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# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Sparsemax Loss op."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import math_ops
__all__ = ["sparsemax_loss"]
def sparsemax_loss(logits, sparsemax, labels, name=None):
"""Computes sparsemax loss function [1].
[1]: https://arxiv.org/abs/1602.02068
Args:
logits: A `Tensor`. Must be one of the following types: `half`, `float32`,
`float64`.
sparsemax: A `Tensor`. Must have the same type as `logits`.
labels: A `Tensor`. Must have the same type as `logits`.
name: A name for the operation (optional).
Returns:
A `Tensor`. Has the same type as `logits`.
"""
with ops.name_scope(name, "sparsemax_loss",
[logits, sparsemax, labels]) as name:
logits = ops.convert_to_tensor(logits, name="logits")
sparsemax = ops.convert_to_tensor(sparsemax, name="sparsemax")
labels = ops.convert_to_tensor(labels, name="labels")
# In the paper, they call the logits z.
# A constant can be substracted from logits to make the algorithm
# more numerically stable in theory. However, there are really no major
# source numerical instability in this algorithm.
z = logits
# sum over support
# Use a conditional where instead of a multiplication to support z = -inf.
# If z = -inf, and there is no support (sparsemax = 0), a multiplication
# would cause 0 * -inf = nan, which is not correct in this case.
sum_s = array_ops.where(
math_ops.logical_or(sparsemax > 0, math_ops.is_nan(sparsemax)),
sparsemax * (z - 0.5 * sparsemax), array_ops.zeros_like(sparsemax))
# - z_k + ||q||^2
q_part = labels * (0.5 * labels - z)
# Fix the case where labels = 0 and z = -inf, where q_part would
# otherwise be 0 * -inf = nan. But since the lables = 0, no cost for
# z = -inf should be consideredself.
# The code below also coveres the case where z = inf. Howeverm in this
# caose the sparsemax will be nan, which means the sum_s will also be nan,
# therefor this case doesn't need addtional special treatment.
q_part_safe = array_ops.where(
math_ops.logical_and(math_ops.equal(labels, 0), math_ops.is_inf(z)),
array_ops.zeros_like(z), q_part)
return math_ops.reduce_sum(sum_s + q_part_safe, axis=1)
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