1293 lines
43 KiB
Python
1293 lines
43 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 math_ops.py."""
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from __future__ import absolute_import
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from __future__ import division
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from __future__ import print_function
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import numpy as np
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from tensorflow.python.eager import context
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from tensorflow.python.framework import constant_op
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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 tensor_util
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from tensorflow.python.ops import array_ops
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from tensorflow.python.ops import gen_array_ops
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from tensorflow.python.ops import gen_math_ops
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from tensorflow.python.ops import math_ops
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def _safe_shape_div(x, y):
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"""Divides `x / y` assuming `x, y >= 0`, treating `0 / 0 = 0`."""
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return x // math_ops.maximum(y, 1)
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@ops.RegisterGradient("ArgMax")
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def _ArgMaxGrad(op, grad):
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del op, grad
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return [None, None]
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@ops.RegisterGradient("ArgMin")
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def _ArgMinGrad(op, grad):
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del op, grad
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return [None, None]
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@ops.RegisterGradient("Sum")
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def _SumGrad(op, grad):
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"""Gradient for Sum."""
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# Fast path for when reducing to a scalar and ndims is known: adds only
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# Reshape and Tile ops (and possibly a Shape).
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input_0_shape = op.inputs[0]._shape_tuple() # pylint: disable=protected-access
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if input_0_shape is not None:
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axes = tensor_util.constant_value(op.inputs[1])
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if axes is not None:
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rank = len(input_0_shape)
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if np.array_equal(axes, np.arange(rank)): # Reduce all dims.
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if context.executing_eagerly():
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ctx = context.context()
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new_shape = ctx.ones_rank_cache().get(rank)
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if new_shape is None:
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new_shape = constant_op.constant([1] * rank, dtype=dtypes.int32)
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ctx.ones_rank_cache().put(rank, new_shape)
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else:
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new_shape = [1] * rank
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grad = array_ops.reshape(grad, new_shape)
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# If shape is not fully defined (but rank is), we use Shape.
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if None not in input_0_shape:
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input_shape = constant_op.constant(input_0_shape, dtype=dtypes.int32)
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else:
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input_shape = array_ops.shape(op.inputs[0])
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return [array_ops.tile(grad, input_shape), None]
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input_shape = array_ops.shape(op.inputs[0])
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# TODO(apassos) remove this once device placement for eager ops makes more
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# sense.
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with ops.colocate_with(input_shape):
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output_shape_kept_dims = math_ops.reduced_shape(input_shape, op.inputs[1])
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tile_scaling = _safe_shape_div(input_shape, output_shape_kept_dims)
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grad = array_ops.reshape(grad, output_shape_kept_dims)
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return [array_ops.tile(grad, tile_scaling), None]
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def _MinOrMaxGrad(op, grad):
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"""Gradient for Min or Max. Amazingly it's precisely the same code."""
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input_shape = array_ops.shape(op.inputs[0])
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output_shape_kept_dims = math_ops.reduced_shape(input_shape, op.inputs[1])
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y = op.outputs[0]
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y = array_ops.reshape(y, output_shape_kept_dims)
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grad = array_ops.reshape(grad, output_shape_kept_dims)
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# Compute the number of selected (maximum or minimum) elements in each
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# reduction dimension. If there are multiple minimum or maximum elements
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# then the gradient will be divided between them.
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indicators = math_ops.cast(math_ops.equal(y, op.inputs[0]), grad.dtype)
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num_selected = array_ops.reshape(
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math_ops.reduce_sum(indicators, op.inputs[1]), output_shape_kept_dims)
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return [math_ops.div(indicators, num_selected) * grad, None]
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@ops.RegisterGradient("Max")
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def _MaxGrad(op, grad):
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"""Gradient for Max."""
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return _MinOrMaxGrad(op, grad)
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@ops.RegisterGradient("Min")
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def _MinGrad(op, grad):
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return _MinOrMaxGrad(op, grad)
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@ops.RegisterGradient("Mean")
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def _MeanGrad(op, grad):
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"""Gradient for Mean."""
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sum_grad = _SumGrad(op, grad)[0]
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input_shape = op.inputs[0]._shape_tuple() # pylint: disable=protected-access
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output_shape = op.outputs[0]._shape_tuple() # pylint: disable=protected-access
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if (input_shape is not None and output_shape is not None and
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None not in input_shape and None not in output_shape):
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input_size = np.prod(input_shape)
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output_size = np.prod(output_shape)
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factor = input_size // max(output_size, 1)
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factor = constant_op.constant(factor, dtype=sum_grad.dtype)
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else:
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input_shape = array_ops.shape(op.inputs[0])
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output_shape = array_ops.shape(op.outputs[0])
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factor = _safe_shape_div(
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math_ops.reduce_prod(input_shape), math_ops.reduce_prod(output_shape))
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return math_ops.truediv(sum_grad, math_ops.cast(factor, sum_grad.dtype)), None
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@ops.RegisterGradient("Prod")
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def _ProdGrad(op, grad):
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"""Gradient for Prod."""
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# The gradient can be expressed by dividing the product by each entry of the
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# input tensor, but this approach can't deal with zeros in the input.
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# Here, we avoid this problem by composing the output as a product of two
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# cumprod operations.
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input_shape = array_ops.shape(op.inputs[0])
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# Reshape reduction indices for the case where the parameter is a scalar
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reduction_indices = array_ops.reshape(op.inputs[1], [-1])
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# Expand grad to full input shape
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output_shape_kept_dims = math_ops.reduced_shape(input_shape, op.inputs[1])
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tile_scaling = _safe_shape_div(input_shape, output_shape_kept_dims)
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grad = array_ops.reshape(grad, output_shape_kept_dims)
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grad = array_ops.tile(grad, tile_scaling)
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# Pack all reduced dimensions into a single one, so we can perform the
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# cumprod ops. If the reduction dims list is empty, it defaults to float32,
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# so we need to cast here. We put all the shape-related ops on CPU to avoid
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# copying back and forth, and since listdiff is CPU only.
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with ops.device("/cpu:0"):
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rank = array_ops.rank(op.inputs[0])
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reduction_indices = (reduction_indices + rank) % rank
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reduced = math_ops.cast(reduction_indices, dtypes.int32)
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idx = math_ops.range(0, rank)
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other, _ = array_ops.setdiff1d(idx, reduced)
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perm = array_ops.concat([reduced, other], 0)
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reduced_num = math_ops.reduce_prod(array_ops.gather(input_shape, reduced))
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other_num = math_ops.reduce_prod(array_ops.gather(input_shape, other))
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permuted = array_ops.transpose(op.inputs[0], perm)
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permuted_shape = array_ops.shape(permuted)
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reshaped = array_ops.reshape(permuted, (reduced_num, other_num))
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# Calculate product, leaving out the current entry
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left = math_ops.cumprod(reshaped, axis=0, exclusive=True)
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right = math_ops.cumprod(reshaped, axis=0, exclusive=True, reverse=True)
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# For complex inputs, the gradient is in the conjugate direction.
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y = array_ops.reshape(math_ops.conj(left) * math_ops.conj(right),
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permuted_shape)
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# Invert the transpose and reshape operations.
