$\infty$-former: Infinite Memory Transformer

Transformers struggle when attending to long contexts, since the amount of computation grows with the context length, and therefore they cannot model long-term memories effectively. Several variations have been proposed to alleviate this problem, but they all have a finite memory capacity, being forced to drop old information. In this paper, we propose the $\infty$-former, which extends the vanilla transformer with an unbounded long-term memory. By making use of a continuous-space attention mechanism to attend over the long-term memory, the $\infty$-former's attention complexity becomes independent of the context length. Thus, it is able to model arbitrarily long contexts and maintain "sticky memories" while keeping a fixed computation budget. Experiments on a synthetic sorting task demonstrate the ability of the $\infty$-former to retain information from long sequences. We also perform experiments on language modeling, by training a model from scratch and by fine-tuning a pre-trained language model, which show benefits of unbounded long-term memories.

Sparse Communication via Mixed Distributions

Neural networks and other machine learning models compute continuous representations, while humans communicate mostly through discrete symbols. Reconciling these two forms of communication is desirable for generating human-readable interpretations or learning discrete latent variable models, while maintaining end-to-end differentiability. Some existing approaches (such as the Gumbel-Softmax transformation) build continuous relaxations that are discrete approximations in the zero-temperature limit, while others (such as sparsemax transformations and the Hard Concrete distribution) produce discrete/continuous hybrids. In this paper, we build rigorous theoretical foundations for these hybrids, which we call "mixed random variables." Our starting point is a new "direct sum" base measure defined on the face lattice of the probability simplex. From this measure, we introduce new entropy and Kullback-Leibler divergence functions that subsume the discrete and differential cases and have interpretations in terms of code optimality. Our framework suggests two strategies for representing and sampling mixed random variables, an extrinsic ("sample-and-project") and an intrinsic one (based on face stratification). We experiment with both approaches on an emergent communication benchmark and on modeling MNIST and Fashion-MNIST data with variational auto-encoders with mixed latent variables.

Sparse Continuous Distributions and Fenchel-Young Losses

Exponential families are widely used in machine learning; they include many distributions in continuous and discrete domains (e.g., Gaussian, Dirichlet, Poisson, and categorical distributions via the softmax transformation). Distributions in each of these families have fixed support. In contrast, for finite domains, there has been recent works on sparse alternatives to softmax (e.g. sparsemax, $\alpha$-entmax, and fusedmax) and corresponding losses, which have varying support. This paper expands that line of work in several directions: first, it extends $\Omega$-regularized prediction maps and Fenchel-Young losses to arbitrary domains (possibly countably infinite or continuous). For linearly parametrized families, we show that minimization of Fenchel-Young losses is equivalent to moment matching of the statistics, generalizing a fundamental property of exponential families. When $\Omega$ is a Tsallis negentropy with parameter $\alpha$, we obtain "deformed exponential families," which include $\alpha$-entmax and sparsemax ($\alpha$ = 2) as particular cases. For quadratic energy functions in continuous domains, the resulting densities are $\beta$-Gaussians, an instance of elliptical distributions that contain as particular cases the Gaussian, biweight, triweight and Epanechnikov densities, and for which we derive closed-form expressions for the variance, Tsallis entropy, and Fenchel-Young loss. When $\Omega$ is a total variation or Sobolev regularizer, we obtain a continuous version of the fusedmax. Finally, we introduce continuous-domain attention mechanisms, deriving efficient gradient backpropagation algorithms for $\alpha \in \{1, 4/3, 3/2, 2\}$. Using them, we demonstrate our sparse continuous distributions for attention-based audio classification and visual question answering, showing that they allow attending to time intervals and compact regions.

Measuring and Increasing Context Usage in Context-Aware Machine Translation

Recent work in neural machine translation has demonstrated both the necessity and feasibility of using inter-sentential context -- context from sentences other than those currently being translated. However, while many current methods present model architectures that theoretically can use this extra context, it is often not clear how much they do actually utilize it at translation time. In this paper, we introduce a new metric, conditional cross-mutual information, to quantify the usage of context by these models. Using this metric, we measure how much document-level machine translation systems use particular varieties of context. We find that target context is referenced more than source context, and that conditioning on a longer context has a diminishing effect on results. We then introduce a new, simple training method, context-aware word dropout, to increase the usage of context by context-aware models. Experiments show that our method increases context usage and that this reflects on the translation quality according to metrics such as BLEU and COMET, as well as performance on anaphoric pronoun resolution and lexical cohesion contrastive datasets.

