Merge changes from github.

PiperOrigin-RevId: 203037623

21 files changed, 82 insertions, 50 deletions

diff --git a/tensorflow/core/api_def/base_api/api_def_GatherNd.pbtxt b/tensorflow/core/api_def/base_api/api_def_GatherNd.pbtxt
index 6cd76ff340..342a1f6b05 100644
--- a/tensorflow/core/api_def/base_api/api_def_GatherNd.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_GatherNd.pbtxt
@@ -25,7 +25,7 @@ END
 (K-1)-dimensional tensor of indices into `params`, where each element defines a
 slice of `params`:
 
-    output[i_0, ..., i_{K-2}] = params[indices[i0, ..., i_{K-2}]]
+    output[\\(i_0, ..., i_{K-2}\\)] = params[indices[\\(i_0, ..., i_{K-2}\\)]]
 
 Whereas in @{tf.gather} `indices` defines slices into the first
 dimension of `params`, in `tf.gather_nd`, `indices` defines slices into the
diff --git a/tensorflow/core/api_def/base_api/api_def_LinSpace.pbtxt b/tensorflow/core/api_def/base_api/api_def_LinSpace.pbtxt
index 94a4ef574d..f706810662 100644
--- a/tensorflow/core/api_def/base_api/api_def_LinSpace.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_LinSpace.pbtxt
@@ -3,19 +3,19 @@ op {
   in_arg {
     name: "start"
     description: <<END
-First entry in the range.
+0-D tensor. First entry in the range.
 END
   }
   in_arg {
     name: "stop"
     description: <<END
-Last entry in the range.
+0-D tensor. Last entry in the range.
 END
   }
   in_arg {
     name: "num"
     description: <<END
-Number of values to generate.
+0-D tensor. Number of values to generate.
 END
   }
   out_arg {
diff --git a/tensorflow/core/api_def/base_api/api_def_MatrixExponential.pbtxt b/tensorflow/core/api_def/base_api/api_def_MatrixExponential.pbtxt
index 0d680f6531..d7b56aec87 100644
--- a/tensorflow/core/api_def/base_api/api_def_MatrixExponential.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_MatrixExponential.pbtxt
@@ -18,7 +18,7 @@ END
   }
   summary: "Computes the matrix exponential of one or more square matrices:"
   description: <<END
-exp(A) = \sum_{n=0}^\infty A^n/n!
+\\(exp(A) = \sum_{n=0}^\infty A^n/n!\\)
 
 The exponential is computed using a combination of the scaling and squaring
 method and the Pade approximation. Details can be founds in:
diff --git a/tensorflow/core/api_def/base_api/api_def_MatrixLogarithm.pbtxt b/tensorflow/core/api_def/base_api/api_def_MatrixLogarithm.pbtxt
index a6c4d0d400..9e80064d15 100644
--- a/tensorflow/core/api_def/base_api/api_def_MatrixLogarithm.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_MatrixLogarithm.pbtxt
@@ -20,7 +20,7 @@ END
   summary: "Computes the matrix logarithm of one or more square matrices:"
   description: <<END
 
-log(exp(A)) = A
+\\(log(exp(A)) = A\\)
 
 This op is only defined for complex matrices. If A is positive-definite and
 real, then casting to a complex matrix, taking the logarithm and casting back
diff --git a/tensorflow/core/api_def/base_api/api_def_ReduceJoin.pbtxt b/tensorflow/core/api_def/base_api/api_def_ReduceJoin.pbtxt
index d13866ddaa..b447d09377 100644
--- a/tensorflow/core/api_def/base_api/api_def_ReduceJoin.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_ReduceJoin.pbtxt
@@ -36,7 +36,7 @@ END
   summary: "Joins a string Tensor across the given dimensions."
   description: <<END
 Computes the string join across dimensions in the given string Tensor of shape
-`[d_0, d_1, ..., d_n-1]`.  Returns a new Tensor created by joining the input
+`[\\(d_0, d_1, ..., d_{n-1}\\)]`.  Returns a new Tensor created by joining the input
 strings with the given separator (default: empty string).  Negative indices are
 counted backwards from the end, with `-1` being equivalent to `n - 1`.  If
 indices are not specified, joins across all dimensions beginning from `n - 1`
diff --git a/tensorflow/core/api_def/base_api/api_def_ScatterNdAdd.pbtxt b/tensorflow/core/api_def/base_api/api_def_ScatterNdAdd.pbtxt
index b0665ebf0e..a9a7646314 100644
--- a/tensorflow/core/api_def/base_api/api_def_ScatterNdAdd.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_ScatterNdAdd.pbtxt
@@ -42,7 +42,7 @@ within a given variable according to `indices`.
 `ref` is a `Tensor` with rank `P` and `indices` is a `Tensor` of rank `Q`.
 
