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
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
|
// Copyright 2016 Google Inc.
//
// 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.!
#include <algorithm>
#include <cfloat>
#include <cmath>
#include <functional>
#include <memory>
#include <numeric>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>
#include "normalizer.h"
#include "pretokenizer_for_training.h"
#include "sentencepiece_trainer.h"
#include "third_party/absl/memory/memory.h"
#include "third_party/esaxx/esa.hxx" // Suffix array library.
#include "unicode_script.h"
#include "unigram_model_trainer.h"
#include "util.h"
namespace sentencepiece {
namespace unigram {
namespace {
double Digamma(double x) {
double result = 0.0;
for (; x < 7; ++x) result -= 1 / x;
x -= 1.0 / 2.0;
const double xx = 1.0 / x;
const double xx2 = xx * xx;
const double xx4 = xx2 * xx2;
result += log(x) + (1.0 / 24.0) * xx2 - (7.0 / 960.0) * xx4 +
(31.0 / 8064.0) * xx4 * xx2 - (127.0 / 30720.0) * xx4 * xx4;
return result;
}
template <typename IT>
void ToLogProb(IT begin, IT end) {
float sum = 0.0;
for (auto it = begin; it != end; ++it) {
sum += it->second;
}
float logsum = std::log(static_cast<double>(sum));
for (auto it = begin; it != end; ++it) {
it->second = std::log(static_cast<double>(it->second)) - logsum;
}
}
} // namespace
TrainerModel::TrainerModel(const TrainerSpec &trainer_spec,
const NormalizerSpec &normalizer_spec)
: trainer_spec_(trainer_spec), normalizer_spec_(normalizer_spec) {}
TrainerModel::~TrainerModel() {}
const TrainerModel::SentencePieces &TrainerModel::GetSentencePieces() const {
return sentencepieces_;
}
void TrainerModel::SetSentencePieces(SentencePieces &&sentencepieces) {
sentencepieces_ = std::move(sentencepieces);
CHECK(!sentencepieces_.empty());
min_score_ = FLT_MAX;
model_proto_data_.Clear();
model_proto_ = &model_proto_data_;
std::vector<std::pair<absl::string_view, int>> pieces;
for (size_t i = 0; i < sentencepieces_.size(); ++i) {
const absl::string_view w = sentencepieces_[i].first; // piece
const float score = sentencepieces_[i].second; // score.
CHECK(!std::isnan(score));
pieces.emplace_back(w, i);
min_score_ = std::min(min_score_, score);
auto *piece = model_proto_data_.add_pieces();
piece->set_piece(w.data(), w.size());
piece->set_score(score);
}
BuildTrie(&pieces);
CHECK(status().ok());
}
// Returns seed sentencepieces for EM training.
template <typename node_int_type>
TrainerModel::SentencePieces Trainer::MakeSeedSentencePieces() const {
CHECK(!sentences_.empty());
CHECK(!required_chars_.empty());
// Pretokenizer applied only in training time.
// Pretokenizer is used as a constraint of piece extractions.
const auto *pretokenizer = SentencePieceTrainer::GetPretokenizerForTraining();
// Merges all sentences into one array with 0x0000 delimiter.
std::vector<char32> array;
std::unordered_map<std::string, int64> all_chars;
constexpr char32 kSentenceBoundary = 0x0000;
for (const auto &w : sentences_) {
const auto ut = string_util::UTF8ToUnicodeText(
pretokenizer ? pretokenizer->PreTokenize(w.first) : w.first);
for (const auto &c : ut) {
array.push_back(c);
if (c != kUNKChar && c != kSentenceBoundary) {
all_chars[string_util::UnicodeCharToUTF8(c)] += w.second;
}
}
}
const node_int_type n = array.size();
std::vector<node_int_type> SA(n); // suffix array
std::vector<node_int_type> L(n); // left boundaries of internal node
std::vector<node_int_type> R(n); // right boundaries of internal node
std::vector<node_int_type> D(n); // depths of internal node
// Makes a suffix array to extract all sub strings occurring
// more than 2 times in the sentence.
constexpr node_int_type kAlphabetSize = 0x110000; // All UCS4 range.
node_int_type node_num = 0;
LOG(INFO) << "Making suffix array...";
CHECK_EQ(0, esaxx(array.begin(), SA.begin(), L.begin(), R.begin(), D.begin(),
n, kAlphabetSize, node_num));
LOG(INFO) << "Extracting frequent sub strings...";
std::vector<std::pair<node_int_type, node_int_type>> substr_index;
for (node_int_type i = 0; i < node_num; ++i) {
const node_int_type offset = SA[L[i]];
const node_int_type len = D[i];
if (len <= 1) {
continue;
}
const char32 *begin = &array[0] + offset;
const char32 *end = &array[0] + offset + len;
// Skips if a substring contains a sentence boundary.
if (std::find(begin, end, kSentenceBoundary) != end) {
continue;
}
const UnicodeText uw(begin, end);
if (!IsValidSentencePiece(uw)) {
continue;
}
// character-wise coverage is the default score.
const node_int_type freq = R[i] - L[i];
const node_int_type score = freq * len;
substr_index.emplace_back(i, score);
}
// all_chars must be included in the seed sentencepieces.