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# Make sure to set the statically known shape information through a reshape.
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out = grad * array_ops.transpose(y, array_ops.invert_permutation(perm))
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return array_ops.reshape(out, input_shape), None
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@ops.RegisterGradient("SegmentSum")
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def _SegmentSumGrad(op, grad):
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"""Gradient for SegmentSum."""
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return array_ops.gather(grad, op.inputs[1]), None
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@ops.RegisterGradient("SegmentMean")
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def _SegmentMeanGrad(op, grad):
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"""Gradient for SegmentMean."""
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input_rank = array_ops.rank(op.inputs[0])
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ones_shape = array_ops.concat([
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array_ops.shape(op.inputs[1]),
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array_ops.fill(array_ops.expand_dims(input_rank - 1, 0), 1)
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], 0)
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ones = array_ops.fill(ones_shape, constant_op.constant(1, dtype=grad.dtype))
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scaled_grad = math_ops.div(grad, math_ops.segment_sum(ones, op.inputs[1]))
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return array_ops.gather(scaled_grad, op.inputs[1]), None
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@ops.RegisterGradient("SparseSegmentSum")
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def _SparseSegmentSumGrad(op, grad):
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"""Gradient for SparseSegmentSum."""
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input_rows = array_ops.shape(op.inputs[0])[0]
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return (math_ops.unsorted_segment_sum(
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array_ops.gather(grad, op.inputs[2]), op.inputs[1], input_rows), None,
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None)
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@ops.RegisterGradient("SparseSegmentSumWithNumSegments")
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def _SparseSegmentSumWithNumSegmentsGrad(op, grad):
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"""Gradient for SparseSegmentSumWithNumSegments."""
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input_rows = array_ops.shape(op.inputs[0])[0]
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return (math_ops.unsorted_segment_sum(
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array_ops.gather(grad, op.inputs[2]), op.inputs[1], input_rows), None,
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None, None)
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@ops.RegisterGradient("SparseSegmentMean")
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def _SparseSegmentMeanGrad(op, grad):
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"""Gradient for SparseSegmentMean."""
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dim0 = array_ops.shape(op.inputs[0])[0]
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return (math_ops.sparse_segment_mean_grad(grad, op.inputs[1], op.inputs[2],
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dim0), None, None)
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@ops.RegisterGradient("SparseSegmentMeanWithNumSegments")
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def _SparseSegmentMeanWithNumSegmentsGrad(op, grad):
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"""Gradient for SparseSegmentMeanWithNumSegments."""
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dim0 = array_ops.shape(op.inputs[0])[0]
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return (math_ops.sparse_segment_mean_grad(grad, op.inputs[1], op.inputs[2],
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dim0), None, None, None)
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@ops.RegisterGradient("SparseSegmentSqrtN")
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def _SparseSegmentSqrtNGrad(op, grad):
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"""Gradient for SparseSegmentSqrtN."""
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dim0 = array_ops.shape(op.inputs[0])[0]
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return (math_ops.sparse_segment_sqrt_n_grad(grad, op.inputs[1], op.inputs[2],
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dim0), None, None)
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@ops.RegisterGradient("SparseSegmentSqrtNWithNumSegments")
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def _SparseSegmentSqrtNWithNumSegmentsGrad(op, grad):
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"""Gradient for SparseSegmentSqrtNWithNumSegments."""
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dim0 = array_ops.shape(op.inputs[0])[0]
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return (math_ops.sparse_segment_sqrt_n_grad(grad, op.inputs[1], op.inputs[2],
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dim0), None, None, None)
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def _SegmentMinOrMaxGrad(op, grad):
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""" Gradient for SegmentMin and SegmentMax. """
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zeros = array_ops.zeros_like(op.inputs[0], dtype=op.inputs[0].dtype)
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# Get the number of selected (minimum or maximum) elements in each segment.
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gathered_outputs = array_ops.gather(op.outputs[0], op.inputs[1])
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is_selected = math_ops.equal(op.inputs[0], gathered_outputs)
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num_selected = math_ops.segment_sum(math_ops.cast(is_selected, grad.dtype),
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op.inputs[1])
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# Compute the gradient for each segment. The gradient for the ith segment is
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# divided evenly among the selected elements in that segment.
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weighted_grads = math_ops.div(grad, num_selected)
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gathered_grads = array_ops.gather(weighted_grads, op.inputs[1])
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return array_ops.where(is_selected, gathered_grads, zeros), None
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@ops.RegisterGradient("SegmentMin")
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def _SegmentMinGrad(op, grad):
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"""Gradient for SegmentMin."""
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return _SegmentMinOrMaxGrad(op, grad)
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@ops.RegisterGradient("SegmentMax")
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def _SegmentMaxGrad(op, grad):
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"""Gradient for SegmentMax."""
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return _SegmentMinOrMaxGrad(op, grad)
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def _GatherDropNegatives(params, ids, zero_clipped_indices=None,
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is_positive=None):
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""" Helper function for unsorted segment ops. Gathers params for
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positive segment ids and gathers 0 for inputs with negative segment id.
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Also returns the clipped indices and a boolean mask with the same shape
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as ids where a positive id is masked as true. With this, the latter two
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can be passed as arguments to this function to reuse them.
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"""
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if zero_clipped_indices is None:
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zero_clipped_indices = math_ops.maximum(ids, array_ops.zeros_like(ids))
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gathered = array_ops.gather(params, zero_clipped_indices)
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if is_positive is None:
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is_positive = math_ops.greater_equal(ids, 0)
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# tf.where(condition, x, y) requires condition to have the same shape as x
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# and y.
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# todo(philjd): remove this if tf.where supports broadcasting (#9284)
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for _ in range(gathered.shape.ndims - is_positive.shape.ndims):
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is_positive = array_ops.expand_dims(is_positive, -1)
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is_positive = (is_positive &
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array_ops.ones_like(gathered, dtype=dtypes.bool))
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# replace gathered params of negative indices with 0
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zero_slice = array_ops.zeros_like(gathered)
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return (array_ops.where(is_positive, gathered, zero_slice),
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zero_clipped_indices, is_positive)
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def _UnsortedSegmentMinOrMaxGrad(op, grad):
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""" Gradient for UnsortedSegmentMin and UnsortedSegmentMax. """
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# Get the number of selected (minimum or maximum) elements in each segment.
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gathered_outputs, zero_clipped_indices, is_positive = \
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_GatherDropNegatives(op.outputs[0], op.inputs[1])
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is_selected = math_ops.equal(op.inputs[0], gathered_outputs)
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is_selected = math_ops.logical_and(is_selected, is_positive)
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num_selected = math_ops.unsorted_segment_sum(
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math_ops.cast(is_selected, grad.dtype), op.inputs[1], op.inputs[2])
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# Compute the gradient for each segment. The gradient for the ith segment is
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# divided evenly among the selected elements in that segment.
