1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
|
# 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.
# ==============================================================================
"""Tests for SparsemaxOp."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from tensorflow.contrib.sparsemax import sparsemax
from tensorflow.python.ops import gradient_checker
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import gradients_impl
from tensorflow.python.framework import constant_op
from tensorflow.python.platform import test
test_obs = 10
class SparsemaxTest(test.TestCase):
def _np_sparsemax(self, z):
z = z - np.mean(z, axis=1)[:, np.newaxis]
# sort z
z_sorted = np.sort(z, axis=1)[:, ::-1]
# calculate k(z)
z_cumsum = np.cumsum(z_sorted, axis=1)
k = np.arange(1, z.shape[1] + 1)
z_check = 1 + k * z_sorted > z_cumsum
# use argmax to get the index by row as .nonzero() doesn't
# take an axis argument. np.argmax return the first index, but the last
# index is required here, use np.flip to get the last index and
# `z.shape[axis]` to compensate for np.flip afterwards.
k_z = z.shape[1] - np.argmax(z_check[:, ::-1], axis=1)
# calculate tau(z)
tau_sum = z_cumsum[np.arange(0, z.shape[0]), k_z - 1]
tau_z = ((tau_sum - 1) / k_z).reshape(-1, 1)
# calculate p
return np.maximum(0, z - tau_z)
def _np_sparsemax_grad(self, z):
# chain rule
grad = np.ones_like(z)
# Construct S(z)
probability = self._np_sparsemax(z)
support = probability > 0
# Calculate \hat{v}, which will be a vector (scalar for each z)
v_hat = np.sum(grad * support, axis=1) / np.sum(support, axis=1)
# Calculates J(z) * v
return support * (grad - v_hat[:, np.newaxis])
def _tf_sparsemax(self, z, dtype, use_gpu):
with self.test_session(use_gpu=use_gpu):
tf_sparsemax_op = sparsemax(z.astype(dtype))
tf_sparsemax_out = tf_sparsemax_op.eval()
return tf_sparsemax_op, tf_sparsemax_out
def _test_sparsemax_against_numpy(self, dtype, random, use_gpu):
"""check sparsemax kernel against numpy"""
z = random.uniform(low=-3, high=3, size=(test_obs, 10))
tf_sparsemax_op, tf_sparsemax_out = self._tf_sparsemax(z, dtype, use_gpu)
p_sparemax = self._np_sparsemax(z).astype(dtype)
self.assertAllCloseAccordingToType(p_sparemax, tf_sparsemax_out,
half_atol=5e-3)
self.assertShapeEqual(p_sparemax, tf_sparsemax_op)
def _test_sparsemax_of_zero(self, dtype, random, use_gpu):
"""check sparsemax proposition 1, part 1"""
z = np.zeros((1, 10))
tf_sparsemax_op, tf_sparsemax_out = self._tf_sparsemax(z, dtype, use_gpu)
p_sparemax = np.ones_like(z, dtype=dtype) / z.size
self.assertAllCloseAccordingToType(p_sparemax, tf_sparsemax_out)
self.assertShapeEqual(p_sparemax, tf_sparsemax_op)
def _test_sparsemax_of_inf(self, dtype, random, use_gpu):
"""check sparsemax proposition 1, part 2"""
z = random.uniform(low=-3, high=3, size=(test_obs, 10))
# assume |A(z)| = 1, as z is continues random
z_sort_arg = np.argsort(z, axis=1)[:, ::-1]
z_sort = np.sort(z, axis=-1)[:, ::-1]
gamma_z = z_sort[:, 0] - z_sort[:, 1]
epsilon = (0.99 * gamma_z * 1).reshape(-1, 1)
# construct the expected 1_A(z) array
p_expected = np.zeros((test_obs, 10), dtype=dtype)
p_expected[np.arange(0, test_obs), z_sort_arg[:, 0]] = 1
tf_sparsemax_op, tf_sparsemax_out = self._tf_sparsemax(
(1 / epsilon) * z, dtype, use_gpu
)
self.assertAllCloseAccordingToType(p_expected, tf_sparsemax_out)
self.assertShapeEqual(p_expected, tf_sparsemax_op)
def _test_constant_add(self, dtype, random, use_gpu):
"""check sparsemax proposition 2"""
z = random.uniform(low=-3, high=3, size=(test_obs, 10)).astype(dtype)
c = random.uniform(low=-3, high=3, size=(test_obs, 1)).astype(dtype)
_, tf_sparsemax_zpc = self._tf_sparsemax(