TrainerModel::SentencePieces seed_sentencepieces;
for (const auto &it : Sorted(all_chars)) {
seed_sentencepieces.emplace_back(it);
}
// Sort by the coverage of sub strings.
for (const auto &p : Sorted(substr_index)) {
const node_int_type offset = SA[L[p.first]];
const node_int_type len = D[p.first];
CHECK_GT(len, 0);
const char32 *begin = &array[offset];
const char32 *end = &array[offset + len];
const UnicodeText uw(begin, end);
CHECK(IsValidSentencePiece(uw)); // just in case.
const std::string w = string_util::UnicodeTextToUTF8(uw);
if (seed_sentencepieces.size() ==
static_cast<size_t>(trainer_spec_.seed_sentencepiece_size())) {
break;
}
CHECK(!port::ContainsKey(all_chars, w));
seed_sentencepieces.emplace_back(w, p.second);
}
ToLogProb(seed_sentencepieces.begin(), seed_sentencepieces.end());
LOG(INFO) << "Initialized " << seed_sentencepieces.size()
<< " seed sentencepieces";
return seed_sentencepieces;
}
std::vector<float> Trainer::RunEStep(const TrainerModel &model, float *obj,
int64 *num_tokens) const {
std::vector<std::vector<float>> expected(trainer_spec_.num_threads());
std::vector<float> objs(trainer_spec_.num_threads(), 0.0);
std::vector<int64> ntokens(trainer_spec_.num_threads(), 0.0);
auto pool = absl::make_unique<ThreadPool>(trainer_spec_.num_threads());
pool->StartWorkers();
int64 all_sentence_freq = 0;
for (const auto &w : sentences_) {
all_sentence_freq += w.second;
}
// Executes E step in parallel
for (int n = 0; n < trainer_spec_.num_threads(); ++n) {
pool->Schedule([&, n]() {
Lattice lattice;
expected[n].resize(model.GetPieceSize(), 0.0);
for (size_t i = n; i < sentences_.size();
i += trainer_spec_.num_threads()) {
const std::string &w = sentences_[i].first;
const int64 freq = sentences_[i].second;
lattice.SetSentence(w);
model.PopulateNodes(&lattice);
const float Z = lattice.PopulateMarginal(freq, &expected[n]);
ntokens[n] += lattice.Viterbi().size();
CHECK(!std::isnan(Z))
<< "likelihood is NAN. Input sentence may be too long";
objs[n] -= Z / all_sentence_freq;
}
});
}
pool.reset(nullptr);
// Merges expectations
for (int n = 1; n < trainer_spec_.num_threads(); ++n) {
objs[0] += objs[n];
ntokens[0] += ntokens[n];
for (size_t k = 0; k < expected[0].size(); ++k) {
expected[0][k] += expected[n][k];
}
}
*obj = objs[0];
*num_tokens = ntokens[0];
CHECK(!std::isnan(*obj));
return expected[0];
}
TrainerModel::SentencePieces Trainer::RunMStep(
const TrainerModel &model, const std::vector<float> &expected) const {
const auto &sentencepieces = model.GetSentencePieces();
CHECK_EQ(sentencepieces.size(), expected.size());
TrainerModel::SentencePieces new_sentencepieces;
float sum = 0.0;
for (size_t i = 0; i < expected.size(); ++i) {
const float freq = expected[i];
// Filter infrequent sentencepieces here.
constexpr float kExpectedFrequencyThreshold = 0.5;
if (freq < kExpectedFrequencyThreshold) {
continue;
}
new_sentencepieces.emplace_back(sentencepieces[i].first, freq);
sum += freq;
}
// Here we do not use the original EM, but use the
// Bayesianified/DPified EM algorithm.