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weighted_grads = math_ops.div(grad, num_selected)
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gathered_grads, _, _ = _GatherDropNegatives(weighted_grads, None,
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zero_clipped_indices,
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is_positive)
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zeros = array_ops.zeros_like(gathered_grads)
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return array_ops.where(is_selected, gathered_grads, zeros), None, None
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@ops.RegisterGradient("UnsortedSegmentSum")
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def _UnsortedSegmentSumGrad(op, grad):
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"""Gradient for UnsortedSegmentSum."""
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return _GatherDropNegatives(grad, op.inputs[1])[0], None, None
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@ops.RegisterGradient("UnsortedSegmentMax")
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def _UnsortedSegmentMaxGrad(op, grad):
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""" Gradient for UnsortedSegmentMax. """
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return _UnsortedSegmentMinOrMaxGrad(op, grad)
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@ops.RegisterGradient("UnsortedSegmentMin")
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def _UnsortedSegmentMinGrad(op, grad):
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""" Gradient for UnsortedSegmentMin. """
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return _UnsortedSegmentMinOrMaxGrad(op, grad)
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@ops.RegisterGradient("UnsortedSegmentProd")
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def _UnsortedSegmentProdGrad(op, grad):
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""" Gradient for UnsortedSegmentProd.
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The gradient can be expressed for each segment by dividing the segment's
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product by each element of the segment input tensor, but this approach can't
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deal with zeros in the input.
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Unlike reduce_prod we can't use cumsum here as individual segments may have
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a different number of elements. Therefore we consider three cases:
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1) A segment input contains no zeros and we can safely divide by the input
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tensor.
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2) A segment contains exactly one zero. Then the gradient of each input of
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the segment is zero except for the 0-input, there the gradient is
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the product of the remaining segment entries.
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3) A segment contains at least two zeros. The gradient is zero for all
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segment inputs.
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"""
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# Note that unsorted_segment_sum will filter out the negative indices,
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# so we don't need to do a logical_and with is_positive here
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is_zero = math_ops.equal(op.inputs[0], 0)
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num_zeros = gen_math_ops.unsorted_segment_sum(
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math_ops.cast(is_zero, dtype=dtypes.int32), op.inputs[1], op.inputs[2])
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# handle case 3 and set the gradient to 0 for segments with more than one
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# 0 as input
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grad = array_ops.where(math_ops.greater(num_zeros, 1),
|
||
|
array_ops.zeros_like(grad), grad)
|
||
|
# replace all zeros with ones and compute the unsorted_segment_prod
|
||
|
non_zero_data = array_ops.where(is_zero, array_ops.ones_like(op.inputs[0]),
|
||
|
op.inputs[0])
|
||
|
non_zero_prod = gen_math_ops.unsorted_segment_prod(
|
||
|
non_zero_data, op.inputs[1], op.inputs[2])
|
||
|
# clip the indices for gather to be positive
|
||
|
zero_clipped_indices = math_ops.maximum(op.inputs[1],
|
||
|
array_ops.zeros_like(op.inputs[1]))
|
||
|
gathered_prod = array_ops.gather(op.outputs[0], zero_clipped_indices)
|
||
|
gathered_non_zero_prod = array_ops.gather(non_zero_prod,
|
||
|
zero_clipped_indices)
|
||
|
prod_divided_by_el = gathered_prod / op.inputs[0] # May contain nan/inf.
|
||
|
# Now fetch the individual results for segments containing 0 and those that
|
||
|
# don't. is_zero will also fetch results for entries with negative index
|
||
|
# but the following gather_drop_negatives sets the corresponding entry in
|
||
|
# grad to 0 for these
|
||
|
partial_derivative = array_ops.where(is_zero, gathered_non_zero_prod,
|
||
|
prod_divided_by_el)
|
||
|
gathered_grad = _GatherDropNegatives(grad, op.inputs[1],
|
||
|
zero_clipped_indices)[0]
|
||
|
return gathered_grad * partial_derivative, None, None
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Abs")
|
||
|
def _AbsGrad(op, grad):
|
||
|
x = op.inputs[0]
|
||
|
return grad * math_ops.sign(x)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Neg")
|
||
|
def _NegGrad(_, grad):
|
||
|
"""Returns -grad."""
|
||
|
return -grad
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Inv")
|
||
|
def _InvGrad(op, grad):
|
||
|
"""Returns -grad * (1 / x^2)."""
|
||
|
y = op.outputs[0] # y = 1 / x
|
||
|
return gen_math_ops.reciprocal_grad(y, grad)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Reciprocal")
|
||
|
def _ReciprocalGrad(op, grad):
|
||
|
"""Returns -grad * (1 / x^2)."""
|
||
|
y = op.outputs[0] # y = 1 / x
|
||
|
return gen_math_ops.reciprocal_grad(y, grad)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("InvGrad")
|
||
|
def _InvGradGrad(op, grad):
|
||
|
b = op.inputs[1]
|
||
|
# op.output[0]: y = -b * conj(a)^2
|
||
|
with ops.control_dependencies([grad]):
|
||
|
ca = math_ops.conj(op.inputs[0])
|
||
|
cg = math_ops.conj(grad)
|
||
|
return cg * -2.0 * b * ca, gen_math_ops.reciprocal_grad(ca, grad)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("ReciprocalGrad")
|
||
|
def _ReciprocalGradGrad(op, grad):
|
||
|
b = op.inputs[1]
|
||
|
# op.output[0]: y = -b * conj(a)^2
|
||
|
with ops.control_dependencies([grad]):
|
||
|
ca = math_ops.conj(op.inputs[0])
|
||
|
cg = math_ops.conj(grad)
|
||
|
return cg * -2.0 * b * ca, gen_math_ops.reciprocal_grad(ca, grad)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Square")
|
||
|
def _SquareGrad(op, grad):
|
||
|
x = op.inputs[0]
|
||
|
# Added control dependencies to prevent 2*x from being computed too early.
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
y = constant_op.constant(2.0, dtype=x.dtype)
|
||
|
return math_ops.multiply(grad, math_ops.multiply(x, y))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Sqrt")
|
||
|
def _SqrtGrad(op, grad):
|
||
|
y = op.outputs[0] # y = x^(1/2)
|
||
|
return gen_math_ops.sqrt_grad(y, grad)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("SqrtGrad")
|
||
|
def _SqrtGradGrad(op, grad):
|
||
|
a = op.inputs[0]
|
||
|
y = op.outputs[0] # y = 0.5 * b / conj(a)
|
||
|
with ops.control_dependencies([grad]):
|
||
|
ga = grad / a
|
||
|
return -math_ops.conj(ga) * y, 0.5 * ga
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Rsqrt")
|
||
|
def _RsqrtGrad(op, grad):
|
||
|
"""Returns -0.5 * grad * conj(y)^3."""
|
||
|
y = op.outputs[0] # y = x^(-1/2)
|
||
|
return gen_math_ops.rsqrt_grad(y, grad)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("RsqrtGrad")
|
||
|
def _RsqrtGradGrad(op, grad):
|
||
|
"""Returns backprop gradient for f(a,b) = -0.5 * b * conj(a)^3."""
