Merge changes from github.

PiperOrigin-RevId: 192850372

3 files changed, 25 insertions, 27 deletions

diff --git a/tensorflow/contrib/kernel_methods/python/losses.py b/tensorflow/contrib/kernel_methods/python/losses.py
index f182fef067..4ef0a66a52 100644
--- a/tensorflow/contrib/kernel_methods/python/losses.py
+++ b/tensorflow/contrib/kernel_methods/python/losses.py
@@ -43,10 +43,10 @@ def sparse_multiclass_hinge_loss(
 
   This is a generalization of standard (binary) hinge loss. For a given instance
   with correct label c*, the loss is given by:
-    loss = max_{c != c*} logits_c - logits_{c*} + 1.
+    $$loss = max_{c != c*} logits_c - logits_{c*} + 1.$$
   or equivalently
-    loss = max_c { logits_c - logits_{c*} + I_{c != c*} }
-  where I_{c != c*} = 1 if c != c* and 0 otherwise.
+    $$loss = max_c { logits_c - logits_{c*} + I_{c != c*} }$$
+  where \\(I_{c != c*} = 1\ \text{if}\ c != c*\\) and 0 otherwise.
 
   Args:
     labels: `Tensor` of shape [batch_size] or [batch_size, 1]. Corresponds to
diff --git a/tensorflow/contrib/kernel_methods/python/mappers/random_fourier_features.py b/tensorflow/contrib/kernel_methods/python/mappers/random_fourier_features.py
index 9dc01124ab..9a721a9d44 100644
--- a/tensorflow/contrib/kernel_methods/python/mappers/random_fourier_features.py
+++ b/tensorflow/contrib/kernel_methods/python/mappers/random_fourier_features.py
@@ -34,33 +34,31 @@ class RandomFourierFeatureMapper(dkm.DenseKernelMapper):
   r"""Class that implements Random Fourier Feature Mapping (RFFM) in TensorFlow.
 
   The RFFM mapping is used to approximate the Gaussian (RBF) kernel:
-  ```
-  exp(-||x-y||_2^2 / (2 * sigma^2))
-  ```
+  $$(exp(-||x-y||_2^2 / (2 * \sigma^2))$$
 
   The implementation of RFFM is based on the following paper:
   "Random Features for Large-Scale Kernel Machines" by Ali Rahimi and Ben Recht.
   (link: https://people.eecs.berkeley.edu/~brecht/papers/07.rah.rec.nips.pdf)
 
-  The mapping uses a matrix `Omega \in R^{d x D}` and a bias vector `b \in R^D`
-  where `d` is the input dimension (number of dense input features) and `D` is
-  the output dimension (i.e., dimension of the feature space the input is mapped
-  to). Each entry of `Omega` is sampled i.i.d. from a (scaled) Gaussian
-  distribution and each entry of `b` is sampled independently and uniformly from
-  [0, 2 * pi].
-
-  For a single input feature vector x in R^d, its RFFM is defined as:
-  ```
-      sqrt(2/D) * cos(x * Omega + b)
-  ```
-  where `cos` is the element-wise cosine function and `x, b` are represented as
-  row vectors. The aforementioned paper shows that the linear kernel of
-  RFFM-mapped vectors approximates the Gaussian kernel of the initial vectors.
+  The mapping uses a matrix \\(\Omega \in R^{d x D}\\) and a bias vector
+  \\(b \in R^D\\) where \\(d\\) is the input dimension (number of dense input
+  features) and \\(D\\) is the output dimension (i.e., dimension of the feature
+  space the input is mapped to). Each entry of \\(\Omega\\) is sampled i.i.d.
+  from a (scaled) Gaussian distribution and each entry of \\(b\\) is sampled
+  independently and uniformly from [0, \\(2 * \pi\\)].
+
+  For a single input feature vector \\(x \in R^d\\), its RFFM is defined as:
+  $$\sqrt(2/D) * cos(x * \Omega + b)$$
+
+  where \\(cos\\) is the element-wise cosine function and \\(x, b\\) are
+  represented as row vectors. The aforementioned paper shows that the linear
+  kernel of RFFM-mapped vectors approximates the Gaussian kernel of the initial
+  vectors.
 
   """
 
   def __init__(self, input_dim, output_dim, stddev=1.0, seed=1, name=None):
-    """Constructs a RandomFourierFeatureMapper instance.
+    r"""Constructs a RandomFourierFeatureMapper instance.
 
     Args:
       input_dim: The dimension (number of features) of the tensors to be mapped.
@@ -68,11 +66,11 @@ class RandomFourierFeatureMapper(dkm.DenseKernelMapper):
       stddev: The standard deviation of the Gaussian kernel to be approximated.
         The error of the classifier trained using this approximation is very
         sensitive to this parameter.
-      seed: An integer used to initialize the parameters (`Omega` and `b`) of
-        the mapper. For repeatable sequences across different invocations of the
-        mapper object (for instance, to ensure consistent mapping both at
-        training and eval/inference if these happen in different invocations),
-        set this to the same integer.
+      seed: An integer used to initialize the parameters (\\(\Omega\\) and
+        \\(b\\)) of the mapper. For repeatable sequences across different
+        invocations of the mapper object (for instance, to ensure consistent
+        mapping both at training and eval/inference if these happen in
+        different invocations), set this to the same integer.
       name: name for the mapper object.
     """
     # TODO(sibyl-vie3Poto): Maybe infer input_dim and/or output_dim (if not explicitly
diff --git a/tensorflow/contrib/kernel_methods/python/mappers/random_fourier_features_test.py b/tensorflow/contrib/kernel_methods/python/mappers/random_fourier_features_test.py
index 6f4a264485..91929184a2 100644
--- a/tensorflow/contrib/kernel_methods/python/mappers/random_fourier_features_test.py
+++ b/tensorflow/contrib/kernel_methods/python/mappers/random_fourier_features_test.py
@@ -34,7 +34,7 @@ def _inner_product(x, y):
   """Inner product between tensors x and y.
 
   The input tensors are assumed to be in ROW representation, that is, the method
-  returns x * y^T.
+  returns \\(x * y^T\\).
 
   Args:
     x: input tensor in row format