1 /*
2 * Copyright (C) 2018 The Android Open Source Project
3 *
4 * Licensed under the Apache License, Version 2.0 (the "License");
5 * you may not use this file except in compliance with the License.
6 * You may obtain a copy of the License at
7 *
8 * http://www.apache.org/licenses/LICENSE-2.0
9 *
10 * Unless required by applicable law or agreed to in writing, software
11 * distributed under the License is distributed on an "AS IS" BASIS,
12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13 * See the License for the specific language governing permissions and
14 * limitations under the License.
15 */
16
17 #include "lang_id/common/math/softmax.h"
18
19 #include <algorithm>
20 #include <vector>
21
22 #include "lang_id/common/lite_base/logging.h"
23 #include "lang_id/common/math/fastexp.h"
24
25 namespace libtextclassifier3 {
26 namespace mobile {
27
ComputeSoftmaxProbability(const std::vector<float> & scores,int label)28 float ComputeSoftmaxProbability(const std::vector<float> &scores, int label) {
29 if ((label < 0) || (static_cast<size_t>(label) >= scores.size())) {
30 SAFTM_LOG(ERROR) << "label " << label << " outside range "
31 << "[0, " << scores.size() << ")";
32 return 0.0f;
33 }
34
35 // Standard softmax formula for label's probability is
36 //
37 // exp(scores[label]) / sum_i exp(scores[i])
38 //
39 // We compute the mathematically equivalent
40 //
41 // 1 / (1 + sum_{i != label} exp(scores[i] - scores[label]))
42 //
43 // which saves two calls to exp().
44 const float label_score = scores[label];
45 float denominator = 1.0f; // Contribution of i == label.
46 for (size_t i = 0; i < scores.size(); ++i) {
47 if (static_cast<int>(i) == label) continue;
48 const float delta_score = scores[i] - label_score;
49
50 // TODO(salcianu): one can optimize the test below, to avoid any float
51 // operation: extract exponent (via bit mask + shift) and check it's >= 4.
52 if (fabs(delta_score) >= 16.0f) {
53 if (delta_score > 0.0f) {
54 // If delta_score >= 16, the denominator (e^delta_score + other positive
55 // terms) is very big and its inverse can be approximated with 0.
56 return 0.0f;
57 } else {
58 // If delta_score <= -16, then e^delta_score < 1.2e-7. Even if we have
59 // 1000 such labels i, their sum is < 1.2e-4 (which gets summed with
60 // 1.0f for i == label). Hence, we can approximate each such label with
61 // 0 and skip the call to VeryFastExp and the update to denominator.
62 continue;
63 }
64 }
65
66 // At this point, delta_score is in (-16.0, 16.0). For such values, vfexp
67 // works fine: no under/overflows (we have tests for that in fastexp_test).
68 // Also, even for 1000 labels, denominator will not overflow.
69 denominator += VeryFastExp(delta_score);
70 }
71 return 1.0f / denominator;
72 }
73
ComputeSoftmax(const std::vector<float> & scores,float alpha)74 std::vector<float> ComputeSoftmax(const std::vector<float> &scores,
75 float alpha) {
76 std::vector<float> softmax;
77 softmax.reserve(scores.size());
78 if (scores.empty()) {
79 return softmax;
80 }
81
82 std::vector<float> exp_scores;
83 exp_scores.reserve(scores.size());
84
85 // Find max value in "scores" vector and rescale to avoid overflows.
86 const float max_score = *std::max_element(scores.begin(), scores.end());
87 float denominator = 0;
88 for (const float score : scores) {
89 // See comments above in ComputeSoftmaxProbability for the reasoning behind
90 // this approximation.
91 const float delta_score = alpha * (score - max_score);
92 const float exp_score = delta_score < -16.0f ? 0 : VeryFastExp(delta_score);
93 exp_scores.push_back(exp_score);
94 denominator += exp_score;
95 }
96
97 for (size_t i = 0; i < scores.size(); ++i) {
98 softmax.push_back(exp_scores[i] / denominator);
99 }
100 return softmax;
101 }
102
103 } // namespace mobile
104 } // namespace nlp_saft
105