|
||
|
a = op.inputs[0] # a = x^{-1/2}
|
||
|
b = op.inputs[1] # backprop gradient for a
|
||
|
with ops.control_dependencies([grad]):
|
||
|
ca = math_ops.conj(a)
|
||
|
cg = math_ops.conj(grad)
|
||
|
grad_a = -1.5 * cg * b * math_ops.square(ca)
|
||
|
grad_b = gen_math_ops.rsqrt_grad(ca, grad)
|
||
|
return grad_a, grad_b
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Exp")
|
||
|
def _ExpGrad(op, grad):
|
||
|
"""Returns grad * exp(x)."""
|
||
|
y = op.outputs[0] # y = e^x
|
||
|
with ops.control_dependencies([grad]):
|
||
|
y = math_ops.conj(y)
|
||
|
return grad * y
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Expm1")
|
||
|
def _Expm1Grad(op, grad):
|
||
|
"""Returns grad * exp(x)."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
y = math_ops.exp(x)
|
||
|
return grad * y
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Log")
|
||
|
def _LogGrad(op, grad):
|
||
|
"""Returns grad * (1/x)."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
return grad * math_ops.reciprocal(x)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Log1p")
|
||
|
def _Log1pGrad(op, grad):
|
||
|
"""Returns grad * (1/(1 + x))."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
return grad * math_ops.reciprocal(1 + x)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Sinh")
|
||
|
def _SinhGrad(op, grad):
|
||
|
"""Returns grad * cosh(x)."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
return grad * math_ops.cosh(x)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Cosh")
|
||
|
def _CoshGrad(op, grad):
|
||
|
"""Returns grad * sinh(x)."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
return grad * math_ops.sinh(x)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Tanh")
|
||
|
def _TanhGrad(op, grad):
|
||
|
"""Returns grad * (1 - tanh(x) * tanh(x))."""
|
||
|
y = op.outputs[0] # y = tanh(x)
|
||
|
with ops.control_dependencies([grad]):
|
||
|
y = math_ops.conj(y)
|
||
|
return gen_math_ops.tanh_grad(y, grad)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Asinh")
|
||
|
def _AsinhGrad(op, grad):
|
||
|
"""Returns grad * 1/cosh(y)."""
|
||
|
y = op.outputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
y = math_ops.conj(y)
|
||
|
return grad / math_ops.cosh(y)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Acosh")
|
||
|
def _AcoshGrad(op, grad):
|
||
|
"""Returns grad * 1/sinh(y)."""
|
||
|
y = op.outputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
y = math_ops.conj(y)
|
||
|
return grad / math_ops.sinh(y)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Atanh")
|
||
|
def _AtanhGrad(op, grad):
|
||
|
"""Returns grad * 1/ (1 - x^2)."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
x2 = math_ops.square(x)
|
||
|
one = constant_op.constant(1, dtype=grad.dtype)
|
||
|
inv = math_ops.reciprocal(math_ops.subtract(one, x2))
|
||
|
return grad * inv
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("TanhGrad")
|
||
|
def _TanhGradGrad(op, grad):
|
||
|
with ops.control_dependencies([grad]):
|
||
|
a = math_ops.conj(op.inputs[0])
|
||
|
b = math_ops.conj(op.inputs[1])
|
||
|
return grad * -2.0 * b * a, gen_math_ops.tanh_grad(a, grad)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Erf")
|
||
|
def _ErfGrad(op, grad):
|
||
|
"""Returns grad * 2/sqrt(pi) * exp(-x**2)."""
|
||
|
x = op.inputs[0]
|
||
|
two_over_root_pi = constant_op.constant(2 / np.sqrt(np.pi), dtype=grad.dtype)
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
return grad * two_over_root_pi * math_ops.exp(-math_ops.square(x))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Erfc")
|
||
|
def _ErfcGrad(op, grad):
|
||
|
"""Returns -grad * 2/sqrt(pi) * exp(-x**2)."""
|
||
|
x = op.inputs[0]
|
||
|
minus_two_over_root_pi = constant_op.constant(
|
||
|
-2 / np.sqrt(np.pi), dtype=grad.dtype)
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
return grad * minus_two_over_root_pi * math_ops.exp(-math_ops.square(x))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Lgamma")
|
||
|
def _LgammaGrad(op, grad):
|
||
|
"""Returns grad * digamma(x)."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
return grad * math_ops.digamma(x)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Digamma")
|
||
|
def _DigammaGrad(op, grad):
|
||
|
"""Compute gradient of the digamma function with respect to its argument."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
return grad * math_ops.polygamma(array_ops.constant(1, dtype=x.dtype), x)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("BesselI0e")
|
||
|
def _BesselI0eGrad(op, grad):
|
||
|
"""Compute gradient of bessel_i0e(x) with respect to its argument."""
|
||
|
x = op.inputs[0]
|
||
|
y = op.outputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
return grad * (math_ops.bessel_i1e(x) - math_ops.sign(x) * y)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("BesselI1e")
|
||
|
def _BesselI1eGrad(op, grad):
|
||
|
"""Compute gradient of bessel_i1e(x) with respect to its argument."""
|
||
|
x = op.inputs[0]
|
||
|
y = op.outputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
# For x = 0, the correct gradient is 0.5.
|
||
|
# However, the main branch gives NaN because of the division by x, so
|
||
|
# we impute the gradient manually.
|
||
|
# An alternative solution is to express the gradient via bessel_i0e and
|
||
|
# bessel_i2e, but the latter is not yet implemented in Eigen.
|
||
|
eps = np.finfo(x.dtype.as_numpy_dtype).eps
|
||
|
zeros = array_ops.zeros_like(x)
|
||
|
x_is_not_tiny = math_ops.abs(x) > eps
|
||
|
safe_x = array_ops.where(x_is_not_tiny, x, eps + zeros)
|
||
|
dy_dx = math_ops.bessel_i0e(safe_x) - y * (
|
||
|
math_ops.sign(safe_x) + math_ops.reciprocal(safe_x))
|
||
|
return grad * array_ops.where(x_is_not_tiny, dy_dx, 0.5 + zeros)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Igamma")
|
||
|
def _IgammaGrad(op, grad):
|
||
|
"""Returns gradient of igamma(a, x) with respect to a and x."""
|
||
|
a = op.inputs[0]
|
||
|
x = op.inputs[1]
|
||
|
sa = array_ops.shape(a)
|
||
|
sx = array_ops.shape(x)
|
||
|
ra, rx = gen_array_ops.broadcast_gradient_args(sa, sx)
|
||
|
|
||
|
with ops.control_dependencies([grad]):
|
||
|
partial_a = gen_math_ops.igamma_grad_a(a, x)
|
||
|
# Perform operations in log space before summing, because Gamma(a)
|
||
|
# and Gamma'(a) can grow large.
|
||
|
partial_x = math_ops.exp(-x + (a - 1) * math_ops.log(x)
|
||
|
- math_ops.lgamma(a))
|
||
|
return (array_ops.reshape(math_ops.reduce_sum(partial_a * grad, ra), sa),
|
||
|
array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Igammac")
|
||
|
def _IgammacGrad(op, grad):
|
||
|
"""Returns gradient of igammac(a, x) = 1 - igamma(a, x) w.r.t. a and x."""