// https://cs.stanford.edu/~pliang/papers/tutorial-acl2007-talk.pdf
// This modification will act as a sparse prior.
const float logsum = Digamma(sum);
for (auto &w : new_sentencepieces) {
w.second = Digamma(w.second) - logsum;
}
return new_sentencepieces;
}
TrainerModel::SentencePieces Trainer::PruneSentencePieces(
const TrainerModel &model) const {
const auto &sentencepieces = model.GetSentencePieces();
Lattice lattice;
std::vector<bool> always_keep(sentencepieces.size(), true);
std::vector<std::vector<int>> alternatives(sentencepieces.size());
// First, segments the current sentencepieces to know
// how each sentencepiece is resegmented if this sentencepiece is removed
// from the vocabulary.
// To do so, we take the second best segmentation of sentencepiece[i].
// alternatives[i] stores the sequence of second best sentencepieces.
for (size_t i = 0; i < sentencepieces.size(); ++i) {
const auto &w = sentencepieces[i];
lattice.SetSentence(w.first);
model.PopulateNodes(&lattice);
const auto nbests = lattice.NBest(2);
if (nbests.size() == 1) {
// No second-best result is found. always keep this sentencepiece.
always_keep[i] = true;
continue;
} else if (nbests[0].size() >= 2) {
// Can safely remove this sentencepiece if its Viterbi path is split.
always_keep[i] = false;
} else if (nbests[0].size() == 1) {
always_keep[i] = true;
for (const auto *node : nbests[1]) {
alternatives[i].push_back(node->id);
}
}
}
// Second, segments all sentences to compute likelihood
// with a unigram language model. inverted[i] stores
// the set of sentence index where the sentencepieces[i] appears.
float vsum = 0.0;
std::vector<float> freq(sentencepieces.size(), 0.0);
std::vector<std::vector<int>> inverted(sentencepieces.size());
{
std::vector<float> vsums(trainer_spec_.num_threads(), 0.0);
std::vector<std::vector<float>> freqs(trainer_spec_.num_threads());
std::vector<std::vector<std::vector<int>>> inverteds(
trainer_spec_.num_threads());
auto pool = absl::make_unique<ThreadPool>(trainer_spec_.num_threads());
pool->StartWorkers();
for (int n = 0; n < trainer_spec_.num_threads(); ++n) {
freqs[n].resize(sentencepieces.size(), 0.0);
inverteds[n].resize(sentencepieces.size());
pool->Schedule([&, n]() {
Lattice lattice;
for (size_t i = n; i < sentences_.size();
i += trainer_spec_.num_threads()) {
const auto &w = sentences_[i];
lattice.SetSentence(w.first);
model.PopulateNodes(&lattice);
vsums[n] += w.second;
for (const auto *node : lattice.Viterbi()) {
if (node->id >= 0) {
freqs[n][node->id] += w.second;
inverteds[n][node->id].push_back(i);
}
}
}
});
}
pool.reset(nullptr);
for (int n = 0; n < trainer_spec_.num_threads(); ++n) {
vsum += vsums[n];
for (size_t i = 0; i < sentencepieces.size(); ++i) {
freq[i] += freqs[n][i];
std::copy(inverteds[n][i].begin(), inverteds[n][i].end(),
std::back_inserter(inverted[i]));
}
}
}
const float sum = std::accumulate(freq.begin(), freq.end(), 0.0);
const float logsum = std::log(static_cast<double>(sum));
std::vector<std::pair<int, float>> candidates;
TrainerModel::SentencePieces new_sentencepieces;
// Finally, computes how likely the LM likelihood is reduced if
// the sentencepiece[i] is removed from the vocabulary.
// Since the exact computation of loss is difficult, we compute the
// loss approximately by assuming that all sentencepiece[i] in the sentences
// are replaced with alternatives[i] when sentencepiece[i] is removed.
for (size_t i = 0; i < sentencepieces.size(); ++i) {
if (freq[i] == 0 || !always_keep[i]) {
// not found in Viterbi path. Can remove this entry safely.
continue;
} else if (alternatives[i].empty()) {
// no alternatives. Keeps this entry.
new_sentencepieces.push_back(sentencepieces[i]);
} else {
float F = 0.0; // the frequency of sentencepieces[i].
for (const int n : inverted[i]) {
F += sentences_[n].second;
}
F /= vsum; // normalizes by all sentence frequency.
// The logprob with the sentencepiece[i].
const float logprob_sp = std::log(static_cast<double>(freq[i])) - logsum;
// After removing the sentencepiece[i], its frequency freq[i] is
// re-assigned to alternatives.
