Machine Translation

Byte Pair Encoding, or BPE, is a subword segmentation algorithm that encodes rare and unknown words as sequences of subword units. The intuition is that various word classes are translatable via smaller units than words, for instance names (via character copying or transliteration), compounds (via compositional translation), and cognates and loanwords (via phonological and morphological transformations). Lei Mao has a detailed blog post that explains how this works.

A Transformer is a model architecture that eschews recurrence and instead relies entirely on an attention mechanism to draw global dependencies between input and output. Before Transformers, the dominant sequence transduction models were based on complex recurrent or convolutional neural networks that include an encoder and a decoder. The Transformer also employs an encoder and decoder, but removing recurrence in favor of attention mechanisms allows for significantly more parallelization than methods like RNNs and CNNs.

Absolute Position Encodings are a type of position embeddings for [Transformer-based models] where positional encodings are added to the input embeddings at the bottoms of the encoder and decoder stacks. The positional encodings have the same dimension $d\_{model}$ as the embeddings, so that the two can be summed. In the original implementation, sine and cosine functions of different frequencies are used: $$ \text{PE}\left(pos, 2i\right) = \sin\left(pos/10000^{2i/d\_{model}}\right) $$ $$ \text{PE}\left(pos, 2i+1\right) = \cos\left(pos/10000^{2i/d\_{model}}\right) $$ where $pos$ is the position and $i$ is the dimension. That is, each dimension of the positional encoding corresponds to a sinusoid. The wavelengths form a geometric progression from $2\pi$ to $10000 \dot 2\pi$. This function was chosen because the authors hypothesized it would allow the model to easily learn to attend by relative positions, since for any fixed offset $k$, $\text{PE}\_{pos+k}$ can be represented as a linear function of $\text{PE}\_{pos}$. Image Source: D2L.ai

BART is a denoising autoencoder for pretraining sequence-to-sequence models. It is trained by (1) corrupting text with an arbitrary noising function, and (2) learning a model to reconstruct the original text. It uses a standard Transformer-based neural machine translation architecture. It uses a standard seq2seq/NMT architecture with a bidirectional encoder (like BERT) and a left-to-right decoder (like GPT). This means the encoder's attention mask is fully visible, like BERT, and the decoder's attention mask is causal, like GPT2.

Adafactor is a stochastic optimization method based on Adam that reduces memory usage while retaining the empirical benefits of adaptivity. This is achieved through maintaining a factored representation of the squared gradient accumulator across training steps. Specifically, by tracking moving averages of the row and column sums of the squared gradients for matrix-valued variables, we are able to reconstruct a low-rank approximation of the exponentially smoothed accumulator at each training step that is optimal with respect to the generalized Kullback-Leibler divergence. For an $n \times m$ matrix, this reduces the memory requirements from $O(n m)$ to $O(n + m)$. Instead of defining the optimization algorithm in terms of absolute step sizes {$\alpha_t$}$\_{t=1}^T$, the authors define the optimization algorithm in terms of relative step sizes {$\rho_t$}$\_{t=1}^T$, which get multiplied by the scale of the parameters. The scale of a parameter vector or matrix is defined as the root-mean-square of its components, lower-bounded by a small constant $\epsilon_2$. The reason for this lower bound is to allow zero-initialized parameters to escape 0. Proposed hyperparameters are: $\epsilon\_{1} = 10^{-30}$, $\epsilon\_{2} = 10^{-3}$, $d=1$, $p\_{t} = \min\left(10^{-2}, \frac{1}{\sqrt{t}}\right)$, $\hat{\beta}\_{2\_{t}} = 1 - t^{-0.8}$.

T5, or Text-to-Text Transfer Transformer, is a Transformer based architecture that uses a text-to-text approach. Every task – including translation, question answering, and classification – is cast as feeding the model text as input and training it to generate some target text. This allows for the use of the same model, loss function, hyperparameters, etc. across our diverse set of tasks. The changes compared to BERT include: - adding a causal decoder to the bidirectional architecture. - replacing the fill-in-the-blank cloze task with a mix of alternative pre-training tasks.