|
||
|
igamma_grad_a, igamma_grad_x = _IgammaGrad(op, grad)
|
||
|
return (-igamma_grad_a, -igamma_grad_x)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Betainc")
|
||
|
def _BetaincGrad(op, grad):
|
||
|
"""Returns gradient of betainc(a, b, x) with respect to x."""
|
||
|
# TODO(ebrevdo): Perhaps add the derivative w.r.t. a, b
|
||
|
a, b, x = op.inputs
|
||
|
|
||
|
# two cases: x is a scalar and a/b are same-shaped tensors, or vice
|
||
|
# versa; so its sufficient to check against shape(a).
|
||
|
sa = array_ops.shape(a)
|
||
|
sx = array_ops.shape(x)
|
||
|
_, rx = gen_array_ops.broadcast_gradient_args(sa, sx)
|
||
|
|
||
|
# Perform operations in log space before summing, because terms
|
||
|
# can grow large.
|
||
|
log_beta = (
|
||
|
gen_math_ops.lgamma(a) + gen_math_ops.lgamma(b) -
|
||
|
gen_math_ops.lgamma(a + b))
|
||
|
partial_x = math_ops.exp((b - 1) * math_ops.log(1 - x) +
|
||
|
(a - 1) * math_ops.log(x) - log_beta)
|
||
|
|
||
|
# TODO(b/36815900): Mark None return values as NotImplemented
|
||
|
return (
|
||
|
None, # da
|
||
|
None, # db
|
||
|
array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Zeta")
|
||
|
def _ZetaGrad(op, grad):
|
||
|
"""Returns gradient of zeta(x, q) with respect to x and q."""
|
||
|
# TODO(tillahoffmann): Add derivative with respect to x
|
||
|
x = op.inputs[0]
|
||
|
q = op.inputs[1]
|
||
|
# Broadcast gradients
|
||
|
sx = array_ops.shape(x)
|
||
|
sq = array_ops.shape(q)
|
||
|
unused_rx, rq = gen_array_ops.broadcast_gradient_args(sx, sq)
|
||
|
# Evaluate gradient
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
q = math_ops.conj(q)
|
||
|
partial_q = -x * math_ops.zeta(x + 1, q)
|
||
|
# TODO(b/36815900): Mark None return values as NotImplemented
|
||
|
return (None,
|
||
|
array_ops.reshape(math_ops.reduce_sum(partial_q * grad, rq), sq))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Polygamma")
|
||
|
def _PolygammaGrad(op, grad):
|
||
|
"""Returns gradient of psi(n, x) with respect to n and x."""
|
||
|
# TODO(tillahoffmann): Add derivative with respect to n
|
||
|
n = op.inputs[0]
|
||
|
x = op.inputs[1]
|
||
|
# Broadcast gradients
|
||
|
sn = array_ops.shape(n)
|
||
|
sx = array_ops.shape(x)
|
||
|
unused_rn, rx = gen_array_ops.broadcast_gradient_args(sn, sx)
|
||
|
# Evaluate gradient
|
||
|
with ops.control_dependencies([grad]):
|
||
|
n = math_ops.conj(n)
|
||
|
x = math_ops.conj(x)
|
||
|
partial_x = math_ops.polygamma(n + 1, x)
|
||
|
# TODO(b/36815900): Mark None return values as NotImplemented
|
||
|
return (None,
|
||
|
array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Sigmoid")
|
||
|
def _SigmoidGrad(op, grad):
|
||
|
"""Returns grad * sigmoid(x) * (1 - sigmoid(x))."""
|
||
|
y = op.outputs[0] # y = sigmoid(x)
|
||
|
with ops.control_dependencies([grad]):
|
||
|
y = math_ops.conj(y)
|
||
|
return gen_math_ops.sigmoid_grad(y, grad)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("SigmoidGrad")
|
||
|
def _SigmoidGradGrad(op, grad):
|
||
|
with ops.control_dependencies([grad]):
|
||
|
a = math_ops.conj(op.inputs[0])
|
||
|
b = math_ops.conj(op.inputs[1])
|
||
|
gb = grad * b
|
||
|
return gb - 2.0 * gb * a, gen_math_ops.sigmoid_grad(a, grad)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Sign")
|
||
|
def _SignGrad(op, _):
|
||
|
"""Returns 0."""
|
||
|
x = op.inputs[0]
|
||
|
return array_ops.zeros(array_ops.shape(x), dtype=x.dtype)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Sin")
|
||
|
def _SinGrad(op, grad):
|
||
|
"""Returns grad * cos(x)."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
return grad * math_ops.cos(x)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Cos")
|
||
|
def _CosGrad(op, grad):
|
||
|
"""Returns grad * -sin(x)."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
return -grad * math_ops.sin(x)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Tan")
|
||
|
def _TanGrad(op, grad):
|
||
|
"""Returns grad * 1/sec^2(x)."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
secx = math_ops.reciprocal(math_ops.cos(x))
|
||
|
secx2 = math_ops.square(secx)
|
||
|
return grad * secx2
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Asin")
|
||
|
def _AsinGrad(op, grad):
|
||
|
"""Returns grad * 1/sqrt(1-x^2)."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
x2 = math_ops.square(x)
|
||
|
one = constant_op.constant(1, dtype=grad.dtype)
|
||
|
den = math_ops.sqrt(math_ops.subtract(one, x2))
|
||
|
inv = math_ops.reciprocal(den)
|
||
|
return grad * inv
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Acos")
|
||
|
def _AcosGrad(op, grad):
|
||
|
"""Returns grad * -1/sqrt(1-x^2)."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
x2 = math_ops.square(x)
|
||
|
one = constant_op.constant(1, dtype=grad.dtype)
|
||
|
den = math_ops.sqrt(math_ops.subtract(one, x2))
|
||
|
inv = math_ops.reciprocal(den)
|
||
|
return -grad * inv
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Atan")
|
||
|
def _AtanGrad(op, grad):
|
||
|
"""Returns grad * 1/ (1 + x^2)."""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
x = math_ops.conj(x)
|
||
|
x2 = math_ops.square(x)
|
||
|
one = constant_op.constant(1, dtype=grad.dtype)
|
||
|
inv = math_ops.reciprocal(math_ops.add(one, x2))
|
||
|
return grad * inv
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Atan2")
|
||
|
def _Atan2Grad(op, grad):
|
||
|
"""Returns grad * x / (x^2 + y^2), grad * -y / (x^2 + y^2)."""
|
||
|
y = op.inputs[0]
|
||
|
x = op.inputs[1]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
grad_inv = grad / (math_ops.square(x) + math_ops.square(y))
|
||
|
return x * grad_inv, -y * grad_inv
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("AddN")
|
||
|
def _AddNGrad(op, grad):
|
||
|
"""Copies the gradient to all inputs."""
|
||
|
# Not broadcasting.
|
||
|
return [grad] * len(op.inputs)
|
||
|
|
||
|
|
||
|
def _ShapesFullySpecifiedAndEqual(x, y, grad):
|
||
|
# pylint: disable=protected-access
|
||
|
x_shape = x._shape_tuple()
|
||
|
y_shape = y._shape_tuple()
|
||
|
grad_shape = grad._shape_tuple()
|
||
|
# pylint: enable=protected-access
|
||
|
return (x_shape == y_shape and x_shape == grad_shape and
|
||
|
x_shape is not None and None not in x_shape)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Add")
|
||
|
def _AddGrad(op, grad):
|
||
|
"""Gradient for Add."""
