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-In this problem set we train neural machine translation (NMT) systems -using end-to-end networks on the IWSLT-2016 dataset. This corpus -consists of Ted Talks translated between German and English. The -utterances of each language are aligned, which allows us to use it to -train translation systems. We implement (1) a sequence to sequence model -as described by (Sutskever et al., 2014); (2) an attention model as -introduced by (Bahdanau et. al., 2014) with dot-product attention -computation as per (Luong et al., 2015); (3) beam search to improve -translation quality, and; (4) visualizations of how the attention -mechanism makes a soft-alignment between words in the source and target -sentences. We also experiment with the effects of batch size, masking -padding, and teacher forcing on the validation set perplexity. - -Problem Description -=================== - -In machine translation, the objective is to translate sentences from a -source language into a target language. In NMT, we approach this task by -jointly training end-to-end deep neural networks to predict the -likelihood of a sequence of output target tokens given a sequence of -input tokens of a different language. More formally, we define machine -translation as translating a source sentence = ,, - = into a target sentence = ,, -= . Using this notation, we can define a translation system -as the function - -

- -where are the parameters of the model specifying the -probability distribution. We learn from data consisting of -aligned sentences in the source and target languages. In the case of -this problem set, German is our source language and English is our -target language. - -Models and Algorithms -===================== - -In the encoder-decoder framework, an encoder reads an input sequence -into a context vector and a decoder is trained to predict an output -token given the context vector and all previously predicted -tokens . In -this way, the decoder defines a probability distribution over a -translation . Formally, - -

- -During generation for unlabeled input sequences, tokens are usually -output until an end-of-sentence token is output or a specified maximum -length is reached. - -In the context of this homework, this conditional probability is modeled -using recurrent neural networks (RNN). With this being the case, we let - = - for simplicity where is the hidden state of -the RNN and is a nonlinear, possibly multi-layered function that -outputs the probability of (Neubig, 2017). - -Encoder-Decoder ---------------- - -Inspired by (Cho et al., 2014) and (Sutskever et al., 2014), the -name encoder-decoder comes from the idea that we can use a model of two -RNNs to translate between languages: one that processes an input -sequence and “encodes” its information as a vector of real numbers -(hidden state), and another that is used to “decode” this vector to -predict the corresponding target sequence . In particular if we let -the encoder be expressed as RNN(), then the decoder is -expressed as RNN() and we can represent the overall model -for time step as follows: - -

- -where is the source language embedding lookup, - is the encoder hidden state, -is the source language embedding lookup, is the -decoder hidden state, and is the softmax to turn -’s hidden state into a probability. - -Note that is initialized to and - = the encoder has seen all words in the -source sentence. In this setup, we are feeding the true target -as the input to the decoder for time step . This is known as teacher -forcing. When we are not employing teacher forcing, as is the case in -some of our experiments, -where = , the most likely output -token from the previous time step (). - -Attention Decoder ------------------ - -To incorporate attention into our decoder, we redefine the conditional -probability of to be - -

- -Here and unlike the formulation of in previous sections, the -probability is conditioned on a distinct context vector for each -target token . The context vector depends on a sequence of -annotations , , to which an encoder maps the input -sequence. The context vector is then computed as a weighted sum of -these annotations: - -

- -where - -

- -and - -

- -is an which scores how well the inputs around -position and the output at position match. The alignment model - is parametrized as a simple feedforward neural network that is -jointly trained with all other components of the translation system. -Note that the alignment is not a latent variable, which allows -backpropagation through this gradient due to its differentiability. -Intuitively, reflects the importance of with respect -to in deciding and generating . It is believed that -giving the decoder an attention mechanism relieves the encoder from -having to encode all information in the source sequence needed for -translation to a fixed-length vector (Bahdanau et al., 2014). - -Beam Search ------------ - -Since the model is only trained to predict the probability of the next -word at a given time step in the target sentence, a decoding procedure -is needed to produce an actual translation, where the goal is to -maximize the probability of all words in the target sentence: - -

- -The simplest approach is to proceed in a greedy fashion, taking the most -likely word under the model at each time step and feeding it back in as -the next input until the end-of-sentence token is produced: - -