Seq2Seq, or Sequence To Sequence, is a model used in sequence prediction tasks, such as language modelling and machine translation. The idea is to use one LSTM, the encoder, to read the input sequence one timestep at a time, to obtain a large fixed dimensional vector representation (a context vector), and then to use another LSTM, the decoder, to extract the output sequence from that vector. The second LSTM is essentially a recurrent neural network language model except that it is conditioned on the input sequence. (Note that this page refers to the original seq2seq not general sequence-to-sequence models)

Shrink and Fine-Tune, or SFT, is a type of distillation that avoids explicit distillation by copying parameters to a student student model and then fine-tuning. Specifically it extracts a student model from the maximally spaced layers of a fine-tuned teacher. Each layer $l \in L'$ is copied fully from $L$. For example, when creating a BART student with 3 decoder layers from the 12 encoder layer 12 decoder layer teacher, we copy the teacher’s full $Enc^{L}$ and decoder layers 0, 6, and 11 to the student. When deciding which layers to copy, we break ties arbitrarily; copying layers 0, 5, and 11 might work just as well. When copy only 1 decoder layer, we copy layer 0. This was found this to work better than copying layer 11. The impact of initialization on performance is measured experimentally in Section 6.1. After initialization, the student model continues to fine-tune on the summarization dataset, with the objective of minimizing $\mathcal{L}\_{Data}$.

A HyperNetwork is a network that generates weights for a main network. The behavior of the main network is the same with any usual neural network: it learns to map some raw inputs to their desired targets; whereas the hypernetwork takes a set of inputs that contain information about the structure of the weights and generates the weight for that layer.

XLM is a Transformer based architecture that is pre-trained using one of three language modelling objectives: 1. Causal Language Modeling - models the probability of a word given the previous words in a sentence. 2. Masked Language Modeling - the masked language modeling objective of BERT. 3. Translation Language Modeling - a (new) translation language modeling objective for improving cross-lingual pre-training. The authors find that both the CLM and MLM approaches provide strong cross-lingual features that can be used for pretraining models.

Relative Position Encodings are a type of position embeddings for Transformer-based models that attempts to exploit pairwise, relative positional information. Relative positional information is supplied to the model on two levels: values and keys. This becomes apparent in the two modified self-attention equations shown below. First, relative positional information is supplied to the model as an additional component to the keys $$ e\_{ij} = \frac{x\_{i}W^{Q}\left(x\_{j}W^{K} + a^{K}\_{ij}\right)^{T}}{\sqrt{d\_{z}}} $$ Here $a$ is an edge representation for the inputs $x\_{i}$ and $x\_{j}$. The softmax operation remains unchanged from vanilla self-attention. Then relative positional information is supplied again as a sub-component of the values matrix: $$ z\_{i} = \sum^{n}\_{j=1}\alpha\_{ij}\left(x\_{j}W^{V} + a\_{ij}^{V}\right)$$ In other words, instead of simply combining semantic embeddings with absolute positional ones, relative positional information is added to keys and values on the fly during attention calculation. Source: Jake Tae Image Source: [Relative Positional Encoding for Transformers with Linear Complexity](https://www.youtube.com/watch?v=qajudaEHuq8

Location Sensitive Attention is an attention mechanism that extends the additive attention mechanism to use cumulative attention weights from previous decoder time steps as an additional feature. This encourages the model to move forward consistently through the input, mitigating potential failure modes where some subsequences are repeated or ignored by the decoder. Starting with additive attention where $h$ is a sequential representation from a BiRNN encoder and ${s}\_{i-1}$ is the $(i − 1)$-th state of a recurrent neural network (e.g. a LSTM or GRU): $$ e\_{i, j} = w^{T}\tanh\left(W{s}\_{i-1} + Vh\_{j} + b\right) $$ where $w$ and $b$ are vectors, $W$ and $V$ are matrices. We extend this to be location-aware by making it take into account the alignment produced at the previous step. First, we extract $k$ vectors $f\_{i,j} \in \mathbb{R}^{k}$ for every position $j$ of the previous alignment $\alpha\_{i−1}$ by convolving it with a matrix $F \in R^{k\times{r}}$: $$ f\_{i} = F ∗ \alpha\_{i−1} $$ These additional vectors $f\_{i,j}$ are then used by the scoring mechanism $e\_{i,j}$: $$ e\_{i,j} = w^{T}\tanh\left(Ws\_{i−1} + Vh\_{j} + Uf\_{i,j} + b\right) $$