|
||
|
x = op.inputs[0]
|
||
|
y = op.inputs[1]
|
||
|
if (isinstance(grad, ops.Tensor) and
|
||
|
_ShapesFullySpecifiedAndEqual(x, y, grad)):
|
||
|
return grad, grad
|
||
|
sx = array_ops.shape(x)
|
||
|
sy = array_ops.shape(y)
|
||
|
rx, ry = gen_array_ops.broadcast_gradient_args(sx, sy)
|
||
|
return (array_ops.reshape(math_ops.reduce_sum(grad, rx), sx),
|
||
|
array_ops.reshape(math_ops.reduce_sum(grad, ry), sy))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Sub")
|
||
|
def _SubGrad(op, grad):
|
||
|
"""Gradient for Sub."""
|
||
|
x = op.inputs[0]
|
||
|
y = op.inputs[1]
|
||
|
if (isinstance(grad, ops.Tensor) and
|
||
|
_ShapesFullySpecifiedAndEqual(x, y, grad)):
|
||
|
return grad, -grad
|
||
|
sx = array_ops.shape(x)
|
||
|
sy = array_ops.shape(y)
|
||
|
rx, ry = gen_array_ops.broadcast_gradient_args(sx, sy)
|
||
|
return (array_ops.reshape(math_ops.reduce_sum(grad, rx), sx),
|
||
|
array_ops.reshape(-math_ops.reduce_sum(grad, ry), sy))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Mul")
|
||
|
def _MulGrad(op, grad):
|
||
|
"""The gradient of scalar multiplication."""
|
||
|
x = op.inputs[0]
|
||
|
y = op.inputs[1]
|
||
|
if (isinstance(grad, ops.Tensor) and
|
||
|
_ShapesFullySpecifiedAndEqual(x, y, grad) and
|
||
|
grad.dtype in (dtypes.int32, dtypes.float32)):
|
||
|
return gen_math_ops.mul(grad, y), gen_math_ops.mul(grad, x)
|
||
|
assert x.dtype.base_dtype == y.dtype.base_dtype, (x.dtype, " vs. ", y.dtype)
|
||
|
sx = array_ops.shape(x)
|
||
|
sy = array_ops.shape(y)
|
||
|
rx, ry = gen_array_ops.broadcast_gradient_args(sx, sy)
|
||
|
x = math_ops.conj(x)
|
||
|
y = math_ops.conj(y)
|
||
|
return (array_ops.reshape(
|
||
|
math_ops.reduce_sum(gen_math_ops.mul(grad, y), rx), sx),
|
||
|
array_ops.reshape(
|
||
|
math_ops.reduce_sum(gen_math_ops.mul(x, grad), ry), sy))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Div")
|
||
|
def _DivGrad(op, grad):
|
||
|
"""The gradient for the Div operator."""
|
||
|
x = op.inputs[0]
|
||
|
y = op.inputs[1]
|
||
|
sx = array_ops.shape(x)
|
||
|
sy = array_ops.shape(y)
|
||
|
rx, ry = gen_array_ops.broadcast_gradient_args(sx, sy)
|
||
|
x = math_ops.conj(x)
|
||
|
y = math_ops.conj(y)
|
||
|
return (array_ops.reshape(math_ops.reduce_sum(math_ops.div(grad, y), rx), sx),
|
||
|
array_ops.reshape(
|
||
|
math_ops.reduce_sum(grad * math_ops.div(math_ops.div(-x, y), y),
|
||
|
ry), sy))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("FloorDiv")
|
||
|
def _FloorDivGrad(_, unused_grad):
|
||
|
"""The gradient for the FloorDiv operator."""
|
||
|
return None, None
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("FloorMod")
|
||
|
def _FloorModGrad(op, grad):
|
||
|
"""Returns grad * (1, -floor(x/y))."""
|
||
|
x = math_ops.conj(op.inputs[0])
|
||
|
y = math_ops.conj(op.inputs[1])
|
||
|
|
||
|
sx = array_ops.shape(x)
|
||
|
sy = array_ops.shape(y)
|
||
|
rx, ry = gen_array_ops.broadcast_gradient_args(sx, sy)
|
||
|
floor_xy = math_ops.floor_div(x, y)
|
||
|
gx = array_ops.reshape(math_ops.reduce_sum(grad, rx), sx)
|
||
|
gy = array_ops.reshape(
|
||
|
math_ops.reduce_sum(grad * math_ops.negative(floor_xy), ry), sy)
|
||
|
return gx, gy
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("TruncateDiv")
|
||
|
def _TruncateDivGrad(_, unused_grad):
|
||
|
return None, None
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("RealDiv")
|
||
|
def _RealDivGrad(op, grad):
|
||
|
"""RealDiv op gradient."""
|
||
|
x = op.inputs[0]
|
||
|
y = op.inputs[1]
|
||
|
sx = array_ops.shape(x)
|
||
|
sy = array_ops.shape(y)
|
||
|
rx, ry = gen_array_ops.broadcast_gradient_args(sx, sy)
|
||
|
x = math_ops.conj(x)
|
||
|
y = math_ops.conj(y)
|
||
|
return (array_ops.reshape(
|
||
|
math_ops.reduce_sum(math_ops.realdiv(grad, y), rx), sx),
|
||
|
array_ops.reshape(
|
||
|
math_ops.reduce_sum(
|
||
|
grad * math_ops.realdiv(math_ops.realdiv(-x, y), y), ry), sy))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Pow")
|
||
|
def _PowGrad(op, grad):
|
||
|
"""Returns grad * (y*x^(y-1), z*log(x))."""
|
||
|
x = op.inputs[0]
|
||
|
y = op.inputs[1]
|
||
|
z = op.outputs[0]
|
||
|
sx = array_ops.shape(x)
|
||
|
sy = array_ops.shape(y)
|
||
|
rx, ry = gen_array_ops.broadcast_gradient_args(sx, sy)
|
||
|
x = math_ops.conj(x)
|
||
|
y = math_ops.conj(y)
|
||
|
z = math_ops.conj(z)
|
||
|
gx = array_ops.reshape(
|
||
|
math_ops.reduce_sum(grad * y * math_ops.pow(x, y - 1), rx), sx)
|
||
|
# Avoid false singularity at x = 0
|
||
|
if x.dtype.is_complex:
|
||
|
# real(x) < 0 is fine for the complex case
|
||
|
log_x = array_ops.where(
|
||
|
math_ops.not_equal(x, 0), math_ops.log(x), array_ops.zeros_like(x))
|
||
|
else:
|
||
|
# There's no sensible real value to return if x < 0, so return 0
|
||
|
log_x = array_ops.where(x > 0, math_ops.log(x), array_ops.zeros_like(x))
|
||
|
gy = array_ops.reshape(math_ops.reduce_sum(grad * z * log_x, ry), sy)
|
||
|
return gx, gy
|
||
|
|
||
|
|
||
|
def _MaximumMinimumGrad(op, grad, selector_op):
|
||
|
"""Factor out the code for the gradient of Maximum or Minimum."""