- -This is not guaranteed to produce the highest-scoring sentence, though, -since in some cases the selection of a lower-probability word at a given -time-step will lead to downstream predictions that produce a -higher-scoring sentence overall. To account for this, we follow -(Sutskever et al., 2014) and use a beam search – instead of greedily -accumulating a single series of tokens across time-steps in the target -sentence, we instead keep track of a fixed-size set of candidate -decodings (the “beam”). At each step, we extend each candidate with all -words in the vocabulary, update the cumulative score for each new -candidate given the probabilities produced by the model, and then skim -off the highest-scoring candidates to keep the size of the beam -constant. (Otherwise it would be a breadth-first search of all possible -permutations.) After the new beam is pruned, any candidates ending with -the end-of-sentence token are removed from the beam and added to a set -of completed candidates, and the beam size is reduced by 1. This -continued until the beam is empty, and complete candidate sentences -have been produced. - -If the final set of candidate sentences is sorted on the summed -log-probabilities of each word, the procedure will strongly favor short -sentences, since the addition of each new word will drive down the joint -probability of the sentence. A range of strategies for length -normalization have been proposed, but we take the simplest approach, -which is to divide the total log-probability of the sentence by the -number of words to get an average per-word log-probability. - -

- -Following (Sutskever et al., 2014) we use beam size of 10. And, in the -interest of speed – when extending candidates with new words at each -time-step, we only consider the 1000 most frequent words under the -model, which gives a significant speedup at little or no cost in -accuracy. - -Experiments -=========== - -We experimented with a number of modifications to the baseline attention -model: - -1. In addition to the standard approach for calculating attention where - the hidden layer $h_t^e$ is dotted with the hidden states at each - time-step from the encoder: - - $\text{attn\_score}(H^{(f)}, h_t^{(e)}) := H_j^{(f) \intercal}h_t^{(e)}$ - - We also implemented the attention scoring as a multi-layer - perceptron as described by (Bahdanau et al., 2014): - - $$\text{attn\_score}(h_t^{(e)}, h_j^{(f)}) := w_{a2}^{\intercal} \operatorname*{tanh}(W_{a1}[h_t^{(e)};h_j^{(f)}])$$ - -2. We tried a range of learning rate schedulers – train for a fixed - number of epochs (4, 8, 10) and then decay by 0.5 each epoch after - that (as described in the reference model); decay by 0.5 every $N$ - epochs, where $N \in \{2, 3, 4\}$; and various values for the decay - ratio gamma. - -3. We implemented the decoder as a bidirectional LSTM as described by - (Bahdanau et al., 2014) which in theory should allow the encoder to - capture information about both the left- and right-hand contexts at - each time step. - -4. Last, we experimented with a wide range of hyperparameter settings: - - - Word embedding dimensions: 200, 300, 500. - - - LSTM hidden layers: 1, 2, 4. - - - LSTM hidden layer dimensions: 200, 500, 1000. - - - SGD and Adam optimizers. - - - Batch lengths of 32 and 64. - - - Clipping gradients to 5. - -Though we didn’t have the resources to conduct a full grid search across -all combinations of these architectures and parameters, our best -performing models used 2-layer LSTMs with dot-product attention. All -final models were optimized with SGD starting with a learning rate of 1. -Early stopping was used to identify the best-performing model on the -validation set. - -*Model* | *Accuracy* | -:---: | :---: | -Encoder-Decoder | 15.612 -Dot Attention – 300d embeddings, 500d LSTMs, Bidirectional encoder | 9.680 -Dot Attention – 500d embeddings, 1000d LSTMs | 9.672 -Dot Attention – 200d embeddings, 200d LSTMs | 9.636 -Dot Attention – 300d embeddings, 500d LSTMs | **9.501** - -Generally, we found that it was difficult to find a single learning rate -scheduler that worked well for different hyperparameter settings – a -decay rate that seemed to work well for the 500-unit LSTM seemed too -slow for the 200-unit model, etc. Given indefinite resources, ideally we -would run a broad grid search to pick the best model. - -See the appendix for visualizations of the attention weights and -comparisons between the translations produced by the beam coder and the -Google Translate predictions. - -Conclusion -========== - -We trained two classes of models – a basic encoder-decoder architecture -as described by (Sutskever et al., 2014) and a series of models that use -dot-product attention to give