354 lines
13 KiB
Python
354 lines
13 KiB
Python
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# Copyright 2015 The TensorFlow Authors. All Rights Reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# ==============================================================================
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"""Gradients for operators defined in sparse_ops.py."""
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from tensorflow.python.framework import dtypes
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from tensorflow.python.framework import ops
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from tensorflow.python.framework import sparse_tensor
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from tensorflow.python.ops import array_ops
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from tensorflow.python.ops import gen_sparse_ops
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from tensorflow.python.ops import math_ops
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from tensorflow.python.ops import sparse_ops
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# TODO(b/31222613): This op may be differentiable, and there may be
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# latent bugs here.
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ops.NotDifferentiable("SparseAddGrad")
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ops.NotDifferentiable("SparseConcat")
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@ops.RegisterGradient("SparseReorder")
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def _SparseReorderGrad(op, unused_output_indices_grad, output_values_grad):
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"""Gradients for the SparseReorder op.
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Args:
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op: the SparseReorder op
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unused_output_indices_grad: the incoming gradients of the output indices
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output_values_grad: the incoming gradients of the output values
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Returns:
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Gradient for each of the 3 input tensors:
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(input_indices, input_values, input_shape)
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The gradients for input_indices and input_shape is None.
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"""
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input_indices = op.inputs[0]
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input_shape = op.inputs[2]
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num_entries = array_ops.shape(input_indices)[0]
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entry_indices = math_ops.range(num_entries)
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sp_unordered = sparse_tensor.SparseTensor(input_indices, entry_indices,
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input_shape)
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sp_ordered = sparse_ops.sparse_reorder(sp_unordered)
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inverted_permutation = array_ops.invert_permutation(sp_ordered.values)
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return (None, array_ops.gather(output_values_grad,
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inverted_permutation), None)
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@ops.RegisterGradient("SparseAdd")
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def _SparseAddGrad(op, *grads):
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"""The backward operator for the SparseAdd op.
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The SparseAdd op calculates A + B, where A, B, and the sum are all represented
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as `SparseTensor` objects. This op takes in the upstream gradient w.r.t.
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non-empty values of the sum, and outputs the gradients w.r.t. the non-empty
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values of A and B.
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Args:
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op: the SparseAdd op
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*grads: the incoming gradients, one element per output of `op`
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Returns:
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Gradient for each of the 6 input tensors of SparseAdd:
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(a_indices, a_values, a_shape, b_indices, b_values, b_shape, thresh)
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The gradients for the indices, shapes, and the threshold are None.
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"""
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val_grad = grads[1]
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a_indices = op.inputs[0]
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b_indices = op.inputs[3]
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sum_indices = op.outputs[0]
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# NOTE: we do not need to take `thresh` into account, since it simply affects
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# the non-zero elements of the sum, and we will peek into `sum_indices` in the
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# gradient op.
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a_val_grad, b_val_grad = gen_sparse_ops.sparse_add_grad(
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val_grad, a_indices, b_indices, sum_indices)
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a_val_grad.set_shape(op.inputs[1].get_shape())
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b_val_grad.set_shape(op.inputs[4].get_shape())
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# (a_indices, a_values, a_shape, b_indices, b_values, b_shape, thresh)
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return (None, a_val_grad, None, None, b_val_grad, None, None)
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@ops.RegisterGradient("SparseTensorDenseAdd")
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def _SparseTensorDenseAddGrad(op, out_grad):
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sp_indices = op.inputs[0]
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# (sparse_indices, sparse_values, sparse_shape, dense)
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return (None, array_ops.gather_nd(out_grad, sp_indices), None, out_grad)
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@ops.RegisterGradient("SparseReduceSum")
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def _SparseReduceSumGrad(op, out_grad):
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"""Similar to gradient for the Sum Op (i.e. tf.reduce_sum())."""
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sp_indices = op.inputs[0]
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sp_shape = op.inputs[2]
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output_shape_kept_dims = math_ops.reduced_shape(sp_shape, op.inputs[3])
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out_grad_reshaped = array_ops.reshape(out_grad, output_shape_kept_dims)
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scale = sp_shape // math_ops.cast(output_shape_kept_dims, dtypes.int64)
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# (sparse_indices, sparse_values, sparse_shape, reduction_axes)
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return (None, array_ops.gather_nd(out_grad_reshaped,
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sp_indices // scale), None, None)
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@ops.RegisterGradient("SparseSlice")
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def _SparseSliceGrad(op, *grads):
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"""The backward operator for the SparseSlice op.
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This op takes in the upstream gradient w.r.t. non-empty values of
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the sliced `SparseTensor`, and outputs the gradients w.r.t.
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the non-empty values of input `SparseTensor`.
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Args:
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op: the SparseSlice op
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*grads: the incoming gradients, one element per output of `op`
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Returns:
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Gradient for each of the 5 input tensors of SparseSlice:
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(indices, values, shape, start, size)
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The gradients for the indices, shape, start and the size are None.
