Noise Contrastive Estimation (NCE) is an approximation method that is used to work around the huge computational cost of large softmax layer. The basic idea is to convert the prediction problem into classification problem at training stage. It has been proved that these two criterions converges to the same minimal point as long as noise distribution is close enough to real one.
NCE bridges the gap between generative models and discriminative models, rather than simply speedup the softmax layer. With NCE, you can turn almost anything into posterior with less effort (I think).
Refs:
NCE:
http://www.cs.helsinki.fi/u/ahyvarin/papers/Gutmann10AISTATS.pdf
NCE on rnnlm:
https://pdfs.semanticscholar.org/144e/357b1339c27cce7a1e69f0899c21d8140c1f.pdf
A review of softmax speedup methods:
NCE vs. IS (Importance Sampling): Nce is a binary classification while IS is sort of multi-class classification problem.
NCE vs. GAN (Generative Adversarial Network):
In NCE, unigram distribution is usually used to approximate the noise distribution because it's fast to
sample from. Sampling from a unigram is equal to multinomial sampling, which is of complexity
Since the unigram distribution can be obtained before training and remains unchanged across training, some works are proposed to make use of this property to speedup the sampling procedure. Alias method is one of them.
By constructing data structures, alias method can reduce the sampling complexity from
Refs:
alias method:
Conventional NCE only perform the contrasting on linear(softmax) layer, that is, given an input of a
linear layer, the model outputs are
In this code base, I use a variant of generic NCE named full-NCE (f-NCE) to clarify. Unlike normal NCE, f-NCE samples the noises at input embedding.
Refs:
whole sentence language model by IBM (ICASSP2018)
Bi-LSTM language model by speechlab,SJTU (ICSLP2016?)
Conventional NCE requires different noise samples per data token. Such computational pattern is not fully GPU-efficient because it needs batched matrix multiplication. A trick is to share the noise samples across the whole mini-batch, thus sparse batched matrix multiplication is converted to more efficient dense matrix multiplication. The batched NCE is already supported by Tensorflow.
A more aggressive approach is to called self contrasting (named by myself). Instead of sampling from noise distribution, the noises are simply the other training tokens the within the same mini-batch.
Ref:
batched NCE
self contrasting:
https://www.isi.edu/natural-language/mt/simple-fast-noise.pdf
There's an example illustrating how to use the NCE module in example folder.
This example is forked from the pytorch/examples repo.
Please run pip install -r requirements first to see if you have the required python lib.
tqdmis used for process bar during trainingdillis a more flexible replacement for pickle
--nce: whether to use NCE as approximation--noise-ratio <50>: numbers of noise samples per batch, the noise is shared among the tokens in a single batch, for training speed.--norm-term <9>: the constant normalization termLn(z)--index-module <linear>: index module to use for NCE module (currently and available, does not support PPL calculating )--train: train or just evaluation existing model--vocab <None>: use vocabulary file if specified, otherwise use the words in train.txt--loss [full, nce, sampled, mix]: choose one of the loss type for training, the loss is converted tofullfor PPL evaluation automatically.
Run NCE criterion with linear module:
python main.py --cuda --noise-ratio 10 --norm-term 9 --nce --trainRun NCE criterion with gru module:
python main.py --cuda --noise-ratio 10 --norm-term 9 --nce --train --index-module gruRun conventional CE criterion:
python main.py --cuda --trainIt's a performance showcase. The dataset is not bundled in this repo however.
The model is trained on concatenated sentences,but the hidden states are not
passed across batches. An <s> is inserted between sentences. The model is
evaluated on <s> padded sentences separately.
Generally a model trained on concatenated sentences performs slightly worse than the one trained on separate sentences. But we saves 50% of training time by reducing the sentence padding operation.
- training samples: 2200000 sentences, 22403872 words
- built vocabulary size: ~30K
- 1080 Ti
- i7 7700K
- pytorch-0.4.0
- cuda-8.0
- cudnn-6.0.1
python main.py --train --batch-size 96 --cuda --loss nce --noise-ratio 500 --nhid 300 \
--emsize 300 --log-interval 1000 --nlayers 1 --dropout 0 --weight-decay 1e-8 \
--data data/swb --min-freq 3 --lr 2 --save nce-500-swb --concat- crossentropy: 6.5 mins/epoch (56K tokens/sec)
- nce: 2 mins/epoch (187K tokens/sec)
The rescore is performed on swbd 50-best, thanks to HexLee.
| training loss type | evaluation type | PPL | WER |
|---|---|---|---|
| 3gram | normed | ?? | 19.4 |
| CE(no concat) | normed(full) | 53 | 13.1 |
| CE | normed(full) | 55 | 13.3 |
| NCE | unnormed(NCE) | invalid | 13.4 |
| NCE | normed(full) | 55 | 13.4 |
| importance sample | normed(full) | 55 | 13.4 |
| importance sample | sampled(500) | invalid | 19.0(worse than w/o rescore) |
example/log/: some log files of this scriptsnce/: the NCE module wrappernce/nce_loss.py: the NCE lossnce/alias_multinomial.py: alias method samplingnce/index_linear.py: an index module used by NCE, as a replacement for normal Linear modulence/index_gru.py: an index module used by NCE, as a replacement for the whole language model module
sample.py: a simple script for NCE linear.example: a word langauge model sample to use NCE as loss.example/vocab.py: a wrapper for vocabulary objectexample/model.py: the wrapper of allnn.Modules.example/generic_model.py: the model wrapper for index_gru NCE moduleexample/main.py: entry pointexample/utils.py: some util functions for better code structure
This example trains a multi-layer LSTM on a language modeling task. By default, the training script uses the PTB dataset, provided.
python main.py --train --cuda --epochs 6 # Train a LSTM on PTB with CUDAThe model will automatically use the cuDNN backend if run on CUDA with cuDNN installed.
During training, if a keyboard interrupt (Ctrl-C) is received, training is stopped and the current model is evaluated against the test dataset.
The main.py script accepts the following arguments:
optional arguments:
-h, --help show this help message and exit
--data DATA location of the data corpus
--emsize EMSIZE size of word embeddings
--nhid NHID humber of hidden units per layer
--nlayers NLAYERS number of layers
--lr LR initial learning rate
--lr-decay learning rate decay when no progress is observed on validation set
--weight-decay weight decay(L2 normalization)
--clip CLIP gradient clipping
--epochs EPOCHS upper epoch limit
--batch-size N batch size
--dropout DROPOUT dropout applied to layers (0 = no dropout)
--seed SEED random seed
--cuda use CUDA
--log-interval N report interval
--save SAVE path to save the final model
--bptt max length of truncated bptt
--concat use concatenated sentence instead of individual sentence- 2019.09.09: Improve numeric stability by directly calculation on logits