the decoder a more flexible representation -of the input. Though we experimented with more complex architectures – -bidirectional LSTMs and multilayer perceptrons for attention weighting – -our best-performing models used the basic dot-product attention. - -Attention visualizations -======================== - -We can visualize the dot-product attention by plotting the weights -assigned to the encoder hidden states for each step during decoding -(using greedy decoding, here). - -![image](att1.png) -![image](att2.png) -![image](att3.png) -![image](att4.png) -![image](att5.png) - -Translation examples -==================== - -We can compare the translations produced by the beam search decoder to -the predictions from Google translate: - -1. - **Source**: - `Arbeit kam später, Heiraten kam später, Kinder kamen später, selbst der Tod kam später.` - - - **Our model**: - `work came later , came later later , children came later later , even the death came later .` - - - **Google**: - `Work came later, marriages came later, children came later, even death came later` - -2. - **Source**: - `Das ist es , was Psychologen einen Aha-Moment nennen .` - - - **Our model**: `That ’s what psychologists call a call .` - - - **Google**: `That’s what psychologists call an aha moment.` - -3. - **Source**: `Dies ist nicht meine Meinung . Das sind Fakten .` - - - **Our model**: `This is not my opinion . These are facts .` - - - **Google**: `This is not my opinion. These are facts.` - -4. - **Source**: - `In den 20ern sollte man sich also weiterbilden über den Körper und die eigenen Möglichkeiten` - - - **Our model**: - `So in the , you should be thinking about the body and the own possibilities .` - - - **Google**: - `In the 20’s you should continue to educate yourself about the body and your own possibilities` - -5. - **Source**: `Wie würde eine solche Zukunft aussehen ?` - - - **Our model**: `What would such a future look like ?` - - - **Google**: `What would such a future look like?` - -References -========== - -Bahdanau, D., Cho, K. & Bengio, Y. Neural Machine Translation by Jointly -Learning to Align and Translate. doi:10.1146/annurev.neuro.26.041002.131047. 2014. - -Cho, K. et al. Learning Phrase Representations using RNN Encoder-Decoder -for Statistical Machine Translation. doi:10.3115/v1/D14-1179. 2014. - -Luong, M.-T., Pham, H. & Manning, C. D. Effective Approaches to -Attention-based Neural Machine Translation. doi:10.18653/v1/D15-1166. 2015. - -Neubig, G. Neural Machine Translation and Sequence-to-sequence Models: A -Tutorial. 2017. - -Sutskever, I., Vinyals, O. & Le, Q. V. Sequence to sequence learning -with neural networks. Advances in Neural Information Processing Systems -(NIPS), pages 3104–3112. 2014. diff --git a/README.tex.md b/README.tex.md index c0603df..d9fed0e 100644 --- a/README.tex.md +++ b/README.tex.md @@ -1,7 +1,7 @@ Introduction ============ -In this problem set we train neural machine translation (NMT) systems +In this repo we train neural machine translation (NMT) systems using end-to-end networks on the IWSLT-2016 dataset. This corpus consists of Ted Talks translated between German and English. The utterances of each language are aligned, which allows us to use it to @@ -153,7 +153,7 @@ The simplest approach is to proceed in a greedy fashion, taking the most likely word under the model at each time step and feeding it back in as the next input until the end-of-sentence token is produced: -$$\hat{e}_t = \operatorname*{argmax}_i p_{t,i}^{(e)}$$ +$$\hat{e}_t = \text{argmax}_i p_{t,i}^{(e)}$$ This is not guaranteed to produce the highest-scoring sentence, though, since in some cases the selection of a lower-probability word at a given @@ -181,7 +181,7 @@ normalization have been proposed, but we take the simplest approach, which is to divide the total log-probability of the sentence by the number of words to get an average per-word log-probability. -$$\hat{E} = \operatorname*{argmax}_E log P(E|F) / |E|$$ +$$\hat{E} = \text{argmax}_E log P(E|F) / |E|$$ Following (Sutskever et al., 2014) we use beam size of 10. And, in the interest of speed – when extending candidates with new words at each @@ -204,7 +204,7 @@ model: We also implemented the attention scoring as a multi-layer perceptron as described by (Bahdanau et al., 2014): - $$\text{attn\_score}(h_t^{(e)}, h_j^{(f)}) := w_{a2}^{\intercal} \operatorname*{tanh}(W_{a1}[h_t^{(e)};h_j^{(f)}])$$ + $$\text{attn\_score}(h_t^{(e)}, h_j^{(f)}) := w_{a2}^{\intercal} \text{tanh}(W_{a1}[h_t^{(e)};h_j^{(f)}])$$ 2. We tried a range of learning rate schedulers – train for a fixed number of epochs (4, 8, 10) and then decay by 0.5 each epoch after @@ -252,32 +252,7 @@ decay rate that seemed to work well for the 500-unit