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"""
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backprop_val_grad = grads[1]
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input_indices = op.inputs[0]
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input_start = op.inputs[3]
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output_indices = op.outputs[0]
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val_grad = gen_sparse_ops.sparse_slice_grad(backprop_val_grad, input_indices,
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input_start, output_indices)
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val_grad.set_shape(op.inputs[1].get_shape())
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# (indices, values, shape, start, size)
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return (None, val_grad, None, None, None)
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@ops.RegisterGradient("SparseTensorDenseMatMul")
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def _SparseTensorDenseMatMulGrad(op, grad):
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"""Gradients for the dense tensor in the SparseTensorDenseMatMul op.
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Args:
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op: the SparseTensorDenseMatMul op
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grad: the incoming gradient
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Returns:
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Gradient for each of the 4 input tensors:
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(sparse_indices, sparse_values, sparse_shape, dense_tensor)
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The gradients for indices and shape are None.
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Raises:
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TypeError: When the two operands don't have the same type.
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"""
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a_indices, a_values, a_shape = op.inputs[:3]
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b = op.inputs[3]
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adj_a = op.get_attr("adjoint_a")
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adj_b = op.get_attr("adjoint_b")
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a_type = a_values.dtype.base_dtype
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b_type = b.dtype.base_dtype
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if a_type != b_type:
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raise TypeError(
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f"SparseTensorDenseMatMul op received operands with different types: "
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f"`{a_type}` and `{b_type}`.")
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# gradient w.r.t. dense
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b_grad = gen_sparse_ops.sparse_tensor_dense_mat_mul(
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a_indices, a_values, a_shape, grad, adjoint_a=not adj_a)
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if adj_b:
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b_grad = array_ops.matrix_transpose(b_grad, conjugate=True)
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# gradient w.r.t. sparse values
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# TODO(zongheng): these gather calls could potentially duplicate rows/cols in
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# memory. If there is a need, we should look into implementing this more
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# intelligently to avoid duplicating data.
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# With no adjoints, a_grad is matmul(grad, adjoint(b)). Since a is sparse, we
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# just want to compute that matmul at the rows/columns of non-zero values. The
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# (r, c) value is sum(grad[r, :] * adjoint(b)[:, c]), where the latter term is
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# more conveniently written as conj(b)[c, :]. That expression is more
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# efficient to calculate as a matmul, after expanding the two terms to be 2D
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# (i.e. a row vector and a column vector).
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#
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# If adj_b then we replace conj(b) by transpose(b); if adj_a we need to
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# adjoint the result, which is equivalent to swapping r and c and taking
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# conjugates.
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# Get grad[r, :] and b[c, :] (or with r and c swapped if adj_a, or with
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# transpose(b) if adj_b), as batches of vectors (with the batch dimension
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# corresponding to the non-zero indices of a).
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rows = a_indices[:, 0]
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cols = a_indices[:, 1]
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parts_a = array_ops.gather(grad, rows if not adj_a else cols)
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parts_b = array_ops.gather(
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b if not adj_b else array_ops.transpose(b), cols if not adj_a else rows)
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if not adj_a and not adj_b:
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# grad[r, :] * conj(b[c, :]) = row(grad[r, :]) @ adjoint(row(b[c, :]))
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a_values_grad = math_ops.matmul(
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array_ops.expand_dims(parts_a, -2),
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array_ops.expand_dims(parts_b, -2),
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adjoint_b=True)
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elif adj_a and not adj_b:
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# conj(grad[c, :] * conj(b[r, :])) = adjoint(col(grad[c, :])) @ col(b[r, :])
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a_values_grad = math_ops.matmul(
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array_ops.expand_dims(parts_a, -1),
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array_ops.expand_dims(parts_b, -1),
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adjoint_a=True)
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elif not adj_a and adj_b:
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# grad[r, :] * transpose(b)[c, :] =
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# row(grad[r, :]) @ col(transpose(b)[c, :])
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a_values_grad = math_ops.matmul(
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array_ops.expand_dims(parts_a, -2), array_ops.expand_dims(parts_b, -1))
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elif adj_a and adj_b:
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# conj(grad[c, :] * transpose(b)[r, :]) =
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# adjoint(col(grad[c, :])) @ adjoint(row(transpose(b)[r, :])
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a_values_grad = math_ops.matmul(
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array_ops.expand_dims(parts_a, -1),
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array_ops.expand_dims(parts_b, -2),
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adjoint_a=True,
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adjoint_b=True)
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# gradients w.r.t. (a_indices, a_values, a_shape, b)
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return (None, array_ops.squeeze(a_values_grad, axis=[-2, -1]), None, b_grad)
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@ops.RegisterGradient("SparseDenseCwiseAdd")
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def _SparseDenseCwiseAddGrad(unused_op, unused_grad):
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raise NotImplementedError(
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"Gradient for SparseDenseCwiseAdd is not implemented.")
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def _SparseDenseCwiseMulOrDivGrad(op, grad, is_mul):
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"""Common code for SparseDenseCwise{Mul,Div} gradients."""
