = np.arange(0, batch * image_height * image_width *
-                                  depth).reshape(image_shape).astype(np.float32)
-                boxes = []
-                for _ in range(num_boxes):
-                  # pylint: disable=unbalanced-tuple-unpacking
-                  y1, y2 = self._randomUniformAvoidAnchors(
-                      low, high, np.linspace(0, 1, image_height), radius, 2)
-                  x1, x2 = self._randomUniformAvoidAnchors(
-                      low, high, np.linspace(0, 1, image_width), radius, 2)
-                  # pylint: enable=unbalanced-tuple-unpacking
-                  boxes.append([y1, x1, y2, x2])
-
-                boxes = np.array(boxes, dtype=np.float32)
-                box_ind = np.arange(batch, dtype=np.int32)
-
-                for use_gpu in [False, True]:
-                  with self.test_session(use_gpu=use_gpu):
-                    image_tensor = tf.constant(image, shape=image_shape)
-                    boxes_tensor = tf.constant(boxes, shape=[num_boxes, 4])
-                    box_ind_tensor = tf.constant(box_ind, shape=[num_boxes])
-                    crops = tf.image.crop_and_resize(
-                        image_tensor,
-                        boxes_tensor,
-                        box_ind_tensor,
-                        tf.constant(crop_size, shape=[2]))
-
-                    err = tf.test.compute_gradient_error(
-                        [image_tensor, boxes_tensor],
-                        [image_shape, boxes_shape],
-                        crops,
-                        crops_shape,
-                        delta=delta,
-                        x_init_value=[image, boxes])
-
-                  self.assertLess(err, 2e-3)
+    image_height = 4
+    for image_width in range(1, 3):
+      for crop_height in range(1, 3):
+        for crop_width in range(2, 4):
+          for depth in range(1, 3):
+            for num_boxes in range(1, 3):
+
+              batch = num_boxes
+              image_shape = [batch, image_height, image_width, depth]
+              crop_size = [crop_height, crop_width]
+              crops_shape = [num_boxes, crop_height, crop_width, depth]
+              boxes_shape = [num_boxes, 4]
+
+              image = np.arange(0, batch * image_height * image_width *
+                                depth).reshape(image_shape).astype(np.float32)
+              boxes = []
+              for _ in range(num_boxes):
+                # pylint: disable=unbalanced-tuple-unpacking
+                y1, y2 = self._randomUniformAvoidAnchors(
+                    low, high, np.linspace(0, 1, image_height), radius, 2)
+                x1, x2 = self._randomUniformAvoidAnchors(
+                    low, high, np.linspace(0, 1, image_width), radius, 2)
+                # pylint: enable=unbalanced-tuple-unpacking
+                boxes.append([y1, x1, y2, x2])
+
+              boxes = np.array(boxes, dtype=np.float32)
+              box_ind = np.arange(batch, dtype=np.int32)
+
+              for use_gpu in [False, True]:
+                with self.test_session(use_gpu=use_gpu):
+                  image_tensor = tf.constant(image, shape=image_shape)
+                  boxes_tensor = tf.constant(boxes, shape=[num_boxes, 4])
+                  box_ind_tensor = tf.constant(box_ind, shape=[num_boxes])
+                  crops = tf.image.crop_and_resize(
+                      image_tensor,
+                      boxes_tensor,
+                      box_ind_tensor,
+                      tf.constant(crop_size, shape=[2]))
+
+                  err = tf.test.compute_gradient_error(
+                      [image_tensor, boxes_tensor], [image_shape, boxes_shape],
+                      crops,
+                      crops_shape,
+                      delta=delta,
+                      x_init_value=[image, boxes])
+
+                self.assertLess(err, 2e-3)
 
 
 if __name__ == "__main__":
diff --git a/tensorflow/python/training/moving_averages.py b/tensorflow/python/training/moving_averages.py
index 9cc1d917ab..4bbb89ff89 100644
--- a/tensorflow/python/training/moving_averages.py
+++ b/tensorflow/python/training/moving_averages.py
@@ -339,7 +339,10 @@ class ExponentialMovingAverage(object):
       by the `ExponentialMovingAverage class` to hold the moving average of
       `var`.
     """
-    return var.op.name + "/" + self._name
+    if var in self._averages:
+      return self._averages[var].op.name
+    return ops.get_default_graph().unique_name(
+        var.op.name + "/" + self._name, mark_as_used=False)
 