Do Context-Aware Translation Models Pay the Right Attention?

Context-aware machine translation models are designed to leverage contextual information, but often fail to do so. As a result, they inaccurately disambiguate pronouns and polysemous words that require context for resolution. In this paper, we ask several questions: What contexts do human translators use to resolve ambiguous words? Are models paying large amounts of attention to the same context? What if we explicitly train them to do so? To answer these questions, we introduce SCAT (Supporting Context for Ambiguous Translations), a new English-French dataset comprising supporting context words for 14K translations that professional translators found useful for pronoun disambiguation. Using SCAT, we perform an in-depth analysis of the context used to disambiguate, examining positional and lexical characteristics of the supporting words. Furthermore, we measure the degree of alignment between the model's attention scores and the supporting context from SCAT, and apply a guided attention strategy to encourage agreement between the two.

Multimodal Continuous Visual Attention Mechanisms

Visual attention mechanisms are a key component of neural network models for computer vision. By focusing on a discrete set of objects or image regions, these mechanisms identify the most relevant features and use them to build more powerful representations. Recently, continuous-domain alternatives to discrete attention models have been proposed, which exploit the continuity of images. These approaches model attention as simple unimodal densities (e.g. a Gaussian), making them less suitable to deal with images whose region of interest has a complex shape or is composed of multiple non-contiguous patches. In this paper, we introduce a new continuous attention mechanism that produces multimodal densities, in the form of mixtures of Gaussians. We use the EM algorithm to obtain a clustering of relevant regions in the image, and a description length penalty to select the number of components in the mixture. Our densities decompose as a linear combination of unimodal attention mechanisms, enabling closed-form Jacobians for the backpropagation step. Experiments on visual question answering in the VQA-v2 dataset show competitive accuracies and a selection of regions that mimics human attention more closely in VQA-HAT. We present several examples that suggest how multimodal attention maps are naturally more interpretable than their unimodal counterparts, showing the ability of our model to automatically segregate objects from ground in complex scenes.

Reconciling the Discrete-Continuous Divide: Towards a Mathematical Theory of Sparse Communication

Neural networks and other machine learning models compute continuous representations, while humans communicate with discrete symbols. Reconciling these two forms of communication is desirable to generate human-readable interpretations or to learn discrete latent variable models, while maintaining end-to-end differentiability. Some existing approaches (such as the Gumbel-softmax transformation) build continuous relaxations that are discrete approximations in the zero-temperature limit, while others (such as sparsemax transformations and the hard concrete distribution) produce discrete/continuous hybrids. In this paper, we build rigorous theoretical foundations for these hybrids. Our starting point is a new "direct sum" base measure defined on the face lattice of the probability simplex. From this measure, we introduce a new entropy function that includes the discrete and differential entropies as particular cases, and has an interpretation in terms of code optimality, as well as two other information-theoretic counterparts that generalize the mutual information and Kullback-Leibler divergences. Finally, we introduce "mixed languages" as strings of hybrid symbols and a new mixed weighted finite state automaton that recognizes a class of regular mixed languages, generalizing closure properties of regular languages.

Smoothing and Shrinking the Sparse Seq2Seq Search Space

Current sequence-to-sequence models are trained to minimize cross-entropy and use softmax to compute the locally normalized probabilities over target sequences. While this setup has led to strong results in a variety of tasks, one unsatisfying aspect is its length bias: models give high scores to short, inadequate hypotheses and often make the empty string the argmax -- the so-called cat got your tongue problem. Recently proposed entmax-based sparse sequence-to-sequence models present a possible solution, since they can shrink the search space by assigning zero probability to bad hypotheses, but their ability to handle word-level tasks with transformers has never been tested. In this work, we show that entmax-based models effectively solve the cat got your tongue problem, removing a major source of model error for neural machine translation. In addition, we generalize label smoothing, a critical regularization technique, to the broader family of Fenchel-Young losses, which includes both cross-entropy and the entmax losses. Our resulting label-smoothed entmax loss models set a new state of the art on multilingual grapheme-to-phoneme conversion and deliver improvements and better calibration properties on cross-lingual morphological inflection and machine translation for 6 language pairs.