 `indices` must be integer tensor, containing indices into `ref`.
-It must be shape `[d_0, ..., d_{Q-2}, K]` where `0 < K <= P`.
+It must be shape `\\([d_0, ..., d_{Q-2}, K]\\)` where `0 < K <= P`.
 
 The innermost dimension of `indices` (with length `K`) corresponds to
 indices into elements (if `K = P`) or slices (if `K < P`) along the `K`th
@@ -50,9 +50,7 @@ dimension of `ref`.
 
 `updates` is `Tensor` of rank `Q-1+P-K` with shape:
 
-```
-[d_0, ..., d_{Q-2}, ref.shape[K], ..., ref.shape[P-1]].
-```
+$$[d_0, ..., d_{Q-2}, ref.shape[K], ..., ref.shape[P-1]].$$
 
 For example, say we want to add 4 scattered elements to a rank-1 tensor to 8
 elements. In Python, that addition would look like this:
diff --git a/tensorflow/core/api_def/base_api/api_def_ScatterNdNonAliasingAdd.pbtxt b/tensorflow/core/api_def/base_api/api_def_ScatterNdNonAliasingAdd.pbtxt
index e5c64c2b90..35116e5f6a 100644
--- a/tensorflow/core/api_def/base_api/api_def_ScatterNdNonAliasingAdd.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_ScatterNdNonAliasingAdd.pbtxt
@@ -37,7 +37,7 @@ respect to both `input` and `updates`.
 `input` is a `Tensor` with rank `P` and `indices` is a `Tensor` of rank `Q`.
 
 `indices` must be integer tensor, containing indices into `input`.
-It must be shape `[d_0, ..., d_{Q-2}, K]` where `0 < K <= P`.
+It must be shape \\([d_0, ..., d_{Q-2}, K]\\) where `0 < K <= P`.
 
 The innermost dimension of `indices` (with length `K`) corresponds to
 indices into elements (if `K = P`) or `(P-K)`-dimensional slices
@@ -45,9 +45,7 @@ indices into elements (if `K = P`) or `(P-K)`-dimensional slices
 
 `updates` is `Tensor` of rank `Q-1+P-K` with shape:
 
-```
-[d_0, ..., d_{Q-2}, input.shape[K], ..., input.shape[P-1]].
-```
+$$[d_0, ..., d_{Q-2}, input.shape[K], ..., input.shape[P-1]].$$
 
 For example, say we want to add 4 scattered elements to a rank-1 tensor to 8
 elements. In Python, that addition would look like this:
diff --git a/tensorflow/core/api_def/base_api/api_def_ScatterNdSub.pbtxt b/tensorflow/core/api_def/base_api/api_def_ScatterNdSub.pbtxt
index 333db017f5..99e5c4908b 100644
--- a/tensorflow/core/api_def/base_api/api_def_ScatterNdSub.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_ScatterNdSub.pbtxt
@@ -42,7 +42,7 @@ within a given variable according to `indices`.
 `ref` is a `Tensor` with rank `P` and `indices` is a `Tensor` of rank `Q`.
 
 `indices` must be integer tensor, containing indices into `ref`.
-It must be shape `[d_0, ..., d_{Q-2}, K]` where `0 < K <= P`.
+It must be shape \\([d_0, ..., d_{Q-2}, K]\\) where `0 < K <= P`.
 