z + c, dtype, use_gpu
)
_, tf_sparsemax_z = self._tf_sparsemax(
z, dtype, use_gpu
)
self.assertAllCloseAccordingToType(tf_sparsemax_zpc, tf_sparsemax_z,
half_atol=5e-3)
def _test_permutation(self, dtype, random, use_gpu):
"""check sparsemax proposition 3"""
z = random.uniform(low=-3, high=3, size=(test_obs, 10))
_, p = self._tf_sparsemax(z, dtype, use_gpu)
for i in range(test_obs):
per = random.permutation(10)
tf_sparsemax_op, tf_sparsemax_out = self._tf_sparsemax(
z[i, per].reshape(1, -1), dtype, use_gpu
)
p_expected = p[i, per].reshape(1, -1)
self.assertAllCloseAccordingToType(p_expected, tf_sparsemax_out,
half_atol=5e-3)
self.assertShapeEqual(p_expected, tf_sparsemax_op)
def _test_diffrence(self, dtype, random, use_gpu):
"""check sparsemax proposition 4"""
z = random.uniform(low=-3, high=3, size=(test_obs, 10))
_, p = self._tf_sparsemax(z, dtype, use_gpu)
etol = {'float16': 1e-2, 'float32': 1e-6, 'float64': 1e-9}[dtype]
for val in range(0, test_obs):
for i in range(0, 10):
for j in range(0, 10):
# check condition, the obesite pair will be checked anyway
if z[val, i] > z[val, j]:
continue
self.assertTrue(
0 <= p[val, j] - p[val, i] <= z[val, j] - z[val, i] + etol,
"0 <= %.10f <= %.10f" % (
p[val, j] - p[val, i], z[val, j] - z[val, i] + etol
)
)
def _test_two_dimentional(self, dtype, random, use_gpu):
"""check two dimentation sparsemax case"""
t = np.linspace(-2, 2, test_obs, dtype=dtype)
z = np.vstack([
t, np.zeros(test_obs, dtype=dtype)
]).T
tf_sparsemax_op, tf_sparsemax_out = self._tf_sparsemax(z, dtype, use_gpu)
p0_expected = np.select([t < -1, t <= 1, t > 1], [0, (t + 1) / 2, 1])
self.assertAllCloseAccordingToType(p0_expected, tf_sparsemax_out[:, 0])
self.assertAllCloseAccordingToType(1 - p0_expected, tf_sparsemax_out[:, 1])
self.assertShapeEqual(z, tf_sparsemax_op)
def _test_gradient_against_estimate(self, dtype, random, use_gpu):
"""check sparsemax Rop, against estimated Rop"""
z = random.uniform(low=-3, high=3, size=(test_obs, 10)).astype(dtype)
logits = array_ops.placeholder(dtype, name='z')
sparsemax_op = sparsemax(logits)
with self.test_session(use_gpu=use_gpu):
err = gradient_checker.compute_gradient_error(
logits, z.shape,
sparsemax_op, z.shape,
x_init_value=z, delta=1e-9
)
self.assertLess(err, 1e-4)
def _test_gradient_against_numpy(self, dtype, random, use_gpu):
"""check sparsemax Rop, against numpy Rop"""
z = random.uniform(low=-3, high=3, size=(test_obs, 10)).astype(dtype)
logits = constant_op.constant(z, name='z')
sparsemax_op = sparsemax(logits)
sparsemax_grad_op = gradients_impl.gradients(sparsemax_op, [logits])[0]
with self.test_session(use_gpu=use_gpu):
tf_grad = sparsemax_grad_op.eval()
np_grad = self._np_sparsemax_grad(z)
self.assertAllCloseAccordingToType(np_grad, tf_grad)
self.assertShapeEqual(np_grad, sparsemax_grad_op)
def _test_dtype(self, dtype):
random = np.random.RandomState(1)
self._test_sparsemax_against_numpy(dtype, random, use_gpu=False)
self._test_sparsemax_of_zero(dtype, random, use_gpu=False)
self._test_sparsemax_of_inf(dtype, random, use_gpu=False)
self._test_constant_add(dtype, random, use_gpu=False)
self._test_permutation(dtype, random, use_gpu=False)
self._test_diffrence(dtype, random, use_gpu=False)
self._test_two_dimentional(dtype, random, use_gpu=False)
# sparsemax is not a smooth function so gradient estimation is only
# possibol for float64.
if dtype == 'float64':
self._test_gradient_against_estimate(dtype, random, use_gpu=False)
self._test_gradient_against_numpy(dtype, random, use_gpu=False)
def testFloat(self):
self._test_dtype('float32')
def testDouble(self):
self._test_dtype('float64')
if __name__ == "__main__":
test.main()
|