LSTM seemed too slow for the 200-unit model, etc. Given indefinite resources, ideally we would run a broad grid search to pick the best model. -See the appendix for visualizations of the attention weights and -comparisons between the translations produced by the beam coder and the -Google Translate predictions. - -Conclusion -========== - -We trained two classes of models – a basic encoder-decoder architecture -as described by (Sutskever et al., 2014) and a series of models that use -dot-product attention to give the decoder a more flexible representation -of the input. Though we experimented with more complex architectures – -bidirectional LSTMs and multilayer perceptrons for attention weighting – -our best-performing models used the basic dot-product attention. - -Attention visualizations -======================== - -We can visualize the dot-product attention by plotting the weights -assigned to the encoder hidden states for each step during decoding -(using greedy decoding, here). - -![image](att1.png) -![image](att2.png) -![image](att3.png) -![image](att4.png) -![image](att5.png) +See the following sections for visualizations of the attention weights and comparisons between the translations produced by the beam coder and the Google Translate predictions. Translation examples ==================== @@ -285,42 +260,34 @@ Translation examples We can compare the translations produced by the beam search decoder to the predictions from Google translate: -1. - **Source**: - `Arbeit kam später, Heiraten kam später, Kinder kamen später, selbst der Tod kam später.` - - - **Our model**: - `work came later , came later later , children came later later , even the death came later .` - - - **Google**: - `Work came later, marriages came later, children came later, even death came later` +*Source* | *Our Model* | *Google* +:---: | :---: | :---: | +Arbeit kam später, Heiraten kam später, Kinder kamen später, selbst der Tod kam später. | work came later , `` came later later , children came later later , even the death came later . | Work came later, marriages came later, children came later, even death came later +Das ist es , was Psychologen einen Aha-Moment nennen. | That ’s what psychologists call a `` call . | That’s what psychologists call an aha moment. +Dies ist nicht meine Meinung. Das sind Fakten.| This is not my opinion . These are facts . | This is not my opinion. These are facts. +In den 20ern sollte man sich also weiterbilden über den Körper und die eigenen Möglichkeiten | So in the `` , you should be thinking about the body and the own possibilities . | In the 20’s you should continue to educate yourself about the body and your own possibilities +Wie würde eine solche Zukunft aussehen? | What would such a future look like ? | What would such a future look like? -2. - **Source**: - `Das ist es , was Psychologen einen Aha-Moment nennen .` - - - **Our model**: `That ’s what psychologists call a call .` - - - **Google**: `That’s what psychologists call an aha moment.` - -3. - **Source**: `Dies ist nicht meine Meinung . Das sind Fakten .` - - - **Our model**: `This is not my opinion . These are facts .` - - - **Google**: `This is not my opinion. These are facts.` - -4. - **Source**: - `In den 20ern sollte man sich also weiterbilden über den Körper und die eigenen Möglichkeiten` +Attention visualizations +======================== - - **Our model**: - `So in the , you should be thinking about the body and the own possibilities .` +We can visualize the dot-product attention by plotting the weights +assigned to the encoder hidden states for each step during decoding. - - **Google**: - `In the 20’s you should continue to educate yourself about the body and your own possibilities` +'Dies ist nicht meine Meinung. Das sind Fakten' --> 'This is not my opinion. These are facts.' +![](imgs/att1.png) -5. - **Source**: `Wie würde eine solche Zukunft aussehen ?` +'Ok, das ist xwar leicht gesagt, aber macht keinen Fehler, denn es geht um sehr viel.' --> 'Ok, that 's easy to say, but do not make a mistake, because it 's about a lot .' +![](imgs/att3.png) - - **Our model**: `What would such a future look like ?` +Conclusion +========== - - **Google**: `What would such a future look like?` +We trained two classes of models – a basic encoder-decoder architecture +as described by (Sutskever et al., 2014) and a series of models that use +dot-product attention to give the decoder a more flexible representation +of the input. Though we experimented with more complex architectures such as +bidirectional LSTMs with multilayer perceptrons for attention weighting, our best-performing models used the basic dot-product attention. 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