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x_indices = op.inputs[0]
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x_shape = op.inputs[2]
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y = op.inputs[3]
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y_shape = math_ops.cast(array_ops.shape(y), dtypes.int64)
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num_added_dims = array_ops.expand_dims(
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array_ops.size(x_shape) - array_ops.size(y_shape), 0)
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augmented_y_shape = array_ops.concat(
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[array_ops.ones(num_added_dims, ops.dtypes.int64), y_shape], 0)
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scaling = x_shape // augmented_y_shape
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scaled_indices = x_indices // scaling
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scaled_indices = array_ops.slice(scaled_indices,
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array_ops.concat([[0], num_added_dims], 0),
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[-1, -1])
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dense_vals = array_ops.gather_nd(y, scaled_indices)
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if is_mul:
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dx = grad * dense_vals
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dy_val = grad * op.inputs[1]
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else:
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dx = grad / dense_vals
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dy_val = grad * (-op.inputs[1] / math_ops.square(dense_vals))
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# indices can repeat after scaling, so we can't use sparse_to_dense().
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dy = sparse_ops.sparse_add(
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array_ops.zeros_like(y),
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sparse_tensor.SparseTensor(scaled_indices, dy_val, y_shape))
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# (sp_indices, sp_vals, sp_shape, dense)
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return (None, dx, None, dy)
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@ops.RegisterGradient("SparseDenseCwiseMul")
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def _SparseDenseCwiseMulGrad(op, grad):
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"""Gradients for SparseDenseCwiseMul."""
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return _SparseDenseCwiseMulOrDivGrad(op, grad, True)
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@ops.RegisterGradient("SparseDenseCwiseDiv")
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def _SparseDenseCwiseDivGrad(op, grad):
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"""Gradients for SparseDenseCwiseDiv."""
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return _SparseDenseCwiseMulOrDivGrad(op, grad, False)
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@ops.RegisterGradient("SparseSoftmax")
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def _SparseSoftmaxGrad(op, grad):
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"""Gradients for SparseSoftmax.
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The calculation is the same as SoftmaxGrad:
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grad_x = grad_softmax * softmax - sum(grad_softmax * softmax) * softmax
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where we now only operate on the non-zero values present in the SparseTensors.
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Args:
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op: the SparseSoftmax op.
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grad: the upstream gradient w.r.t. the non-zero SparseSoftmax output values.
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Returns:
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Gradients w.r.t. the input (sp_indices, sp_values, sp_shape).
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"""
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indices, shape = op.inputs[0], op.inputs[2]
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out_vals = op.outputs[0]
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sp_output = sparse_tensor.SparseTensor(indices, out_vals, shape)
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sp_grad = sparse_tensor.SparseTensor(indices, grad, shape)
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sp_product = sparse_tensor.SparseTensor(indices,
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sp_output.values * sp_grad.values,
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shape)
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# [..., B, 1], dense.
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sum_reduced = -sparse_ops.sparse_reduce_sum(sp_product, [-1], keepdims=True)
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# sparse [..., B, C] + dense [..., B, 1] with broadcast; outputs sparse.
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sp_sum = sparse_ops.sparse_dense_cwise_add(sp_grad, sum_reduced)
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grad_x = sp_sum.values * sp_output.values
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return [None, grad_x, None]
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@ops.RegisterGradient("SparseSparseMaximum")
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def _SparseSparseMaximumGrad(unused_op, unused_grad):
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raise NotImplementedError(
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"Gradient for SparseSparseMaximum is not implemented.")
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@ops.RegisterGradient("SparseSparseMinimum")
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def _SparseSparseMinimumGrad(unused_op, unused_grad):
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raise NotImplementedError(
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"Gradient for SparseSparseMinimum is not implemented.")
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@ops.RegisterGradient("SparseFillEmptyRows")
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def _SparseFillEmptyRowsGrad(op, unused_grad_output_indices, output_grad_values,
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unused_grad_empty_row_indicator,
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|
unused_grad_reverse_index_map):
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|
"""Gradients for SparseFillEmptyRows."""
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|
reverse_index_map = op.outputs[3]
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|
|
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||
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|
d_values, d_default_value = gen_sparse_ops.sparse_fill_empty_rows_grad(
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||
|
|
reverse_index_map=reverse_index_map, grad_values=output_grad_values)
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||
|
|
|
||
|
|
# d_indices, d_values, d_dense_shape, d_default_value.
|
||
|
|
return [None, d_values, None, d_default_value]
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||
|
|
|
||
|
|
|
||
|
|
@ops.RegisterGradient("SparseToDense")
|
||
|
|
def _SparseToDenseGrad(op, grad):
|
||
|
|
sparse_indices, output_shape, _, _ = op.inputs
|
||
|
|
|
||
|
|
sparse_values_grad = array_ops.gather_nd(grad, sparse_indices)
|
||
|
|
default_value_grad = math_ops.reduce_sum(grad) - math_ops.reduce_sum(
|
||
|
|
sparse_values_grad)
|
||
|
|
return [
|
||
|
|
array_ops.zeros_like(sparse_indices),
|
||
|
|
array_ops.zeros_like(output_shape), sparse_values_grad, default_value_grad
|
||
|
|
]
|