Population Based Training, or PBT, is an optimization method for finding parameters and hyperparameters, and extends upon parallel search methods and sequential optimisation methods. It leverages information sharing across a population of concurrently running optimisation processes, and allows for online propagation/transfer of parameters and hyperparameters between members of the population based on their performance. Furthermore, unlike most other adaptation schemes, the method is capable of performing online adaptation of hyperparameters -- which can be particularly important in problems with highly non-stationary learning dynamics, such as reinforcement learning settings. PBT is decentralised and asynchronous, although it could also be executed semi-serially or with partial synchrony if there is a binding budget constraint.

The Universal Transformer is a generalization of the Transformer architecture. Universal Transformers combine the parallelizability and global receptive field of feed-forward sequence models like the Transformer with the recurrent inductive bias of RNNs. They also utilise a dynamic per-position halting mechanism.

SRU, or Simple Recurrent Unit, is a recurrent neural unit with a light form of recurrence. SRU exhibits the same level of parallelism as convolution and feed-forward nets. This is achieved by balancing sequential dependence and independence: while the state computation of SRU is time-dependent, each state dimension is independent. This simplification enables CUDA-level optimizations that parallelize the computation across hidden dimensions and time steps, effectively using the full capacity of modern GPUs. SRU also replaces the use of convolutions (i.e., ngram filters), as in QRNN and KNN, with more recurrent connections. This retains modeling capacity, while using less computation (and hyper-parameters). Additionally, SRU improves the training of deep recurrent models by employing highway connections and a parameter initialization scheme tailored for gradient propagation in deep architectures. A single layer of SRU involves the following computation: $$ \mathbf{f}\_{t} =\sigma\left(\mathbf{W}\_{f} \mathbf{x}\_{t}+\mathbf{v}\_{f} \odot \mathbf{c}\_{t-1}+\mathbf{b}\_{f}\right) $$ $$ \mathbf{c}\_{t} =\mathbf{f}\_{t} \odot \mathbf{c}\_{t-1}+\left(1-\mathbf{f}\_{t}\right) \odot\left(\mathbf{W} \mathbf{x}\_{t}\right) \\ $$ $$ \mathbf{r}\_{t} =\sigma\left(\mathbf{W}\_{r} \mathbf{x}\_{t}+\mathbf{v}\_{r} \odot \mathbf{c}\_{t-1}+\mathbf{b}\_{r}\right) \\ $$ $$ \mathbf{h}\_{t} =\mathbf{r}\_{t} \odot \mathbf{c}\_{t}+\left(1-\mathbf{r}\_{t}\right) \odot \mathbf{x}\_{t} $$ where $\mathbf{W}, \mathbf{W}\_{f}$ and $\mathbf{W}\_{r}$ are parameter matrices and $\mathbf{v}\_{f}, \mathbf{v}\_{r}, \mathbf{b}\_{f}$ and $\mathbf{b}_{v}$ are parameter vectors to be learnt during training. The complete architecture decomposes to two sub-components: a light recurrence and a highway network, The light recurrence component successively reads the input vectors $\mathbf{x}\_{t}$ and computes the sequence of states $\mathbf{c}\_{t}$ capturing sequential information. The computation resembles other recurrent networks such as LSTM, GRU and RAN. Specifically, a forget gate $\mathbf{f}\_{t}$ controls the information flow and the state vector $\mathbf{c}\_{t}$ is determined by adaptively averaging the previous state $\mathbf{c}\_{t-1}$ and the current observation $\mathbf{W} \mathbf{x}_{+}$according to $\mathbf{f}\_{t}$.