// new_sum = current_sum - freq[i] + freq[i] * alternatives.size()
// = current_sum + freq[i] (alternatives - 1)
const float logsum_alt = std::log(
static_cast<double>(sum + freq[i] * (alternatives.size() - 1)));
// The frequencies of altenatives are increased by freq[i].
float logprob_alt = 0.0;
for (const int n : alternatives[i]) {
logprob_alt +=
(std::log(static_cast<double>(freq[n] + freq[i])) - logsum_alt);
}
// loss: the diff of likelihood after removing the sentencepieces[i].
const float loss = F * (logprob_sp - logprob_alt);
candidates.emplace_back(i, loss);
}
}
const int pruned_size =
std::max<int>(desired_vocab_size_,
trainer_spec_.shrinking_factor() * sentencepieces.size());
// Keeps trainer_spec_.shrinking_factor * sentencepieces.size() pieces.
// shrinking_factor is 0.75 by default.
for (const auto &w : Sorted(candidates)) {
if (new_sentencepieces.size() == static_cast<size_t>(pruned_size)) {
break;
}
new_sentencepieces.emplace_back(sentencepieces[w.first]);
}
return new_sentencepieces;
}
TrainerModel::SentencePieces Trainer::FinalizeSentencePieces(
const TrainerModel &model) const {
const auto &sentencepieces = model.GetSentencePieces();
std::unordered_map<std::string, float> final_sentencepieces;
std::unordered_map<std::string, float> sp(sentencepieces.begin(),
sentencepieces.end());
// required_chars_ must be included in the final sentencepieces.
float min_score_penalty = 0.0;
constexpr float kMinScorePenaltyDelta = 0.0001;
for (const auto &w : Sorted(required_chars_)) {
const std::string s = string_util::UnicodeCharToUTF8(w.first);
if (port::ContainsKey(sp, s)) {
final_sentencepieces[s] = sp[s];
} else {
// Add penalty to avoid required pieces from having the same score.
// Since the required_chars_ is sorted, frequent pieces have
// less penalties.
final_sentencepieces[s] = model.min_score() + min_score_penalty;
min_score_penalty += kMinScorePenaltyDelta;
}
}
const int vocab_size_size = trainer_spec_.vocab_size() - meta_pieces_.size();
CHECK_GT(vocab_size_size, 0);
// Then keeps sentencepieces with higher scores.
for (const auto &w : Sorted(sentencepieces)) {
if (port::ContainsKey(final_sentencepieces, w.first)) {
continue;
}
if (static_cast<size_t>(vocab_size_size) == final_sentencepieces.size()) {
break;
}
final_sentencepieces[w.first] = w.second;
}
return Sorted(final_sentencepieces);
}
util::Status Trainer::Train() {
RETURN_IF_ERROR(status());
CHECK_EQ_OR_RETURN(TrainerSpec::UNIGRAM, trainer_spec_.model_type());
CHECK_OR_RETURN(normalizer_spec_.escape_whitespaces());
TrainerModel model(trainer_spec_, normalizer_spec_);
RETURN_IF_ERROR(model.status());
RETURN_IF_ERROR(LoadSentences());
if (trainer_spec_.train_extremely_large_corpus()) {
auto seed_sentencepieces = MakeSeedSentencePieces<int64>();
model.SetSentencePieces(std::move(seed_sentencepieces));
} else {
auto seed_sentencepieces = MakeSeedSentencePieces<int32>();
model.SetSentencePieces(std::move(seed_sentencepieces));
}
if (trainer_spec_.split_by_whitespace()) {
SplitSentencesByWhitespace();
}
LOG(INFO) << "Using " << sentences_.size() << " sentences for EM training";
desired_vocab_size_ = static_cast<size_t>(trainer_spec_.vocab_size() * 1.1);
while (true) {
// Sub-EM iteration.
for (int iter = 0; iter < trainer_spec_.num_sub_iterations(); ++iter) {
// Executes E step
float objective = 0.0;
int64 num_tokens = 0;
const auto expected = RunEStep(model, &objective, &num_tokens);
// Executes M step.
auto new_sentencepieces = RunMStep(model, expected);
model.SetSentencePieces(std::move(new_sentencepieces));
LOG(INFO) << "EM sub_iter=" << iter << " size=" << model.GetPieceSize()
<< " obj=" << objective << " num_tokens=" << num_tokens
<< " num_tokens/piece="
<< 1.0 * num_tokens / model.GetPieceSize();
} // end of Sub EM iteration
// Stops the iteration when the size of sentences reaches to the
// desired symbol size.
if (model.GetPieceSize() <= desired_vocab_size_) {
break;
}
// Prunes pieces.
auto new_sentencepieces = PruneSentencePieces(model);
model.SetSentencePieces(std::move(new_sentencepieces));
} // end of EM iteration
// Finally, adjusts the size of sentencepices to be |vocab_size|.
final_pieces_ = FinalizeSentencePieces(model);
return Save();
}
} // namespace unigram
} // namespace sentencepiece
|