Characterizing the Expressivity of Transformer Language Models

Transformer-based language models (LMs) have achieved widespread empirical success, but their theoretical expressive power remains only partially understood. Prior work often relies on idealized models with assumptions -- such as arbitrary numerical precision and hard attention -- that diverge from real-world transformers. In this work, we provide an exact characterization of fixed-precision transformers with strict future masking and soft attention, an idealization that more closely mirrors practical implementations. We show that these models are precisely as expressive as a specific fragment of linear temporal logic that includes only a single temporal operator: the past operator. We further relate this logic to established classes in formal language theory, automata theory, and algebra, yielding a rich and unified theoretical framework for understanding transformer expressivity. Finally, we present empirical results that align closely with our theory: transformers trained on languages within their theoretical capacity generalize perfectly over lengths, while they consistently fail to generalize on languages beyond it.

Towards Developmentally Plausible Rewards: Communicative Success as a Learning Signal for Interactive Language Models

We propose a method for training language models in an interactive setting inspired by child language acquisition. In our setting, a speaker attempts to communicate some information to a listener in a single-turn dialogue and receives a reward if communicative success is achieved. Unlike earlier related work using image--caption data for interactive reference games, we operationalize communicative success in a more abstract language-only question--answering setting. First, we present a feasibility study demonstrating that our reward provides an indirect signal about grammaticality. Second, we conduct experiments using reinforcement learning to fine-tune language models. We observe that cognitively plausible constraints on the communication channel lead to interpretable changes in speaker behavior. However, we do not yet see improvements on linguistic evaluations from our training regime. We outline potential modifications to the task design and training configuration that could better position future work to use our methodology to observe the benefits of interaction on language learning in computational cognitive models.

Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlo

A wide range of LM applications require generating text that conforms to syntactic or semantic constraints. Imposing such constraints can be naturally framed as probabilistic conditioning, but exact generation from the resulting distribution -- which can differ substantially from the LM's base distribution -- is generally intractable. In this work, we develop an architecture for controlled LM generation based on sequential Monte Carlo (SMC). Our SMC framework allows us to flexibly incorporate domain- and problem-specific constraints at inference time, and efficiently reallocate computational resources in light of new information during the course of generation. By comparing to a number of alternatives and ablations on four challenging domains -- Python code generation for data science, text-to-SQL, goal inference, and molecule synthesis -- we demonstrate that, with little overhead, our approach allows small open-source language models to outperform models over 8x larger, as well as closed-source, fine-tuned ones. In support of the probabilistic perspective, we show that these performance improvements are driven by better approximation to the posterior distribution. Our system builds on the framework of Lew et al. (2023) and integrates with its language model probabilistic programming language, giving users a simple, programmable way to apply SMC to a broad variety of controlled generation problems.

Better Estimation of the KL Divergence Between Language Models

Estimating the Kullback--Leibler (KL) divergence between language models has many applications, e.g., reinforcement learning from human feedback (RLHF), interpretability, and knowledge distillation. However, computing the exact KL divergence between two arbitrary language models is intractable. Thus, practitioners often resort to the use of sampling-based estimators. While it is easy to fashion a simple Monte Carlo (MC) estimator that provides an unbiased estimate of the KL divergence between language models, this estimator notoriously suffers from high variance, and can even result in a negative estimate of the KL divergence, a non-negative quantity. In this paper, we introduce a Rao--Blackwellized estimator that is also unbiased and provably has variance less than or equal to that of the standard Monte Carlo estimator. In an empirical study on sentiment-controlled fine-tuning, we show that our estimator provides more stable KL estimates and reduces variance substantially in practice. Additionally, we derive an analogous Rao--Blackwellized estimator of the gradient of the KL divergence, which leads to more stable training and produces models that more frequently appear on the Pareto frontier of reward vs. KL compared to the ones trained with the MC estimator of the gradient.

Findings of the BabyLM Challenge: Sample-Efficient Pretraining on Developmentally Plausible Corpora

Children can acquire language from less than 100 million words of input. Large language models are far less data-efficient: they typically require 3 or 4 orders of magnitude more data and still do not perform as well as humans on many evaluations. These intensive resource demands limit the ability of researchers to train new models and use existing models as developmentally plausible cognitive models. The BabyLM Challenge is a communal effort in which participants compete to optimize language model training on a fixed data budget. Submissions are compared on various evaluation tasks targeting grammatical ability, downstream task performance, and generalization. Participants can submit to up to three tracks with progressively looser data restrictions. From over 30 submissions, we extract concrete recommendations on how best to train data-efficient language models, and on where future efforts should (and perhaps should not) focus. The winning submissions using the LTG-BERT architecture (Samuel et al., 2023) outperformed models trained on trillions of words. Other submissions achieved strong results through training on shorter input sequences or training a student model on a pretrained teacher. Curriculum learning attempts, which accounted for a large number of submissions, were largely unsuccessful, though some showed modest improvements.

