Provably Learning Attention with Queries

We study the problem of learning Transformer-based sequence models with black-box access to their outputs. In this setting, a learner may adaptively query the oracle with any sequence of vectors and observe the corresponding real-valued output. We begin with the simplest case, a single-head softmax-attention regressor. We show that for a model with width $d$, there is an elementary algorithm to learn the parameters of single-head attention exactly with $O(d^2)$ queries. Further, we show that if there exists an algorithm to learn ReLU feedforward networks (FFNs), then the single-head algorithm can be easily adapted to learn one-layer Transformers with single-head attention. Next, motivated by the regime where the head dimension $r \ll d$, we provide a randomised algorithm that learns single-head attention-based models with $O(rd)$ queries via compressed sensing arguments. We also study robustness to noisy oracle access, proving that under mild norm and margin conditions, the parameters can be estimated to $\varepsilon$ accuracy with a polynomial number of queries even when outputs are only provided up to additive tolerance. Finally, we show that multi-head attention parameters are not identifiable from value queries in general -- distinct parameterisations can induce the same input-output map. Hence, guarantees analogous to the single-head setting are impossible without additional structural assumptions.

Systematicity between Forms and Meanings across Languages Supports Efficient Communication

Languages vary widely in how meanings map to word forms. These mappings have been found to support efficient communication; however, this theory does not account for systematic relations within word forms. We examine how a restricted set of grammatical meanings (e.g. person, number) are expressed on verbs and pronouns across typologically diverse languages. Consistent with prior work, we find that verb and pronoun forms are shaped by competing communicative pressures for simplicity (minimizing the inventory of grammatical distinctions) and accuracy (enabling recovery of intended meanings). Crucially, our proposed model uses a novel measure of complexity (inverse of simplicity) based on the learnability of meaning-to-form mappings. This innovation captures fine-grained regularities in linguistic form, allowing better discrimination between attested and unattested systems, and establishes a new connection from efficient communication theory to systematicity in natural language.

System-Mediated Attention Imbalances Make Vision-Language Models Say Yes

Vision-language model (VLM) hallucination is commonly linked to imbalanced allocation of attention across input modalities: system, image and text. However, existing mitigation strategies tend towards an image-centric interpretation of these imbalances, often prioritising increased image attention while giving less consideration to the roles of the other modalities. In this study, we evaluate a more holistic, system-mediated account, which attributes these imbalances to functionally redundant system weights that reduce attention to image and textual inputs. We show that this framework offers a useful empirical perspective on the yes-bias, a common form of hallucination in which VLMs indiscriminately respond 'yes'. Causally redistributing attention from the system modality to image and textual inputs substantially suppresses this bias, often outperforming existing approaches. We further present evidence suggesting that system-mediated attention imbalances contribute to the yes-bias by encouraging a default reliance on coarse input representations, which are effective for some tasks but ill-suited to others. Taken together, these findings firmly establish system attention as a key factor in VLM hallucination and highlight its potential as a lever for mitigation.

The Bayesian Origin of the Probability Weighting Function in Human Representation of Probabilities

Understanding the representation of probability in the human mind has been of great interest to understanding human decision making. Classical paradoxes in decision making suggest that human perception distorts probability magnitudes. Previous accounts postulate a Probability Weighting Function that transforms perceived probabilities; however, its motivation has been debated. Recent work has sought to motivate this function in terms of noisy representations of probabilities in the human mind. Here, we present an account of the Probability Weighting Function grounded in rational inference over optimal decoding from noisy neural encoding of quantities. We show that our model accurately accounts for behavior in a lottery task and a dot counting task. It further accounts for adaptation to a bimodal short-term prior. Taken together, our results provide a unifying account grounding the human representation of probability in rational inference.

