Stack Attention: Improving the Ability of Transformers to Model Hierarchical Patterns

Attention, specifically scaled dot-product attention, has proven effective for natural language, but it does not have a mechanism for handling hierarchical patterns of arbitrary nesting depth, which limits its ability to recognize certain syntactic structures. To address this shortcoming, we propose stack attention: an attention operator that incorporates stacks, inspired by their theoretical connections to context-free languages (CFLs). We show that stack attention is analogous to standard attention, but with a latent model of syntax that requires no syntactic supervision. We propose two variants: one related to deterministic pushdown automata (PDAs) and one based on nondeterministic PDAs, which allows transformers to recognize arbitrary CFLs. We show that transformers with stack attention are very effective at learning CFLs that standard transformers struggle on, achieving strong results on a CFL with theoretically maximal parsing difficulty. We also show that stack attention is more effective at natural language modeling under a constrained parameter budget, and we include results on machine translation.

Nondeterministic Stacks in Neural Networks

Human language is full of compositional syntactic structures, and although neural networks have contributed to groundbreaking improvements in computer systems that process language, widely-used neural network architectures still exhibit limitations in their ability to process syntax. To address this issue, prior work has proposed adding stack data structures to neural networks, drawing inspiration from theoretical connections between syntax and stacks. However, these methods employ deterministic stacks that are designed to track one parse at a time, whereas syntactic ambiguity, which requires a nondeterministic stack to parse, is extremely common in language. In this dissertation, we remedy this discrepancy by proposing a method of incorporating nondeterministic stacks into neural networks. We develop a differentiable data structure that efficiently simulates a nondeterministic pushdown automaton, representing an exponential number of computations with a dynamic programming algorithm. We incorporate this module into two predominant architectures: recurrent neural networks (RNNs) and transformers. We show that this raises their formal recognition power to arbitrary context-free languages, and also aids training, even on deterministic context-free languages. Empirically, neural networks with nondeterministic stacks learn context-free languages much more effectively than prior stack-augmented models, including a language with theoretically maximal parsing difficulty. We also show that an RNN augmented with a nondeterminsitic stack is capable of surprisingly powerful behavior, such as learning cross-serial dependencies, a well-known non-context-free pattern. We demonstrate improvements on natural language modeling and provide analysis on a syntactic generalization benchmark. This work represents an important step toward building systems that learn to use syntax in more human-like fashion.

Algorithms for Weighted Pushdown Automata

Weighted pushdown automata (WPDAs) are at the core of many natural language processing tasks, like syntax-based statistical machine translation and transition-based dependency parsing. As most existing dynamic programming algorithms are designed for context-free grammars (CFGs), algorithms for PDAs often resort to a PDA-to-CFG conversion. In this paper, we develop novel algorithms that operate directly on WPDAs. Our algorithms are inspired by Lang's algorithm, but use a more general definition of pushdown automaton and either reduce the space requirements by a factor of $|\Gamma|$ (the size of the stack alphabet) or reduce the runtime by a factor of more than $|Q|$ (the number of states). When run on the same class of PDAs as Lang's algorithm, our algorithm is both more space-efficient by a factor of $|\Gamma|$ and more time-efficient by a factor of $|Q| \cdot |\Gamma|$.

The Surprising Computational Power of Nondeterministic Stack RNNs

Traditional recurrent neural networks (RNNs) have a fixed, finite number of memory cells. In theory (assuming bounded range and precision), this limits their formal language recognition power to regular languages, and in practice, RNNs have been shown to be unable to learn many context-free languages (CFLs). In order to expand the class of languages RNNs recognize, prior work has augmented RNNs with a nondeterministic stack data structure, putting them on par with pushdown automata and increasing their language recognition power to CFLs. Nondeterminism is needed for recognizing all CFLs (not just deterministic CFLs), but in this paper, we show that nondeterminism and the neural controller interact to produce two more unexpected abilities. First, the nondeterministic stack RNN can recognize not only CFLs, but also many non-context-free languages. Second, it can recognize languages with much larger alphabet sizes than one might expect given the size of its stack alphabet. Finally, to increase the information capacity in the stack and allow it to solve more complicated tasks with large alphabet sizes, we propose a new version of the nondeterministic stack that simulates stacks of vectors rather than discrete symbols. We demonstrate perplexity improvements with this new model on the Penn Treebank language modeling benchmark.

Learning Hierarchical Structures with Differentiable Nondeterministic Stacks

Learning hierarchical structures in sequential data -- from simple algorithmic patterns to natural language -- in a reliable, generalizable way remains a challenging problem for neural language models. Past work has shown that recurrent neural networks (RNNs) struggle to generalize on held-out algorithmic or syntactic patterns without supervision or some inductive bias. To remedy this, many papers have explored augmenting RNNs with various differentiable stacks, by analogy with finite automata and pushdown automata. In this paper, we present a stack RNN model based on the recently proposed Nondeterministic Stack RNN (NS-RNN) that achieves lower cross-entropy than all previous stack RNNs on five context-free language modeling tasks (within 0.05 nats of the information-theoretic lower bound), including a task in which the NS-RNN previously failed to outperform a deterministic stack RNN baseline. Our model assigns arbitrary positive weights instead of probabilities to stack actions, and we provide an analysis of why this improves training. We also propose a restricted version of the NS-RNN that makes it practical to use for language modeling on natural language and present results on the Penn Treebank corpus.

Learning Context-Free Languages with Nondeterministic Stack RNNs

We present a differentiable stack data structure that simultaneously and tractably encodes an exponential number of stack configurations, based on Lang's algorithm for simulating nondeterministic pushdown automata. We call the combination of this data structure with a recurrent neural network (RNN) controller a Nondeterministic Stack RNN. We compare our model against existing stack RNNs on various formal languages, demonstrating that our model converges more reliably to algorithmic behavior on deterministic tasks, and achieves lower cross-entropy on inherently nondeterministic tasks.

Efficiency through Auto-Sizing: Notre Dame NLP's Submission to the WNGT 2019 Efficiency Task

This paper describes the Notre Dame Natural Language Processing Group's (NDNLP) submission to the WNGT 2019 shared task (Hayashi et al., 2019). We investigated the impact of auto-sizing (Murray and Chiang, 2015; Murray et al., 2019) to the Transformer network (Vaswani et al., 2017) with the goal of substantially reducing the number of parameters in the model. Our method was able to eliminate more than 25% of the model's parameters while suffering a decrease of only 1.1 BLEU.