CoVe, or Contextualized Word Vectors, uses a deep LSTM encoder from an attentional sequence-to-sequence model trained for machine translation to contextualize word vectors. $\text{CoVe}$ word embeddings are therefore a function of the entire input sequence. These word embeddings can then be used in downstream tasks by concatenating them with $\text{GloVe}$ embeddings: $$ v = \left[\text{GloVe}\left(x\right), \text{CoVe}\left(x\right)\right]$$ and then feeding these in as features for the task-specific models.

The Levenshtein Transformer (LevT) is a type of transformer that aims to address the lack of flexibility of previous decoding models. Notably, in previous frameworks, the length of generated sequences is either fixed or monotonically increased as the decoding proceeds. The authors argue this is incompatible with human-level intelligence where humans can revise, replace, revoke or delete any part of their generated text. Hence, LevT is proposed to bridge this gap by breaking the in-so-far standardized decoding mechanism and replacing it with two basic operations — insertion and deletion. LevT is trained using imitation learning. The resulted model contains two policies and they are executed in an alternate manner. The authors argue that with this model decoding becomes more flexible. For example, when the decoder is given an empty token, it falls back to a normal sequence generation model. On the other hand, the decoder acts as a refinement model when the initial state is a low-quality generated sequence. One crucial component in LevT framework is the learning algorithm. The authors leverage the characteristics of insertion and deletion — they are complementary but also adversarial. The algorithm they propose is called “dual policy learning”. The idea is that when training one policy (insertion or deletion), we use the output from its adversary at the previous iteration as input. An expert policy, on the other hand, is drawn to provide a correction signal.

DynamicConv is a type of convolution for sequential modelling where it has kernels that vary over time as a learned function of the individual time steps. It builds upon LightConv and takes the same form but uses a time-step dependent kernel: $$ \text{DynamicConv}\left(X, i, c\right) = \text{LightConv}\left(X, f\left(X\_{i}\right)\_{h,:}, i, c\right) $$

Residual Multi-Layer Perceptrons, or ResMLP, is an architecture built entirely upon multi-layer perceptrons for image classification. It is a simple residual network that alternates (i) a linear layer in which image patches interact, independently and identically across channels, and (ii) a two-layer feed-forward network in which channels interact independently per patch. At the end of the network, the patch representations are average pooled, and fed to a linear classifier. Layer normalization is replaced with a simpler affine transformation, thanks to the absence of self-attention layers which makes training more stable. The affine operator is applied at the beginning ("pre-normalization") and end ("post-normalization") of each residual block. As a pre-normalization, Aff replaces LayerNorm without using channel-wise statistics. Initialization is achieved as $\mathbf{\alpha}=\mathbf{1}$, and $\mathbf{\beta}=\mathbf{0}$. As a post-normalization, Aff is similar to LayerScale and $\mathbf{\alpha}$ is initialized with the same small value.

GPipe is a distributed model parallel method for neural networks. With GPipe, each model can be specified as a sequence of layers, and consecutive groups of layers can be partitioned into cells. Each cell is then placed on a separate accelerator. Based on this partitioned setup, batch splitting is applied. A mini-batch of training examples is split into smaller micro-batches, then the execution of each set of micro-batches is pipelined over cells. Synchronous mini-batch gradient descent is applied for training, where gradients are accumulated across all micro-batches in a mini-batch and applied at the end of a mini-batch.

GShard is a intra-layer parallel distributed method. It consists of set of simple APIs for annotations, and a compiler extension in XLA for automatic parallelization.

Feedback Memory is a type of attention module used in the Feedback Transformer architecture. It allows a transformer to to use the most abstract representations from the past directly as inputs for the current timestep. This means that the model does not form its representation in parallel, but sequentially token by token. More precisely, we replace the context inputs to attention modules with memory vectors that are computed over the past, i.e.: $$ \mathbf{z}^{l}\_{t} = \text{Attn}\left(\mathbf{x}^{l}\_{t}, \left[\mathbf{m}\_{t−\tau}, \dots, \mathbf{m}\_{t−1}\right]\right) $$ where a memory vector $\mathbf{m}\_{t}$ is computed by summing the representations of each layer at the $t$-th time step: $$ \mathbf{m}\_{t} = \sum^{L}\_{l=0}\text{Softmax}\left(w^{l}\right)\mathbf{x}\_{t}^{l} $$ where $w^{l}$ are learnable scalar parameters. Here $l = 0$ corresponds to token embeddings. The weighting of different layers by a softmax output gives the model more flexibility as it can average them or select one of them. This modification of the self-attention input adapts the computation of the Transformer from parallel to sequential, summarized in the Figure. Indeed, it gives the ability to formulate the representation $\mathbf{x}^{l}\_{t+1}$ based on past representations from any layer $l'$, while in a standard Transformer this is only true for $l > l'$. This change can be viewed as exposing all previous computations to all future computations, providing better representations of the input. Such capacity would allow much shallower models to capture the same level of abstraction as a deeper architecture.