 The innermost dimension of `indices` (with length `K`) corresponds to
 indices into elements (if `K = P`) or slices (if `K < P`) along the `K`th
@@ -50,9 +50,7 @@ dimension of `ref`.
 
 `updates` is `Tensor` of rank `Q-1+P-K` with shape:
 
-```
-[d_0, ..., d_{Q-2}, ref.shape[K], ..., ref.shape[P-1]].
-```
+$$[d_0, ..., d_{Q-2}, ref.shape[K], ..., ref.shape[P-1]].$$
 
 For example, say we want to subtract 4 scattered elements from a rank-1 tensor
 with 8 elements. In Python, that subtraction would look like this:
diff --git a/tensorflow/core/api_def/base_api/api_def_ScatterNdUpdate.pbtxt b/tensorflow/core/api_def/base_api/api_def_ScatterNdUpdate.pbtxt
index 33d98262d5..cb57c171b9 100644
--- a/tensorflow/core/api_def/base_api/api_def_ScatterNdUpdate.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_ScatterNdUpdate.pbtxt
@@ -42,7 +42,7 @@ variable according to `indices`.
 `ref` is a `Tensor` with rank `P` and `indices` is a `Tensor` of rank `Q`.
 
 `indices` must be integer tensor, containing indices into `ref`.
-It must be shape `[d_0, ..., d_{Q-2}, K]` where `0 < K <= P`.
+It must be shape \\([d_0, ..., d_{Q-2}, K]\\) where `0 < K <= P`.
 
 The innermost dimension of `indices` (with length `K`) corresponds to
 indices into elements (if `K = P`) or slices (if `K < P`) along the `K`th
@@ -50,9 +50,7 @@ dimension of `ref`.
 
 `updates` is `Tensor` of rank `Q-1+P-K` with shape:
 
-```
-[d_0, ..., d_{Q-2}, ref.shape[K], ..., ref.shape[P-1]].
-```
+$$[d_0, ..., d_{Q-2}, ref.shape[K], ..., ref.shape[P-1]].$$
 
 For example, say we want to update 4 scattered elements to a rank-1 tensor to
 8 elements. In Python, that update would look like this:
diff --git a/tensorflow/core/api_def/base_api/api_def_Softmax.pbtxt b/tensorflow/core/api_def/base_api/api_def_Softmax.pbtxt
index 43884824c9..b51b468c3d 100644
--- a/tensorflow/core/api_def/base_api/api_def_Softmax.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_Softmax.pbtxt
@@ -16,6 +16,6 @@ END
   description: <<END
 For each batch `i` and class `j` we have
 
-    softmax[i, j] = exp(logits[i, j]) / sum_j(exp(logits[i, j]))
+    $$softmax[i, j] = exp(logits[i, j]) / sum_j(exp(logits[i, j]))$$
 END
 }
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseApplyAdagrad.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseApplyAdagrad.pbtxt
index 1698e2def0..06409d8db2 100644
--- a/tensorflow/core/api_def/base_api/api_def_SparseApplyAdagrad.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_SparseApplyAdagrad.pbtxt
@@ -47,7 +47,7 @@ END
   summary: "Update relevant entries in \'*var\' and \'*accum\' according to the adagrad scheme."
   description: <<END
 That is for rows we have grad for, we update var and accum as follows:
-accum += grad * grad
-var -= lr * grad * (1 / sqrt(accum))
+$$accum += grad * grad$$
+$$var -= lr * grad * (1 / sqrt(accum))$$
 END
 }
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseApplyCenteredRMSProp.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseApplyCenteredRMSProp.pbtxt
index 2c6a36bf45..b3f2d3ea62 100644
--- a/tensorflow/core/api_def/base_api/api_def_SparseApplyCenteredRMSProp.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_SparseApplyCenteredRMSProp.pbtxt
@@ -83,8 +83,8 @@ mean_square = decay * mean_square + (1-decay) * gradient ** 2
 mean_grad = decay * mean_grad + (1-decay) * gradient
 Delta = learning_rate * gradient / sqrt(mean_square + epsilon - mean_grad ** 2)
 