|
||
|
x = op.inputs[0]
|
||
|
y = op.inputs[1]
|
||
|
gdtype = grad.dtype
|
||
|
sx = array_ops.shape(x)
|
||
|
sy = array_ops.shape(y)
|
||
|
gradshape = array_ops.shape(grad)
|
||
|
zeros = array_ops.zeros(gradshape, gdtype)
|
||
|
xmask = selector_op(x, y)
|
||
|
rx, ry = gen_array_ops.broadcast_gradient_args(sx, sy)
|
||
|
xgrad = array_ops.where(xmask, grad, zeros)
|
||
|
ygrad = array_ops.where(xmask, zeros, grad)
|
||
|
gx = array_ops.reshape(math_ops.reduce_sum(xgrad, rx), sx)
|
||
|
gy = array_ops.reshape(math_ops.reduce_sum(ygrad, ry), sy)
|
||
|
return (gx, gy)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Maximum")
|
||
|
def _MaximumGrad(op, grad):
|
||
|
"""Returns grad*(x > y, x <= y) with type of grad."""
|
||
|
return _MaximumMinimumGrad(op, grad, math_ops.greater_equal)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Minimum")
|
||
|
def _MinimumGrad(op, grad):
|
||
|
"""Returns grad*(x < y, x >= y) with type of grad."""
|
||
|
return _MaximumMinimumGrad(op, grad, math_ops.less_equal)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("SquaredDifference")
|
||
|
def _SquaredDifferenceGrad(op, grad):
|
||
|
"""Returns the gradient for (x-y)^2."""
|
||
|
x = op.inputs[0]
|
||
|
y = op.inputs[1]
|
||
|
sx = array_ops.shape(x)
|
||
|
sy = array_ops.shape(y)
|
||
|
rx, ry = gen_array_ops.broadcast_gradient_args(sx, sy)
|
||
|
with ops.control_dependencies([grad]):
|
||
|
# The parens ensure that if grad is IndexedSlices, it'll get multiplied by
|
||
|
# Tensor (not a number like 2.0) which causes it to convert to Tensor.
|
||
|
x_grad = math_ops.scalar_mul(2.0, grad) * (x - y)
|
||
|
return (array_ops.reshape(math_ops.reduce_sum(x_grad, rx), sx),
|
||
|
-array_ops.reshape(math_ops.reduce_sum(x_grad, ry), sy))
|
||
|
|
||
|
|
||
|
# Logical operations have no gradients.
|
||
|
ops.NotDifferentiable("Less")
|
||
|
ops.NotDifferentiable("LessEqual")
|
||
|
ops.NotDifferentiable("Greater")
|
||
|
ops.NotDifferentiable("GreaterEqual")
|
||
|
ops.NotDifferentiable("Equal")
|
||
|
ops.NotDifferentiable("ApproximateEqual")
|
||
|
ops.NotDifferentiable("NotEqual")
|
||
|
ops.NotDifferentiable("LogicalAnd")
|
||
|
ops.NotDifferentiable("LogicalOr")
|
||
|
ops.NotDifferentiable("LogicalNot")
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Select")
|
||
|
def _SelectGrad(op, grad):
|
||
|
c = op.inputs[0]
|
||
|
x = op.inputs[1]
|
||
|
zeros = array_ops.zeros_like(x)
|
||
|
return (None, array_ops.where(c, grad, zeros), array_ops.where(
|
||
|
c, zeros, grad))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("MatMul")
|
||
|
def _MatMulGrad(op, grad):
|
||
|
"""Gradient for MatMul."""
|
||
|
|
||
|
t_a = op.get_attr("transpose_a")
|
||
|
t_b = op.get_attr("transpose_b")
|
||
|
a = math_ops.conj(op.inputs[0])
|
||
|
b = math_ops.conj(op.inputs[1])
|
||
|
if not t_a and not t_b:
|
||
|
grad_a = gen_math_ops.mat_mul(grad, b, transpose_b=True)
|
||
|
grad_b = gen_math_ops.mat_mul(a, grad, transpose_a=True)
|
||
|
elif not t_a and t_b:
|
||
|
grad_a = gen_math_ops.mat_mul(grad, b)
|
||
|
grad_b = gen_math_ops.mat_mul(grad, a, transpose_a=True)
|
||
|
elif t_a and not t_b:
|
||
|
grad_a = gen_math_ops.mat_mul(b, grad, transpose_b=True)
|
||
|
grad_b = gen_math_ops.mat_mul(a, grad)
|
||
|
elif t_a and t_b:
|
||
|
grad_a = gen_math_ops.mat_mul(b, grad, transpose_a=True, transpose_b=True)
|
||
|
grad_b = gen_math_ops.mat_mul(grad, a, transpose_a=True, transpose_b=True)
|
||
|
return grad_a, grad_b
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("SparseMatMul")
|
||
|
def _SparseMatMulGrad(op, grad):
|
||
|
"""Gradient for SparseMatMul."""
|
||
|
|
||
|
t_a = op.get_attr("transpose_a")
|
||
|
t_b = op.get_attr("transpose_b")
|
||
|
is_sparse = {
|
||
|
op.inputs[0]: op.get_attr("a_is_sparse"),
|
||
|
op.inputs[1]: op.get_attr("b_is_sparse"),
|
||
|
# Use heuristic to figure out if grad might be sparse
|
||
|
grad: not context.executing_eagerly() and (grad.op.type == "ReluGrad")
|
||
|
}
|
||
|
|
||
|
def _SparseMatMul(t1, t2, out_dtype, transpose_a=False, transpose_b=False):
|
||
|
"""Helper function to create SparseMatMul op."""