   def variables_to_restore(self, moving_avg_variables=None):
     """Returns a map of names to `Variables` to restore.
diff --git a/tensorflow/python/training/moving_averages_test.py b/tensorflow/python/training/moving_averages_test.py
index 437f2170fb..413c38e601 100644
--- a/tensorflow/python/training/moving_averages_test.py
+++ b/tensorflow/python/training/moving_averages_test.py
@@ -208,6 +208,37 @@ class ExponentialMovingAverageTest(tf.test.TestCase):
       self.assertEqual(ema.average_name(v1), ema.average(v1).op.name)
       self.assertEqual(ema.average_name(tensor2), ema.average(tensor2).op.name)
 
+  def testAverageVariablesNamesRespectScope(self):
+    # See discussion on #2740.
+    with self.test_session():
+      with tf.variable_scope("scope1"):
+        v0 = tf.Variable(10.0, name="v0")
+        v1 = tf.Variable(30.0, name="v1")
+        # Add a non-trainable variable.
+        v2 = tf.Variable(20.0, name="v2", trainable=False)
+        tensor2 = v0 + v1
+      with tf.variable_scope("scope2"):
+        ema = tf.train.ExponentialMovingAverage(0.25, name="foo_avg")
+        self.assertEqual("scope2/scope1/v0/foo_avg", ema.average_name(v0))
+        self.assertEqual("scope2/scope1/v1/foo_avg", ema.average_name(v1))
+        self.assertEqual("scope2/scope1/add/foo_avg", ema.average_name(tensor2))
+        ema.apply([v0, v1, tensor2])
+        vars_to_restore = ema.variables_to_restore()
+        # vars_to_restore should contain the following:
+        # {scope2/scope1/v0/foo_avg : v0,
+        #  scope2/scope1/v1/foo_avg : v1,
+        #  scope2/scope1/add/foo_avg : add/foo_avg
+        #  scope1/v2 : v2}
+        self.assertEqual(sorted(vars_to_restore.keys()),
+                         sorted([ema.average_name(v0),
+                                 ema.average_name(v1),
+                                 ema.average_name(tensor2),
+                                 v2.op.name]))
+        self.assertEqual(ema.average_name(v0), ema.average(v0).op.name)
+        self.assertEqual(ema.average_name(v1), ema.average(v1).op.name)
+        self.assertEqual(ema.average_name(tensor2),
+                         ema.average(tensor2).op.name)
+
   def testSubsetAverageVariablesNames(self):
     with self.test_session():
       v0 = tf.Variable(10.0, name="v0")
diff --git a/tensorflow/python/training/slot_creator_test.py b/tensorflow/python/training/slot_creator_test.py
index 8a11e44d1e..4e2b980751 100644
--- a/tensorflow/python/training/slot_creator_test.py
+++ b/tensorflow/python/training/slot_creator_test.py
@@ -73,5 +73,13 @@ class SlotCreatorTest(tf.test.TestCase):
       self.assertEqual(slot.dtype.base_dtype, tf.float32)
       self.assertAllEqual(slot.eval(), [0.0, 0.0])
 
+  def testCreateSlotFromVariableRespectsScope(self):
+    # See discussion on #2740.
+    with self.test_session():
+      with tf.variable_scope("scope"):
+        v = tf.Variable([1.0, 2.5], name="var")
+        slot = slot_creator.create_slot(v, v.initialized_value(), name="slot")
+        self.assertEqual(slot.op.name, "scope/scope/var/slot")
+
 if __name__ == "__main__":
   tf.test.main()
diff --git a/tensorflow/python/training/training.py b/tensorflow/python/training/training.py
index e6ae335d94..8135a86021 100644
--- a/tensorflow/python/training/training.py
+++ b/tensorflow/python/training/training.py
@@ -198,7 +198,7 @@ from tensorflow.core.example.feature_pb2 import *
 from tensorflow.core.protobuf.saver_pb2 import *
 
 # Utility op.  Open Source. TODO(touts): move to nn?
-from tensorflow.python.training.learning_rate_decay import exponential_decay
+from tensorflow.python.training.learning_rate_decay import *
 
 
 # Distributed computing support