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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 op."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import nn
from tensorflow.python.platform import resource_loader
__all__ = ["sparsemax"]
def sparsemax(logits, name=None):
"""Computes sparsemax activations [1].
For each batch `i` and class `j` we have
sparsemax[i, j] = max(logits[i, j] - tau(logits[i, :]), 0)
[1]: https://arxiv.org/abs/1602.02068
Args:
logits: A `Tensor`. Must be one of the following types: `half`, `float32`,
`float64`.
name: A name for the operation (optional).
Returns:
A `Tensor`. Has the same type as `logits`.
"""
with ops.name_scope(name, "sparsemax", [logits]) as name:
logits = ops.convert_to_tensor(logits, name="logits")
obs = array_ops.shape(logits)[0]
dims = array_ops.shape(logits)[1]
z = logits - math_ops.reduce_mean(logits, axis=1)[:, array_ops.newaxis]
# sort z
z_sorted, _ = nn.top_k(z, k=dims)
# calculate k(z)
z_cumsum = math_ops.cumsum(z_sorted, axis=1)
k = math_ops.range(
1, math_ops.cast(dims, logits.dtype) + 1, dtype=logits.dtype)
z_check = 1 + k * z_sorted > z_cumsum
# because the z_check vector is always [1,1,...1,0,0,...0] finding the
# (index + 1) of the last `1` is the same as just summing the number of 1.
k_z = math_ops.reduce_sum(math_ops.cast(z_check, dtypes.int32), axis=1)
# calculate tau(z)
indices = array_ops.stack([math_ops.range(0, obs), k_z - 1], axis=1)
tau_sum = array_ops.gather_nd(z_cumsum, indices)
tau_z = (tau_sum - 1) / math_ops.cast(k_z, logits.dtype)
# calculate p
return math_ops.maximum(
math_ops.cast(0, logits.dtype), z - tau_z[:, array_ops.newaxis])
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