arXiv subjects

Jonathan Rawski

Publications and source records attributed to Jonathan Rawski.

5 recordsLinked to original sources

arXiv2025

Probability Distributions Computed by Autoregressive Transformers

Most expressivity results for transformers treat them as language recognizers -- devices that accept or reject strings -- rather than as they are used in practice: as language models that generate strings autoregressively and probabilistically. We characterize the probability distributions that transformer language models can express. We show that making transformer language recognizers autoregressive can sometimes increase their expressivity, and that making them probabilistic can break equivalences that hold in the non-probabilistic case. Our overall contribution is to tease apart what functions transformers are capable of expressing in their most common use case as language models.

cs.CL↗

arXiv2024

Transformers as Transducers

We study the sequence-to-sequence mapping capacity of transformers by relating them to finite transducers, and find that they can express surprisingly large classes of transductions. We do so using variants of RASP, a programming language designed to help people "think like transformers," as an intermediate representation. We extend the existing Boolean variant B-RASP to sequence-to-sequence functions and show that it computes exactly the first-order rational functions (such as string rotation). Then, we introduce two new extensions. B-RASP[pos] enables calculations on positions (such as copying the first half of a string) and contains all first-order regular functions. S-RASP adds prefix sum, which enables additional arithmetic operations (such as squaring a string) and contains all first-order polyregular functions. Finally, we show that masked average-hard attention transformers can simulate S-RASP.

cs.FL↗

arXiv2022

Benchmarking Compositionality with Formal Languages

Recombining known primitive concepts into larger novel combinations is a quintessentially human cognitive capability. Whether large neural models in NLP can acquire this ability while learning from data is an open question. In this paper, we investigate this problem from the perspective of formal languages. We use deterministic finite-state transducers to make an unbounded number of datasets with controllable properties governing compositionality. By randomly sampling over many transducers, we explore which of their properties contribute to learnability of a compositional relation by a neural network. We find that the models either learn the relations completely or not at all. The key is transition coverage, setting a soft learnability limit at 400 examples per transition.

cs.CL↗

arXiv2019

Tensor Product Representations of Subregular Formal Languages

This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over these models define subregular classes of languages. The semantics of such statements can be compiled into tensor structures, using multilinear maps as function application for evaluation. This method is applied to consider two properly subregular languages over different string models.

cs.FL↗

arXiv2019

Learning with Partially Ordered Representations

This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one unary relation. We consider unconventional string models where positions can have multiple, shared properties, which are arguably useful in many applications. We show the structures given by these models are partially ordered, and present a learning algorithm that exploits this ordering relation to effectively prune the hypothesis space. We prove this learning algorithm, which takes positive examples as input, finds the most general grammar which covers the data.

cs.FL↗