Michael G. Hahn

Thomas Hikaru Clark, Clara Meister, Tiago Pimentel et al. · cambridge

While natural languages differ widely in both canonical word order and word order flexibility, their word orders still follow shared cross-linguistic statistical patterns, often attributed to functional pressures. In the effort to identify these pressures, prior work has compared real and counterfactual word orders. Yet one functional pressure has been overlooked in such investigations: the uniform information density (UID) hypothesis, which holds that information should be spread evenly throughout an utterance. Here, we ask whether a pressure for UID may have influenced word order patterns cross-linguistically. To this end, we use computational models to test whether real orders lead to greater information uniformity than counterfactual orders. In our empirical study of 10 typologically diverse languages, we find that: (i) among SVO languages, real word orders consistently have greater uniformity than reverse word orders, and (ii) only linguistically implausible counterfactual orders consistently exceed the uniformity of real orders. These findings are compatible with a pressure for information uniformity in the development and usage of natural languages.

Michael Hahn, Navin Goyal

Scaling large language models (LLMs) leads to an emergent capacity to learn in-context from example demonstrations. Despite progress, theoretical understanding of this phenomenon remains limited. We argue that in-context learning relies on recombination of compositional operations found in natural language data. We derive an information-theoretic bound showing how in-context learning abilities arise from generic next-token prediction when the pretraining distribution has sufficient amounts of compositional structure, under linguistically motivated assumptions. A second bound provides a theoretical justification for the empirical success of prompting LLMs to output intermediate steps towards an answer. To validate theoretical predictions, we introduce a controlled setup for inducing in-context learning; unlike previous approaches, it accounts for the compositional nature of language. Trained transformers can perform in-context learning for a range of tasks, in a manner consistent with the theoretical results. Mirroring real-world LLMs in a miniature setup, in-context learning emerges when scaling parameters and data, and models perform better when prompted to output intermediate steps. Probing shows that in-context learning is supported by a representation of the input's compositional structure. Taken together, these results provide a step towards theoretical understanding of emergent behavior in large language models.

Mayank Jobanputra, Yana Veitsman, Yash Sarrof et al.

Transformers have theoretical limitations in modeling certain sequence-to-sequence tasks, yet it remains largely unclear if these limitations play a role in large-scale pretrained LLMs, or whether LLMs might effectively overcome these constraints in practice due to the scale of both the models themselves and their pretraining data. We explore how these architectural constraints manifest after pretraining, by studying a family of $\textit{retrieval}$ and $\textit{copying}$ tasks inspired by Liu et al. [2024a]. We use a recently proposed framework for studying length generalization [Huang et al., 2025] to provide guarantees for each of our settings. Empirically, we observe an $\textit{induction-versus-anti-induction}$ asymmetry, where pretrained models are better at retrieving tokens to the right (induction) rather than the left (anti-induction) of a query token. This asymmetry disappears upon targeted fine-tuning if length-generalization is guaranteed by theory. Mechanistic analysis reveals that this asymmetry is connected to the differences in the strength of induction versus anti-induction circuits within pretrained transformers. We validate our findings through practical experiments on real-world tasks demonstrating reliability risks. Our results highlight that pretraining selectively enhances certain transformer capabilities, but does not overcome fundamental length-generalization limits.

Satwik Bhattamishra, Michael Hahn, Phil Blunsom et al.

Transformer architectures have been widely adopted in foundation models. Due to their high inference costs, there is renewed interest in exploring the potential of efficient recurrent architectures (RNNs). In this paper, we analyze the differences in the representational capabilities of Transformers and RNNs across several tasks of practical relevance, including index lookup, nearest neighbor, recognizing bounded Dyck languages, and string equality. For the tasks considered, our results show separations based on the size of the model required for different architectures. For example, we show that a one-layer Transformer of logarithmic width can perform index lookup, whereas an RNN requires a hidden state of linear size. Conversely, while constant-size RNNs can recognize bounded Dyck languages, we show that one-layer Transformers require a linear size for this task. Furthermore, we show that two-layer Transformers of logarithmic size can perform decision tasks such as string equality or disjointness, whereas both one-layer Transformers and recurrent models require linear size for these tasks. We also show that a log-size two-layer Transformer can implement the nearest neighbor algorithm in its forward pass; on the other hand recurrent models require linear size. Our constructions are based on the existence of $N$ nearly orthogonal vectors in $O(\log N)$ dimensional space and our lower bounds are based on reductions from communication complexity problems. We supplement our theoretical results with experiments that highlight the differences in the performance of these architectures on practical-size sequences.

Michael Hahn, Marco Baroni

Recurrent neural networks (RNNs) have reached striking performance in many natural language processing tasks. This has renewed interest in whether these generic sequence processing devices are inducing genuine linguistic knowledge. Nearly all current analytical studies, however, initialize the RNNs with a vocabulary of known words, and feed them tokenized input during training. We present a multi-lingual study of the linguistic knowledge encoded in RNNs trained as character-level language models, on input data with word boundaries removed. These networks face a tougher and more cognitively realistic task, having to discover any useful linguistic unit from scratch based on input statistics. The results show that our "near tabula rasa" RNNs are mostly able to solve morphological, syntactic and semantic tasks that intuitively presuppose word-level knowledge, and indeed they learned, to some extent, to track word boundaries. Our study opens the door to speculations about the necessity of an explicit, rigid word lexicon in language learning and usage.

Michael Hahn, Frank Keller

Research on human reading has long documented that reading behavior shows task-specific effects, but it has been challenging to build general models predicting what reading behavior humans will show in a given task. We introduce NEAT, a computational model of the allocation of attention in human reading, based on the hypothesis that human reading optimizes a tradeoff between economy of attention and success at a task. Our model is implemented using contemporary neural network modeling techniques, and makes explicit and testable predictions about how the allocation of attention varies across different tasks. We test this in an eyetracking study comparing two versions of a reading comprehension task, finding that our model successfully accounts for reading behavior across the tasks. Our work thus provides evidence that task effects can be modeled as optimal adaptation to task demands.