End-to-End Training for Hard Attention Transducers

Overview

This repository contains PyTorch-based implementations of end-to-end trainable transducers using hard attention instead of soft attention. There is one autoregressive and one non-autoregressive transducer.

What are transducers?

Transducers are a type of sequence transduction model often used for string rewriting or morphology related tasks. Instead of directly predicting the target sequence from the source sequence, as is the case in typical machine translation and other sequence-to-sequence models, transducers predict edit operations. The edit operations considered here are:

• Delete: Remove the respective source symbol
• Copy: Copy the respective source symbol to the target sequence
• Substitution: Replace the respective source symbol by a target symbol (there is 1 substitution action for each symbol in the target alphabet)
• Insertion: Predict a symbol in the target sequence (there is 1 insertion action for each symbol in the target alphabet)

For each symbol in the source sequence, the transducer predicts a number of edit operations, which then determine how the source sequence is transformed to yield the predicted target sequence.

What is hard attention?

Typically, sequence-to-sequence models use soft attention, where the result of attention is a weighted sum of all attention keys (as in query-key-value-attention). In contrast, hard attention selects one and only one key to attend to. In the context of transducers, this means that decoding of transduction actions always attends to exactly one source symbol, instead of soft attention over source symbols.

What is end-to-end training?

End-to-end training means the property of a neural model that all computations that are required to calculate the loss are differentiable wrt. model parameters. An example of a non-end-to-end trainable model is the approach described by Makarov and Clematide (2018): Since their decoding strategy takes each previously predicted edit action into account, this information must be available at training time, either by sampling or by using an external aligner, which are both not differentiable computations (if we view the aligner as part of the optimisation goal).

Note that hard attention is inherently a non-differentiable operation. However, end-to-end training be done efficiently by marginalising over all possible alignments using dynamic programming. For detailed description, see Wu et al. (2018) and Wu and Cotterell (2019). In this implementation, differently from Wu et al. (2018), we employ monotonic hard attention and attention positions are determined by the predicted actions, i.e. the attention position can only stay the same of move to the next source symbol. The main idea of end-to-end training for this variant is described by Yu et al. (2016) and Libovický and Fraser (2022).

Model Descriptions

Encoder

The implemented encoder is a BiLSTM encoder. Also, SOS and a EOS tokens are added to source sequences and the initial hidden states are made trainable. Important parameters of the encoder are (names as parameters in make_settings from settings.py:

• embedding_size
• hidden_size
• hidden_layers
• dropout

Feature Encoder

In case you use feature, as is usually the case for e.g. morphological inflection tasks, set the use_feature parameter in make_settings (from settings.py) to True. Features are a sequence of feature symbols, for example inflection tags. The feature encoder also is a BiLSTM encoder with trainable initial hidden states, but you can skip the LSTM by setting features_num_layers to 0. Then, each feature symbol is only embedded but not contextualised.

For each predicted edit action (autoregressive model) or source symbol (non-autoregressive model), feature symbol encodings are combined to a single vector representing the entire feature symbol sequence. This implementation includes 2 methods to do so:

• Mean, Max, Sum pooling: Ignores the encoder/decoder information and simply pools the encoded feature sequence
• MLP, Dot Product Attention: Lets the encoder/decoder queries (soft) attend to feature encodings and encodes the feature sequence by the resulting weighted sum of feature symbol encodings

Parameters of the feature encoder are:

• features_num_layers: Number of LSTM layers in feature encoder, no LSTM if 0
• features_pooling: Type of feature sequence pooling, can be 'mean', ''sum', 'max', 'mlp', 'dot'

Hidden size, embedding size, and dropout are the same as for the source sequence encoder.

Autoregressive Decoder

The autoregressive decoder is a LSTM predicting the next edit action from the previous decoder hidden state, last predicted target symbol and optionally features. In contrast to Makarov and Clematide (2018), this implementation does not use the last predicted action but the last predicted symbol, which avoids having to provide ground-truth actions at training time.

During decoding, the decoder hidden state is only updates if a new symbol is predicted (i.e. no Delete action). Note that the edit actions allow for online decoding of the predicted target sequence. Hard Attention starts with the first (the SOS) symbol and shifts to the next symbol when predicting a Delete, Substitution, or CopyShift (which is a shortcut for Copy followed by Delete) action.

At training time, the ground-truth target sequence is known, and so we can use teacher forcing to train the model. Furthermore, we marginalise over possible alignments of source symbols to target symbols and possible edit operations. Using dynamic programming, we calculate the probability of predicting target sequence prefix $t_{1:n}$ from source sequence prefix $s_{1:m}$ recursively by

$$ \begin{align} P(t_{1:n}|s_{1:m}) = \quad &P_{\text{del}}(s_m) \cdot P(t_{1:n}|s_{1:m-1}) \\ &+ P_{\text{copy-shift}}(s_m) \cdot P(t_{1:n-1}|s_{1:m-1}) \cdot \delta_{t_n = s_m} \\ &+ P_{\text{sub}}(t_n|s_m) \cdot P(t_{1:n-1}|s_{1:m-1}) \\ &+ P_{\text{copy}}(s_m) \cdot P(t_{1:n-1}|s_{1:m}) \cdot \delta_{t_n = s_m} \\ &+ P_{\text{ins}}(t_n|s_m) \cdot P(t_{1:n-1}|s_{1:m}) \end{align} $$

where $P_{\text{del}}, P_{\text{copy-shift}}, P_{\text{sub}}, P_{\text{copy}}, P_{\text{ins}}$ are the probabilities for Delete, CopyShift, Substitution, Copy, and Insertion. $\delta_{t_n = s_m}$ is the indicator function stating whether copying is possible (target symbol equals source symbol).