LayerDrop is a form of structured dropout for Transformer models which has a regularization effect during training and allows for efficient pruning at inference time. It randomly drops layers from the Transformer according to an "every other" strategy where pruning with a rate $p$ means dropping the layers at depth $d$ such that $d = 0\left\(\text{mod}\left(\text{floor}\left(\frac{1}{p}\right)\right)\right)$.

CRISS, or Cross-lingual Retrievial for Iterative Self-Supervised Training (CRISS), is a self-supervised learning method for multilingual sequence generation. CRISS is developed based on the finding that the encoder outputs of multilingual denoising autoencoder can be used as language agnostic representation to retrieve parallel sentence pairs, and training the model on these retrieved sentence pairs can further improve its sentence retrieval and translation capabilities in an iterative manner. Using only unlabeled data from many different languages, CRISS iteratively mines for parallel sentences across languages, trains a new better multilingual model using these mined sentence pairs, mines again for better parallel sentences, and repeats.

Class-MLP is an alternative to average pooling, which is an adaptation of the class-attention token introduced in CaiT. In CaiT, this consists of two layers that have the same structure as the transformer, but in which only the class token is updated based on the frozen patch embeddings. In Class-MLP, the same approach is used, but after aggregating the patches with a linear layer, we replace the attention-based interaction between the class and patch embeddings by simple linear layers, still keeping the patch embeddings frozen. This increases the performance, at the expense of adding some parameters and computational cost. This pooling variant is referred to as “class-MLP”, since the purpose of these few layers is to replace average pooling.

Gated Transformer-XL, or GTrXL, is a Transformer-based architecture for reinforcement learning. It introduces architectural modifications that improve the stability and learning speed of the original Transformer and XL variant. Changes include: - Placing the layer normalization on only the input stream of the submodules. A key benefit to this reordering is that it now enables an identity map from the input of the transformer at the first layer to the output of the transformer after the last layer. This is in contrast to the canonical transformer, where there are a series of layer normalization operations that non-linearly transform the state encoding. - Replacing residual connections with gating layers. The authors' experiments found that GRUs were the most effective form of gating.

Subformer is a Transformer that combines sandwich-style parameter sharing, which overcomes naive cross-layer parameter sharing in generative models, and self-attentive embedding factorization (SAFE). In SAFE, a small self-attention layer is used to reduce embedding parameter count.

A Feedback Transformer is a type of sequential transformer that exposes all previous representations to all future representations, meaning the lowest representation of the current timestep is formed from the highest-level abstract representation of the past. This feedback nature allows this architecture to perform recursive computation, building stronger representations iteratively upon previous states. To achieve this, the self-attention mechanism of the standard Transformer is modified so it attends to higher level representations rather than lower ones.

FixUp Initialization, or Fixed-Update Initialization, is an initialization method that rescales the standard initialization of residual branches by adjusting for the network architecture. Fixup aims to enables training very deep residual networks stably at a maximal learning rate without normalization. The steps are as follows: 1. Initialize the classification layer and the last layer of each residual branch to 0. 2. Initialize every other layer using a standard method, e.g. Kaiming Initialization, and scale only the weight layers inside residual branches by $L^{\frac{1}{2m-2}}$. 3. Add a scalar multiplier (initialized at 1) in every branch and a scalar bias (initialized at 0) before each convolution, linear, and element-wise activation layer.

