arXiv subjects

Jiaoda Li

Publications and source records attributed to Jiaoda Li.

11 recordsLinked to original sources

arXiv2026

Disentangling the Expressivity of RoPE

Two accounts recur in explanations of the success of rotary position embeddings (RoPE). Expressivity studies associate periodic position information with modular predicates, whereas mechanistic and long-context studies emphasize positional anchors and local offsets. We formalize both accounts for fully uniform, finite-precision soft-attention transformers. We find that, if every rotary component is periodic, RoPE transformers recognize exactly the languages definable in past temporal logic with modular predicates. Conventional RoPE is different: The rotations it computes never repeat. This yields a precision-dependent bounded simulation of fixed-offset look-back operators, rather than an all-length modular characterization. Controlled experiments match this separation: Constructed periodic schedules length-generalize on modular languages, while conventional RoPE behaves more like a bounded locality bias and can impair tasks requiring position-invariant access to distant context. Altogether, our findings shed light on RoPE transformers, bringing theoretical expressivity characterizations closer to models used in practice.

cs.LG↗

arXiv2026

Characterizing the Expressivity of Local Attention in Transformers

The transformer is the most popular neural architecture for language modeling. The cornerstone of the transformer is its global attention mechanism, which lets the model aggregate information from all preceding tokens before generating the next token. One common variant of attention is called local attention, which restricts each token to aggregating information from a bounded window of predecessors, reducing the quadratic cost of global attention to linear. Although this restriction is usually motivated by efficiency, it has also been found to improve model quality, a phenomenon that has so far lacked a satisfactory explanation. We provide a formal account of this phenomenon in terms of recognizer expressivity. It has been shown that fixed-precision transformers with global attention correspond to a fragment of linear temporal logic containing a single past operator. We additionally prove that adding local attention introduces a second temporal operator, strictly enlarging the class of recognizable regular languages. Moreover, global and local attention are expressively complementary: neither subsumes the other, and combining them yields the richest fragment. Experiments on formal language recognition and natural language modeling corroborate the theory, showing that hybrid global--local transformers outperform their global-only counterparts.

cs.CL↗

arXiv2026

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↗

arXiv2025

Characterizing the Expressivity of Fixed-Precision Transformer Language Models

Transformer-based language models (LMs) have achieved widespread empirical success, but their theoretical expressive power remains only partially understood. In this work, we analyze a restricted idealization of fixed-precision transformers with strict future masking, soft attention, and no positional encodings. We establish that this class of models is exactly as expressive as a specific fragment of linear temporal logic that contains only a single temporal operator: the past operator. We further connect this fragment to established classes in formal language theory, automata theory, and algebra, yielding a unified framework for understanding transformer expressivity under this idealization. Finally, we present empirical results that align closely with our theory: transformers trained on languages within their characterized expressive capacity generalize reliably across sequence lengths, while they consistently fail to generalize on languages beyond it.

cs.CL↗

arXiv2025

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.

cs.LG↗

arXiv2024

What Do Language Models Learn in Context? The Structured Task Hypothesis

Large language models (LLMs) exhibit an intriguing ability to learn a novel task from in-context examples presented in a demonstration, termed in-context learning (ICL). Understandably, a swath of research has been dedicated to uncovering the theories underpinning ICL. One popular hypothesis explains ICL by task selection. LLMs identify the task based on the demonstration and generalize it to the prompt. Another popular hypothesis is that ICL is a form of meta-learning, i.e., the models learn a learning algorithm at pre-training time and apply it to the demonstration. Finally, a third hypothesis argues that LLMs use the demonstration to select a composition of tasks learned during pre-training to perform ICL. In this paper, we empirically explore these three hypotheses that explain LLMs' ability to learn in context with a suite of experiments derived from common text classification tasks. We invalidate the first two hypotheses with counterexamples and provide evidence in support of the last hypothesis. Our results suggest an LLM could learn a novel task in context via composing tasks learned during pre-training.