|
||
|
|
||
|
assert t1 in is_sparse and t2 in is_sparse
|
||
|
t1_sparse = is_sparse[t1]
|
||
|
t2_sparse = is_sparse[t2]
|
||
|
if transpose_b:
|
||
|
t2 = array_ops.transpose(t2)
|
||
|
transpose_b = False
|
||
|
prod = math_ops.matmul(
|
||
|
t1,
|
||
|
t2,
|
||
|
transpose_a=transpose_a,
|
||
|
transpose_b=transpose_b,
|
||
|
a_is_sparse=t1_sparse,
|
||
|
b_is_sparse=t2_sparse)
|
||
|
if prod.dtype != out_dtype:
|
||
|
prod = math_ops.cast(prod, out_dtype)
|
||
|
return prod
|
||
|
|
||
|
dtype_a = op.inputs[0].dtype
|
||
|
dtype_b = op.inputs[1].dtype
|
||
|
if not t_a and not t_b:
|
||
|
return (_SparseMatMul(grad, op.inputs[1], dtype_a, transpose_b=True),
|
||
|
_SparseMatMul(op.inputs[0], grad, dtype_b, transpose_a=True))
|
||
|
elif not t_a and t_b:
|
||
|
return (_SparseMatMul(grad, op.inputs[1], dtype_a),
|
||
|
_SparseMatMul(grad, op.inputs[0], dtype_b, transpose_a=True))
|
||
|
elif t_a and not t_b:
|
||
|
return (_SparseMatMul(op.inputs[1], grad, dtype_a, transpose_b=True),
|
||
|
_SparseMatMul(op.inputs[0], grad, dtype_b))
|
||
|
elif t_a and t_b:
|
||
|
return (_SparseMatMul(
|
||
|
op.inputs[1], grad, dtype_a, transpose_a=True, transpose_b=True),
|
||
|
_SparseMatMul(
|
||
|
grad, op.inputs[0], dtype_b, transpose_a=True,
|
||
|
transpose_b=True))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Floor")
|
||
|
def _FloorGrad(_, unused_grad):
|
||
|
return [None]
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Ceil")
|
||
|
def _CeilGrad(_, unused_grad):
|
||
|
return [None]
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Round")
|
||
|
def _RoundGrad(_, unused_grad):
|
||
|
return [None]
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Rint")
|
||
|
def _RintGrad(_, unused_grad):
|
||
|
# the gradient of Rint is zero
|
||
|
return [None]
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("BatchMatMul")
|
||
|
def _BatchMatMul(op, grad):
|
||
|
"""Returns the gradient of x and y given the gradient of x * y."""
|
||
|
x = op.inputs[0]
|
||
|
y = op.inputs[1]
|
||
|
adj_x = op.get_attr("adj_x")
|
||
|
adj_y = op.get_attr("adj_y")
|
||
|
|
||
|
if not adj_x:
|
||
|
if not adj_y:
|
||
|
grad_x = math_ops.matmul(grad, y, adjoint_a=False, adjoint_b=True)
|
||
|
grad_y = math_ops.matmul(x, grad, adjoint_a=True, adjoint_b=False)
|
||
|
else:
|
||
|
grad_x = math_ops.matmul(grad, y, adjoint_a=False, adjoint_b=False)
|
||
|
grad_y = math_ops.matmul(grad, x, adjoint_a=True, adjoint_b=False)
|
||
|
else:
|
||
|
if not adj_y:
|
||
|
grad_x = math_ops.matmul(y, grad, adjoint_a=False, adjoint_b=True)
|
||
|
grad_y = math_ops.matmul(x, grad, adjoint_a=False, adjoint_b=False)
|
||
|
else:
|
||
|
grad_x = math_ops.matmul(y, grad, adjoint_a=True, adjoint_b=True)
|
||
|
grad_y = math_ops.matmul(grad, x, adjoint_a=True, adjoint_b=True)
|
||
|
|
||
|
return grad_x, grad_y
|
||
|
|
||
|
|
||
|
ops.NotDifferentiable("Range")
|
||
|
ops.NotDifferentiable("LinSpace")
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Complex")
|
||
|
def _ComplexGrad(op, grad):
|
||
|
"""Returns the real and imaginary components of 'grad', respectively."""
|
||
|
x = op.inputs[0]
|
||
|
y = op.inputs[1]
|
||
|
sx = array_ops.shape(x)
|
||
|
sy = array_ops.shape(y)
|
||
|
rx, ry = gen_array_ops.broadcast_gradient_args(sx, sy)
|
||
|
return (array_ops.reshape(math_ops.reduce_sum(math_ops.real(grad), rx), sx),
|
||
|
array_ops.reshape(math_ops.reduce_sum(math_ops.imag(grad), ry), sy))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Real")
|
||
|
def _RealGrad(_, grad):
|
||
|
"""Returns 'grad' as the real part and set the imaginary part 0."""
|
||
|
zero = constant_op.constant(0, dtype=grad.dtype)
|
||
|
return math_ops.complex(grad, zero)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Imag")
|
||
|
def _ImagGrad(_, grad):
|
||
|
"""Returns 'grad' as the imaginary part and set the real part 0."""
|
||
|
zero = constant_op.constant(0, dtype=grad.dtype)
|
||
|
return math_ops.complex(zero, grad)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Angle")
|
||
|
def _AngleGrad(op, grad):
|
||
|
"""Returns -grad / (Im(x) + iRe(x))"""
|
||
|
x = op.inputs[0]
|
||
|
with ops.control_dependencies([grad]):
|
||
|
re = math_ops.real(x)
|
||
|
im = math_ops.imag(x)
|
||
|
z = math_ops.reciprocal(math_ops.complex(im, re))
|
||
|
zero = constant_op.constant(0, dtype=grad.dtype)
|
||
|
complex_grad = math_ops.complex(grad, zero)
|
||
|
return -complex_grad * z
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Conj")
|
||
|
def _ConjGrad(_, grad):
|
||
|
"""Returns the complex conjugate of grad."""
|
||
|
return math_ops.conj(grad)
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("ComplexAbs")
|
||
|
def _ComplexAbsGrad(op, grad):
|
||
|
"""Returns the gradient of ComplexAbs."""
|
||
|
# TODO(b/27786104): The cast to complex could be removed once arithmetic
|
||
|
# supports mixtures of complex64 and real values.
|
||
|
return (math_ops.complex(grad, array_ops.zeros_like(grad)) * math_ops.sign(
|
||
|
op.inputs[0]))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Cast")
|
||
|
def _CastGrad(op, grad):
|
||
|
t = [
|
||
|
dtypes.float16, dtypes.float32, dtypes.float64, dtypes.bfloat16,
|
||
|
dtypes.complex64, dtypes.complex128
|
||
|
]
|
||
|
src_type = op.inputs[0].dtype.base_dtype
|
||
|
dst_type = grad.dtype.base_dtype
|
||
|
if src_type in t and dst_type in t:
|
||
|
return math_ops.cast(grad, src_type)
|
||
|
else:
|
||
|
return None
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Cross")
|
||
|
def _CrossGrad(op, grad):
|
||
|
u = op.inputs[0]
|
||
|
v = op.inputs[1]
|
||
|
return (math_ops.cross(v, grad), math_ops.cross(grad, u))
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Cumsum")
|
||
|
def _CumsumGrad(op, grad):
|
||
|
axis = op.inputs[1]
|
||
|
exclusive = op.get_attr("exclusive")
|
||
|
reverse = op.get_attr("reverse")
|
||
|
return [
|
||
|
math_ops.cumsum(grad, axis, exclusive=exclusive, reverse=not reverse),
|
||
|
None
|
||
|
]
|
||
|
|
||
|
|
||
|
@ops.RegisterGradient("Cumprod")
|
||
|
def _CumprodGrad(op, grad):
|
||
|
x = op.inputs[0]
|
||
|
axis = op.inputs[1]
|
||
|
exclusive = op.get_attr("exclusive")
|
||
|
reverse = op.get_attr("reverse")
|
||
|
|
||
|
# TODO This fails when x contains 0 and should be fixed
|
||
|
prod = math_ops.cumprod(x, axis, exclusive=exclusive, reverse=reverse)
|
||
|
out = math_ops.cumsum(
|
||
|
prod * grad, axis, exclusive=exclusive, reverse=not reverse)
|
||
|
return [out / x, None]
|