Fast Controlled Generation from Language Models with Adaptive Weighted Rejection Sampling

The dominant approach to generating from language models subject to some constraint is locally constrained decoding (LCD), incrementally sampling tokens at each time step such that the constraint is never violated. Typically, this is achieved through token masking: looping over the vocabulary and excluding non-conforming tokens. There are two important problems with this approach. (i) Evaluating the constraint on every token can be prohibitively expensive -- LM vocabularies often exceed $100,000$ tokens. (ii) LCD can distort the global distribution over strings, sampling tokens based only on local information, even if they lead down dead-end paths. This work introduces a new algorithm that addresses both these problems. First, to avoid evaluating a constraint on the full vocabulary at each step of generation, we propose an adaptive rejection sampling algorithm that typically requires orders of magnitude fewer constraint evaluations. Second, we show how this algorithm can be extended to produce low-variance, unbiased estimates of importance weights at a very small additional cost -- estimates that can be soundly used within previously proposed sequential Monte Carlo algorithms to correct for the myopic behavior of local constraint enforcement. Through extensive empirical evaluation in text-to-SQL, molecular synthesis, goal inference, pattern matching, and JSON domains, we show that our approach is superior to state-of-the-art baselines, supporting a broader class of constraints and improving both runtime and performance. Additional theoretical and empirical analyses show that our method's runtime efficiency is driven by its dynamic use of computation, scaling with the divergence between the unconstrained and constrained LM, and as a consequence, runtime improvements are greater for better models.

Taxonomy-Aware Evaluation of Vision-Language Models

When a vision-language model (VLM) is prompted to identify an entity depicted in an image, it may answer 'I see a conifer,' rather than the specific label 'norway spruce'. This raises two issues for evaluation: First, the unconstrained generated text needs to be mapped to the evaluation label space (i.e., 'conifer'). Second, a useful classification measure should give partial credit to less-specific, but not incorrect, answers ('norway spruce' being a type of 'conifer'). To meet these requirements, we propose a framework for evaluating unconstrained text predictions, such as those generated from a vision-language model, against a taxonomy. Specifically, we propose the use of hierarchical precision and recall measures to assess the level of correctness and specificity of predictions with regard to a taxonomy. Experimentally, we first show that existing text similarity measures do not capture taxonomic similarity well. We then develop and compare different methods to map textual VLM predictions onto a taxonomy. This allows us to compute hierarchical similarity measures between the generated text and the ground truth labels. Finally, we analyze modern VLMs on fine-grained visual classification tasks based on our proposed taxonomic evaluation scheme.

Unique Hard Attention: A Tale of Two Sides

Understanding the expressive power of transformers has recently attracted attention, as it offers insights into their abilities and limitations. Many studies analyze unique hard attention transformers, where attention selects a single position that maximizes the attention scores. When multiple positions achieve the maximum score, either the rightmost or the leftmost of those is chosen. In this paper, we highlight the importance of this seeming triviality. Recently, finite-precision transformers with both leftmost- and rightmost-hard attention were shown to be equivalent to Linear Temporal Logic (LTL). We show that this no longer holds with only leftmost-hard attention -- in that case, they correspond to a \emph{strictly weaker} fragment of LTL. Furthermore, we show that models with leftmost-hard attention are equivalent to \emph{soft} attention, suggesting they may better approximate real-world transformers than right-attention models. These findings refine the landscape of transformer expressivity and underscore the role of attention directionality.

Can Language Models Learn Typologically Implausible Languages?

Grammatical features across human languages show intriguing correlations often attributed to learning biases in humans. However, empirical evidence has been limited to experiments with highly simplified artificial languages, and whether these correlations arise from domain-general or language-specific biases remains a matter of debate. Language models (LMs) provide an opportunity to study artificial language learning at a large scale and with a high degree of naturalism. In this paper, we begin with an in-depth discussion of how LMs allow us to better determine the role of domain-general learning biases in language universals. We then assess learnability differences for LMs resulting from typologically plausible and implausible languages closely following the word-order universals identified by linguistic typologists. We conduct a symmetrical cross-lingual study training and testing LMs on an array of highly naturalistic but counterfactual versions of the English (head-initial) and Japanese (head-final) languages. Compared to similar work, our datasets are more naturalistic and fall closer to the boundary of plausibility. Our experiments show that these LMs are often slower to learn these subtly implausible languages, while ultimately achieving similar performance on some metrics regardless of typological plausibility. These findings lend credence to the conclusion that LMs do show some typologically-aligned learning preferences, and that the typological patterns may result from, at least to some degree, domain-general learning biases.

A Distributional Perspective on Word Learning in Neural Language Models

Language models (LMs) are increasingly being studied as models of human language learners. Due to the nascency of the field, it is not well-established whether LMs exhibit similar learning dynamics to humans, and there are few direct comparisons between learning trajectories in humans and models. Word learning trajectories for children are relatively well-documented, and recent work has tried to extend these investigations to language models. However, there are no widely agreed-upon metrics for word learning in language models. We take a distributional approach to this problem, defining lexical knowledge in terms of properties of the learned distribution for a target word. We argue that distributional signatures studied in prior work fail to capture key distributional information. Thus, we propose an array of signatures that improve on earlier approaches by capturing knowledge of both where the target word can and cannot occur as well as gradient preferences about the word's appropriateness. We obtain learning trajectories for a selection of small language models we train from scratch, study the relationship between different distributional signatures, compare how well they align with human word learning trajectories and interpretable lexical features, and address basic methodological questions about estimating these distributional signatures. Our metrics largely capture complementary information, suggesting that it is important not to rely on a single metric. However, across all metrics, language models' learning trajectories fail to correlate with those of children.