SRU++ is a self-attentive recurrent unit that combines fast recurrence and attention for sequence modeling, extending the SRU unit. The key modification of SRU++ is to incorporate more expressive non-linear operations into the recurrent network. Specifically, given the input sequence represented as a matrix $\mathbf{X} \in \mathbb{R}^{L \times d}$, the attention component computes the query, key and value representations using the following multiplications, $$ \mathbf{Q} =\mathbf{W}^{q} \mathbf{X}^{\top} $$ $$ \mathbf{K} =\mathbf{W}^{k} \mathbf{Q} \\ $$ $$ \mathbf{V} =\mathbf{W}^{v} \mathbf{Q} $$ where $\mathbf{W}^{q} \in \mathbb{R}^{d^{\prime} \times d}, \mathbf{W}^{k}, \mathbf{W}^{v} \in \mathbb{R}^{d^{\prime} \times d^{\prime}}$ are model parameters. $d^{\prime}$ is the attention dimension that is typically much smaller than $d$. Note that the keys $\mathbf{K}$ and values $\mathbf{V}$ are computed using $\mathbf{Q}$ instead of $\mathbf{X}$ such that the weight matrices $\mathbf{W}^{k}$ and $\mathbf{W}^{v}$ are significantly smaller. Next, we compute a weighted average output $\mathbf{A} \in \mathbb{R}^{d^{\prime} \times L}$ using scaled dot-product attention: $$ \mathbf{A}^{\top}=\operatorname{softmax}\left(\frac{\mathbf{Q}^{\top} \mathbf{K}}{\sqrt{d^{\prime}}}\right) \mathbf{V}^{\top} $$ The final output $U$ required by the elementwise recurrence is obtained by another linear projection, $$ \mathbf{U}^{\top}=\mathbf{W}^{o}(\mathbf{Q}+\alpha \cdot \mathbf{A}) $$ where $\alpha \in \mathbb{R}$ is a learned scalar and $\mathbf{W}\_{o} \in \mathbb{R}^{3 d \times d^{\prime}}$ is a parameter matrix. $\mathbf{Q}+\alpha \cdot \mathbf{A}$ is a residual connection which improves gradient propagation and stabilizes training. We initialize $\alpha$ to zero and as a result, $$ \mathbf{U}^{\top}=\mathbf{W}^{o} \mathbf{Q}=\left(\mathbf{W}^{o} \mathbf{W}^{q}\right) \mathbf{X}^{\top} $$ initially falls back to a linear transformation of the input $X$ skipping the attention transformation. Intuitively, skipping attention encourages leveraging recurrence to capture sequential patterns during early stage of training. As $|\alpha|$ grows, the attention mechanism can learn long-range dependencies for the model. In addition, $\mathbf{W}^{o} \mathbf{W}^{q}$ can be interpreted as applying a matrix factorization trick with a small inner dimension $d^{\prime}<d$, reducing the total number of parameters. The Figure compares the differences of SRU, SRU with this factorization trick (but without attention), and SRU++. The last modification is adding layer normalization to each SRU++ layer. We apply normalization after the attention operation and before the matrix multiplication with $\mathbf{W}^{o}$ $$ \mathbf{U}^{\top}=\mathbf{W}^{o} \operatorname{layernorm}(\mathbf{Q}+\alpha \cdot \mathbf{A}) $$ This implementation is post-layer normalization in which the normalization is added after the residual connection.

A Sandwich Transformer is a variant of a Transformer that reorders sublayers in the architecture to achieve better performance. The reordering is based on the authors' analysis that models with more self-attention toward the bottom and more feedforward sublayers toward the top tend to perform better in general.

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The Adaptively Sparse Transformer is a type of Transformer.

The BP-Transformer (BPT) is a type of Transformer that is motivated by the need to find a better balance between capability and computational complexity for self-attention. The architecture partitions the input sequence into different multi-scale spans via binary partitioning (BP). It incorporates an inductive bias of attending the context information from fine-grain to coarse-grain as the relative distance increases. The farther the context information is, the coarser its representation is. BPT can be regard as graph neural network, whose nodes are the multi-scale spans. A token node can attend the smaller-scale span for the closer context and the larger-scale span for the longer distance context. The representations of nodes are updated with Graph Self-Attention.