To use the autoregressive model, set the autoregressive parameter in make_settings to True.

Non-Autoregressive Decoder

The non-autoregressive decoder is based on an idea proposed by Libovický and Helcl (2018): From each source symbol, predict $\tau$ edit actions. In the original formulation, $\tau$ is a fixed parameter. While this is sufficient for many problems like grapheme-to-phoneme conversion, it may not be sufficient for problems where source symbols generate long target sequences, which may be the case for inflections in some agglutinative languages. Therefore, this implementation offers predicting a flexible number of edit actions from each source symbol using a LSTM, or concatenation of the symbol encoding to learned positional embeddings.

The main difference to simply removing the dependence on the last predicted target symbol from the autoregressive decoder LSTM is that the non-autoregressive version allows to decode from all source symbols in parallel, while the mentioned alternative would still be autoregressive in the sense that it needs the previously predicted edit action to decide whether to shift hard attention or stay with the current symbol.

In case of a flexible $\tau$, at training time $\tau$ is set to the longest target sequence in the batch. At test time, we can use some upper bound derived from either the training data or the test source sequences. Also, using learned positional embeddings instead of LSTM for decoding requires setting a maximum number of edit operations that can be predicted from a single source symbol. This is the parameter max_targets_per_symbol in make_settings.

Training stays the same as in the autoregressive case, except that the hard attention alignment process becomes hierarchical: We can shift hard attention from one source symbol to the next by predicting Delete, Substitution, or CopyShift actions, and can shift the hard attention within the predictions from one source symbol predicting Insertion or Copy actions. Therefore, we calculate the probability of predicting target sequence prefix $t_{1:n}$ from source sequence prefix $s_{1:m}$ and symbol prediction index $1 \leq q \leq \tau$ recursively by

$$P(t_{1:n}|s_{1:m}, q) = \sum_{1\leq r \leq \tau} \quad \left(P_{\text{del}}(s_m) \cdot P_(t_{1:n}|s_{1:m-1}, r) + P_{\text{copy-shift}}(s_m, r) \cdot P(t_{1:n-1}|s_{1:m-1}, r) \cdot \delta_{t_n = s_m} + P_{\text{sub}}(t_n|s_m, r) \cdot P(t_{1:n-1}|s_{1:m-1}, r)\right)$$

if $q = 1$ and

$$P(t_{1:n}|s_{1:m}, q) = P_{\text{copy}}(s_m, q) \cdot P(t_{1:n-1}|s_{1:m}, q-1) \cdot \delta_{t_n = s_m} + P_{\text{ins}}(t_n|s_m, q) \cdot P(t_{1:n-1}|s_{1:m}, q-1) $$

if $q > 1$.

To use the non-autoregressive model, set autoregressive in make_settings to False. To set the decoder you can set the parameter non_autoregressive_decoder to:

• 'fixed'' for predicting a fixed number of tau edit actions from each source symbol
• 'position' for predicting a flexible number of edit operations, where position information is only available through learned position embeddings
• 'lstm' for predicting a flexible number of edit operations, where position information is available through a LSTM decoder that receives the source symbol encoding as input and operates on every source symbol independently

To use flexible $\tau$, it is also necessary to set the tau parameter to None. To use fixed $\tau$, it is necessary to set the tau parameter to some integer $>0$. Please note that in the case of fixed $\tau$, the model explicitly parametrises all $\tau$ prediction positions using a MLP, therefore choosing a large $\tau$ also causes a large number of parameters.

Usage

You need 3 ingredients to use this code: First, make datasets

from dataset import RawDataset

train_data = RawDataset(
    sources: List[List[str]]=train_sources,
    targets: List[List[str]]=train_targets,
    features: Optional[List[List[str]]] = train_features
)
development_data = RawDataset(
    sources: List[List[str]]=development_sources,
    targets: List[List[str]]=development_targets,
    features: Optional[List[List[str]]] = development_features
)

Here, sources, targets and features are datasets containing sequences of symbols encoded as strings.

Next, define settings:

from settings import make_settings

settings = make_settings(
    use_features: bool = True,
    autoregressive: bool = True,
    name: str = 'test', 
    save_path: str = "./saved_models"
)

There are many hyperparameters, which are described in settings.py. The required arguments are use_features, which tells the transducer whether to use provided features, autoregressive, which tells the transducer whether to use the autoregressive or non-autoregressive model, and name and save_path, which are used to name and save checkpoints. It is also recommended to pass your device.

Finally, you can train a model:

from transducer import Transducer

model = Transducer(settings=settings)
model = model.fit(
    train_data: RawDataset=train_data,
    development_data: RawDataset=development_data
)

predictions = model.predict(test_sources: List[List[str]])

Predictions come as a list of a namedtuple called TransducerPrediction, which has 2 attributes, namely the predicted symbols prediction and also the alignment alignment of predicted symbols and actions to source symbols.

References

• Monotonic Hard Attention Transducers: Makarov and Clematide (2018a), Makarov and Clematide (2018b), Clematide and Makarov (2021), Wehrli et al. (2022)
• Hard Attention in general: Wu et al. (2018) and Wu and Cotterell (2019)
• End-to-End Training for Hard Attention: Yu et al. (2016), Libovický and Fraser (2022)
• Non-Autoregressive Models: Libovický and Helcl (2018)