-ms <- rho * ms_{t-1} + (1-rho) * grad * grad
-mom <- momentum * mom_{t-1} + lr * grad / sqrt(ms + epsilon)
-var <- var - mom
+$$ms <- rho * ms_{t-1} + (1-rho) * grad * grad$$
+$$mom <- momentum * mom_{t-1} + lr * grad / sqrt(ms + epsilon)$$
+$$var <- var - mom$$
 END
 }
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseApplyFtrl.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseApplyFtrl.pbtxt
index 524b5c5a47..9a6b6bca5f 100644
--- a/tensorflow/core/api_def/base_api/api_def_SparseApplyFtrl.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_SparseApplyFtrl.pbtxt
@@ -71,10 +71,10 @@ END
   summary: "Update relevant entries in \'*var\' according to the Ftrl-proximal scheme."
   description: <<END
 That is for rows we have grad for, we update var, accum and linear as follows:
-accum_new = accum + grad * grad
-linear += grad + (accum_new^(-lr_power) - accum^(-lr_power)) / lr * var
-quadratic = 1.0 / (accum_new^(lr_power) * lr) + 2 * l2
-var = (sign(linear) * l1 - linear) / quadratic if |linear| > l1 else 0.0
-accum = accum_new
+$$accum_new = accum + grad * grad$$
+$$linear += grad + (accum_{new}^{-lr_{power}} - accum^{-lr_{power}} / lr * var$$
+$$quadratic = 1.0 / (accum_{new}^{lr_{power}} * lr) + 2 * l2$$
+$$var = (sign(linear) * l1 - linear) / quadratic\ if\ |linear| > l1\ else\ 0.0$$
+$$accum = accum_{new}$$
 END
 }
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseApplyMomentum.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseApplyMomentum.pbtxt
index 8d9ac9ea3f..17dbb488de 100644
--- a/tensorflow/core/api_def/base_api/api_def_SparseApplyMomentum.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_SparseApplyMomentum.pbtxt
@@ -64,7 +64,7 @@ Set use_nesterov = True if you want to use Nesterov momentum.
 
 That is for rows we have grad for, we update var and accum as follows:
 
-accum = accum * momentum + grad
-var -= lr * accum
+$$accum = accum * momentum + grad$$
+$$var -= lr * accum$$
 END
 }
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseApplyProximalAdagrad.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseApplyProximalAdagrad.pbtxt
index 80541b91c7..0b24f2ddd1 100644
--- a/tensorflow/core/api_def/base_api/api_def_SparseApplyProximalAdagrad.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_SparseApplyProximalAdagrad.pbtxt
@@ -58,9 +58,9 @@ END
   summary: "Sparse update entries in \'*var\' and \'*accum\' according to FOBOS algorithm."
   description: <<END
 That is for rows we have grad for, we update var and accum as follows:
-accum += grad * grad
-prox_v = var
-prox_v -= lr * grad * (1 / sqrt(accum))
-var = sign(prox_v)/(1+lr*l2) * max{|prox_v|-lr*l1,0}
+$$accum += grad * grad$$
+$$prox_v = var$$
+$$prox_v -= lr * grad * (1 / sqrt(accum))$$
+$$var = sign(prox_v)/(1+lr*l2) * max{|prox_v|-lr*l1,0}$$
 END
 }
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseApplyProximalGradientDescent.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseApplyProximalGradientDescent.pbtxt
index 5200e5516d..9dc53860e5 100644
--- a/tensorflow/core/api_def/base_api/api_def_SparseApplyProximalGradientDescent.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_SparseApplyProximalGradientDescent.pbtxt
@@ -52,7 +52,7 @@ END
   summary: "Sparse update \'*var\' as FOBOS algorithm with fixed learning rate."
   description: <<END
 That is for rows we have grad for, we update var as follows:
-prox_v = var - alpha * grad
-var = sign(prox_v)/(1+alpha*l2) * max{|prox_v|-alpha*l1,0}
+$$prox_v = var - alpha * grad$$
+$$var = sign(prox_v)/(1+alpha*l2) * max{|prox_v|-alpha*l1,0}$$
 END
 }
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseApplyRMSProp.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseApplyRMSProp.pbtxt
index a4dbd608b8..ee9f57fa9d 100644
--- a/tensorflow/core/api_def/base_api/api_def_SparseApplyRMSProp.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_SparseApplyRMSProp.pbtxt
@@ -71,8 +71,8 @@ and mom will not update in iterations during which the grad is zero.
 mean_square = decay * mean_square + (1-decay) * gradient ** 2
 Delta = learning_rate * gradient / sqrt(mean_square + epsilon)
 