cs.CL↗

arXiv2024

A Transformer with Stack Attention

Natural languages are believed to be (mildly) context-sensitive. Despite underpinning remarkably capable large language models, transformers are unable to model many context-free language tasks. In an attempt to address this limitation in the modeling power of transformer-based language models, we propose augmenting them with a differentiable, stack-based attention mechanism. Our stack-based attention mechanism can be incorporated into any transformer-based language model and adds a level of interpretability to the model. We show that the addition of our stack-based attention mechanism enables the transformer to model some, but not all, deterministic context-free languages.

cs.CL↗

arXiv2023

Towards a Mechanistic Interpretation of Multi-Step Reasoning Capabilities of Language Models

Recent work has shown that language models (LMs) have strong multi-step (i.e., procedural) reasoning capabilities. However, it is unclear whether LMs perform these tasks by cheating with answers memorized from pretraining corpus, or, via a multi-step reasoning mechanism. In this paper, we try to answer this question by exploring a mechanistic interpretation of LMs for multi-step reasoning tasks. Concretely, we hypothesize that the LM implicitly embeds a reasoning tree resembling the correct reasoning process within it. We test this hypothesis by introducing a new probing approach (called MechanisticProbe) that recovers the reasoning tree from the model's attention patterns. We use our probe to analyze two LMs: GPT-2 on a synthetic task (k-th smallest element), and LLaMA on two simple language-based reasoning tasks (ProofWriter & AI2 Reasoning Challenge). We show that MechanisticProbe is able to detect the information of the reasoning tree from the model's attentions for most examples, suggesting that the LM indeed is going through a process of multi-step reasoning within its architecture in many cases.

cs.CL↗

arXiv2023

Differentiable Subset Pruning of Transformer Heads

Multi-head attention, a collection of several attention mechanisms that independently attend to different parts of the input, is the key ingredient in the Transformer. Recent work has shown, however, that a large proportion of the heads in a Transformer's multi-head attention mechanism can be safely pruned away without significantly harming the performance of the model; such pruning leads to models that are noticeably smaller and faster in practice. Our work introduces a new head pruning technique that we term differentiable subset pruning. Intuitively, our method learns per-head importance variables and then enforces a user-specified hard constraint on the number of unpruned heads. The importance variables are learned via stochastic gradient descent. We conduct experiments on natural language inference and machine translation; we show that differentiable subset pruning performs comparably or better than previous works while offering precise control of the sparsity level.

cs.CL↗

arXiv2022

Probing via Prompting

Probing is a popular method to discern what linguistic information is contained in the representations of pre-trained language models. However, the mechanism of selecting the probe model has recently been subject to intense debate, as it is not clear if the probes are merely extracting information or modeling the linguistic property themselves. To address this challenge, this paper introduces a novel model-free approach to probing, by formulating probing as a prompting task. We conduct experiments on five probing tasks and show that our approach is comparable or better at extracting information than diagnostic probes while learning much less on its own. We further combine the probing via prompting approach with attention head pruning to analyze where the model stores the linguistic information in its architecture. We then examine the usefulness of a specific linguistic property for pre-training by removing the heads that are essential to that property and evaluating the resulting model's performance on language modeling.

cs.CL↗

arXiv2021

Vision Matters When It Should: Sanity Checking Multimodal Machine Translation Models

Multimodal machine translation (MMT) systems have been shown to outperform their text-only neural machine translation (NMT) counterparts when visual context is available. However, recent studies have also shown that the performance of MMT models is only marginally impacted when the associated image is replaced with an unrelated image or noise, which suggests that the visual context might not be exploited by the model at all. We hypothesize that this might be caused by the nature of the commonly used evaluation benchmark, also known as Multi30K, where the translations of image captions were prepared without actually showing the images to human translators. In this paper, we present a qualitative study that examines the role of datasets in stimulating the leverage of visual modality and we propose methods to highlight the importance of visual signals in the datasets which demonstrate improvements in reliance of models on the source images. Our findings suggest the research on effective MMT architectures is currently impaired by the lack of suitable datasets and careful consideration must be taken in creation of future MMT datasets, for which we also provide useful insights.

cs.CL↗