One Size Fits None: Rethinking Fairness in Medical AI

Machine learning (ML) models are increasingly used to support clinical decision-making. However, real-world medical datasets are often noisy, incomplete, and imbalanced, leading to performance disparities across patient subgroups. These differences raise fairness concerns, particularly when they reinforce existing disadvantages for marginalized groups. In this work, we analyze several medical prediction tasks and demonstrate how model performance varies with patient characteristics. While ML models may demonstrate good overall performance, we argue that subgroup-level evaluation is essential before integrating them into clinical workflows. By conducting a performance analysis at the subgroup level, differences can be clearly identified-allowing, on the one hand, for performance disparities to be considered in clinical practice, and on the other hand, for these insights to inform the responsible development of more effective models. Thereby, our work contributes to a practical discussion around the subgroup-sensitive development and deployment of medical ML models and the interconnectedness of fairness and transparency.

Position: Pause Recycling LoRAs and Prioritize Mechanisms to Uncover Limits and Effectiveness

Merging or routing low-rank adapters (LoRAs) has emerged as a popular solution for enhancing large language models, particularly when data access is restricted by regulatory or domain-specific constraints. This position paper argues that the research community should shift its focus from developing new merging or routing algorithms to understanding the conditions under which reusing LoRAs is truly effective. Through theoretical analysis and synthetic two-hop reasoning and math word-problem tasks, we examine whether reusing LoRAs enables genuine compositional generalization or merely reflects shallow pattern matching. Evaluating two data-agnostic methods--parameter averaging and dynamic adapter selection--we found that reusing LoRAs often fails to logically integrate knowledge across disjoint fine-tuning datasets, especially when such knowledge is underrepresented during pretraining. Our empirical results, supported by theoretical insights into LoRA's limited expressiveness, highlight the preconditions and constraints of reusing them for unseen tasks and cast doubt on its feasibility as a truly data-free approach. We advocate for pausing the pursuit of novel methods for recycling LoRAs and emphasize the need for rigorous mechanisms to guide future academic research in adapter-based model merging and practical system designs for practitioners.

Born a Transformer -- Always a Transformer?

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. [2024]. We use the recently proposed C-RASP framework for studying length generalization [Huang et al., 2025b] 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.

Language models can learn implicit multi-hop reasoning, but only if they have lots of training data

Implicit reasoning is the ability of a language model to solve multi-hop reasoning tasks in a single forward pass, without chain of thought. We investigate this capability using GPT2-style language models trained from scratch on controlled $k$-hop reasoning datasets ($k = 2, 3, 4$). We show that while such models can indeed learn implicit $k$-hop reasoning, the required training data grows exponentially in $k$, and the required number of transformer layers grows linearly in $k$. We offer a theoretical explanation for why this depth growth is necessary. We further find that the data requirement can be mitigated, but not eliminated, through curriculum learning.

Contextualize-then-Aggregate: Circuits for In-Context Learning in Gemma-2 2B

In-Context Learning (ICL) is an intriguing ability of large language models (LLMs). Despite a substantial amount of work on its behavioral aspects and how it emerges in miniature setups, it remains unclear which mechanism assembles task information from the individual examples in a fewshot prompt. We use causal interventions to identify information flow in Gemma-2 2B for five naturalistic ICL tasks. We find that the model infers task information using a two-step strategy we call contextualize-then-aggregate: In the lower layers, the model builds up representations of individual fewshot examples, which are contextualized by preceding examples through connections between fewshot input and output tokens across the sequence. In the higher layers, these representations are aggregated to identify the task and prepare prediction of the next output. The importance of the contextualization step differs between tasks, and it may become more important in the presence of ambiguous examples. Overall, by providing rigorous causal analysis, our results shed light on the mechanisms through which ICL happens in language models.

Lower Bounds for Chain-of-Thought Reasoning in Hard-Attention Transformers

Chain-of-thought reasoning and scratchpads have emerged as critical tools for enhancing the computational capabilities of transformers. While theoretical results show that polynomial-length scratchpads can extend transformers' expressivity from $TC^0$ to $PTIME$, their required length remains poorly understood. Empirical evidence even suggests that transformers need scratchpads even for many problems in $TC^0$, such as Parity or Multiplication, challenging optimistic bounds derived from circuit complexity. In this work, we initiate the study of systematic lower bounds for the number of CoT steps across different algorithmic problems, in the hard-attention regime. We study a variety of algorithmic problems, and provide bounds that are tight up to logarithmic factors. Overall, these results contribute to emerging understanding of the power and limitations of chain-of-thought reasoning.