-ms <- rho * ms_{t-1} + (1-rho) * grad * grad
-mom <- momentum * mom_{t-1} + lr * grad / sqrt(ms + epsilon)
-var <- var - mom
+$$ms <- rho * ms_{t-1} + (1-rho) * grad * grad$$
+$$mom <- momentum * mom_{t-1} + lr * grad / sqrt(ms + epsilon)$$
+$$var <- var - mom$$
 END
 }
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseSliceGrad.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseSliceGrad.pbtxt
new file mode 100644
index 0000000000..51af6adcf1
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseSliceGrad.pbtxt
@@ -0,0 +1,40 @@
+op {
+  graph_op_name: "SparseSliceGrad"
+  in_arg {
+    name: "backprop_val_grad"
+    description: <<END
+1-D. The gradient with respect to
+the non-empty values of the sliced `SparseTensor`.
+END
+  }
+  in_arg {
+    name: "input_indices"
+    description: <<END
+2-D.  The `indices` of the input `SparseTensor`.
+END
+  }
+  in_arg {
+    name: "input_start"
+    description: <<END
+1-D. tensor represents the start of the slice.
+END
+  }
+  in_arg {
+    name: "output_indices"
+    description: <<END
+2-D.  The `indices` of the sliced `SparseTensor`.
+END
+  }
+  out_arg {
+    name: "val_grad"
+    description: <<END
+1-D. The gradient with respect to the non-empty values of input `SparseTensor`.
+END
+  }
+  summary: "The gradient operator for the SparseSlice op."
+  description: <<END
+This op takes in the upstream gradient w.r.t. non-empty values of
+the sliced `SparseTensor`, and outputs the gradients w.r.t.
+the non-empty values of input `SparseTensor`.
+END
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_UnsortedSegmentSum.pbtxt b/tensorflow/core/api_def/base_api/api_def_UnsortedSegmentSum.pbtxt
index eb5d0d1247..9aeabd030d 100644
--- a/tensorflow/core/api_def/base_api/api_def_UnsortedSegmentSum.pbtxt
+++ b/tensorflow/core/api_def/base_api/api_def_UnsortedSegmentSum.pbtxt
@@ -20,7 +20,7 @@ Read @{$math_ops#Segmentation$the section on segmentation} for an explanation of
 segments.
 
 Computes a tensor such that
-`(output[i] = sum_{j...} data[j...]` where the sum is over tuples `j...` such
+\\(output[i] = sum_{j...} data[j...]\\) where the sum is over tuples `j...` such
 that `segment_ids[j...] == i`.  Unlike `SegmentSum`, `segment_ids`
 need not be sorted and need not cover all values in the full
 range of valid values.
diff --git a/tensorflow/core/api_def/python_api/api_def_BroadcastTo.pbtxt b/tensorflow/core/api_def/python_api/api_def_BroadcastTo.pbtxt
deleted file mode 100644
index 083eeced81..0000000000
--- a/tensorflow/core/api_def/python_api/api_def_BroadcastTo.pbtxt
+++ /dev/null
@@ -1,4 +0,0 @@
-op {
-  graph_op_name: "BroadcastTo"
-  visibility: HIDDEN
-}
diff --git a/tensorflow/core/api_def/python_api/api_def_SparseSliceGrad.pbtxt b/tensorflow/core/api_def/python_api/api_def_SparseSliceGrad.pbtxt
new file mode 100644
index 0000000000..6ea8df46ec
--- /dev/null
+++ b/tensorflow/core/api_def/python_api/api_def_SparseSliceGrad.pbtxt
@@ -0,0 +1,4 @@
+op {
+  graph_op_name: "SparseSliceGrad"
+  visibility: HIDDEN
+}