We investigate the mechanisms underlying a range of list-processing tasks in LLMs, and we find that they have learned to encode a compact, causal representation of a general filtering operation that mirrors the generic ``filter'' function of functional programming. Using causal mediation analysis on a diverse set of list-processing tasks, we find that a small number of attention heads, which we dub *filter heads*, encode a compact representation of the filtering predicate in their query states at certain tokens. We demonstrate that this predicate representation is general and portable: it can be extracted and reapplied to execute the same filtering operation on different collections, presented in different formats, languages, or even in tasks. However, we also identify situations where LMs can exploit a different strategy for filtering: eagerly evaluating if an item satisfies the predicate and storing this intermediate result as a flag directly in the item representations. Our results reveal that transformer LMs can develop human-interpretable implementations of abstract computational operations that generalize in ways that are surprisingly similar to strategies used in traditional functional programming patterns.

Large reasoning models (LRMs) produce a textual chain of thought (CoT) in the process of solving a problem, which serves as a potentially powerful tool to understand the problem by surfacing a human-readable, natural-language explanation. However, it is unclear whether these explanations generalize, i.e. whether they capture general patterns about the underlying problem rather than patterns which are esoteric to the LRM. This is a crucial question in understanding or discovering new concepts, e.g. in AI for science. We study this generalization question by evaluating a specific notion of generalizability: whether explanations produced by one LRM induce the same behavior when given to other LRMs. We find that CoT explanations often exhibit this form of generalization (i.e. they increase consistency between LRMs) and that this increased generalization is correlated with human preference rankings and post-training with reinforcement learning. We further analyze the conditions under which explanations yield consistent answers and propose a straightforward, sentence-level ensembling strategy that improves consistency. Taken together, these results prescribe caution when using LRM explanations to yield new insights and outline a framework for characterizing LRM explanation generalization.

How do protein structure prediction models fold proteins? We investigate this question through causal interventions on the folding trunks of ESMFold, OpenFold, and Boltz-1. Across all three models, we find a shared two-stage computational structure. In the first stage, early blocks initialize pairwise biochemical signals: features like charge propagate from sequence into pairwise representations through architecture-specific pathways. In the second stage, late blocks develop pairwise spatial features: distance and contact information accumulate in the pairwise representation. We verify these mechanisms causally by showing that steering charge and distance features induces predictable structural changes. Furthermore, these representations are functionally interchangeable: pairwise states can be linearly aligned and substituted across models. Together, these results suggest that folding trunks with different architectures, inputs, and training procedures converge on a shared representational organization for mapping sequence chemistry into spatial geometry.

Distilled diffusion models generate images in far fewer timesteps but suffer from reduced sample diversity when generating multiple outputs from the same prompt. To understand this phenomenon, we first investigate whether distillation damages concept representations by examining if the required diversity is properly learned. Surprisingly, distilled models retain the base model’s representational structure: control mechanisms like Concept Sliders and LoRAs transfer seamlessly without retraining, and Slider-Space analysis reveals distilled models possess variational directions needed for diversity yet fail to activate them. This redirects our investigation to understanding how the generation dynamics differ between base and distilled models. Using ${{\hat{\mathbf x}}_0}$ trajectory visualization, we discover distilled models commit to their final image structure almost immediately at the first timestep, while base models distribute structural decisions across many steps. To test whether this first-step commitment causes the diversity loss, we introduce diversity distillation, a hybrid approach using the base model for only the first critical timestep before switching to the distilled model. This single intervention restores sample diversity while maintaining computational efficiency. We provide both causal validation and theoretical support showing why the very first timestep concentrates the diversity bottleneck in distilled models. Our code and data are available at distillation.baulab.info

We investigate the mechanisms that arise when transformers are trained to solve arithmetic on sequences where tokens are variables whose meaning is determined only through their interactions. While previous work has found that transformers develop geometric embeddings that mirror algebraic structure, those previous findings emerge from settings where arithmetic-valued tokens have fixed meanings. We devise a new task in which the assignment of symbols to specific algebraic group elements varies from one sequence to another. Despite this challenging setup, transformers achieve near-perfect accuracy on the task and even generalize to unseen algebraic groups. We develop targeted data distributions to create causal tests of a set of hypothesized mechanisms, and we isolate three mechanisms the models learn: commutative copying where a dedicated head copies answers, identity element recognition that distinguishes identity-containing facts, and closure-based cancellation that tracks group membership to constrain valid answers. Complementary to the geometric representations found in fixed-symbol settings, our findings show that models develop symbolic reasoning mechanisms when trained to reason in-context with variables whose meanings are not fixed.

How a vision-language model internally solves the task of describing an image is far from obvious. We find that the model develops a specific mechanism for this: a small set of attention heads in its language-model backbone, which we call gaze heads, whose attention tracks the image region the model is currently describing. We find them with a simple correlation score from a few forward passes, using comic strips as a controlled testbed where narrative order is laid out spatially. These gaze heads do not just track the image tokens being described: redirecting their attention to a chosen region forces the VLM to describe that region instead. A single attention-mask intervention on the top-100 gaze heads, fewer than 9

Interpretability provides a toolset for understanding how and why language models behave in certain ways. However, there is little unity in the field: Most studies use ad-hoc evaluations and do not share theoretical foundations, making it difficult to measure progress and compare the pros and cons of different techniques. Furthermore, while mechanistic understanding is frequently discussed, the basic causal units underlying these mechanisms are often not explicitly defined. In this article, we propose a perspective on interpretability research grounded in causal mediation analysis. Specifically, we describe the history and current state of interpretability taxonomized according to the types of causal units (mediators) utilized, as well as methods used to search over mediators. We discuss the pros and cons of each mediator, providing insights as to when particular kinds of mediators and search methods are most appropriate. We argue that this framing yields a more cohesive narrative of the field and helps researchers select appropriate methods based on their research objective. Our analysis yields actionable recommendations for future work, including the discovery of new mediators and the development of standardized evaluations tailored to these goals.

The mechanisms behind LLMs' broad over-generalization beyond training examples remain unclear. Emergent misalignment (EM) offers a striking case study: finetuning on narrow tasks induces broad misalignment to semantically-unrelated test domains. In this work, we propose the Piggyback Hypothesis: the chat-template tokens can piggyback the finetuned behaviour onto out-of-domain queries. We validate this hypothesis by showing that subtle perturbations to the prefix (tokens preceding all user queries), or patching the prefix representations with those from the unfinetuned model, can restore alignment without changing the user query. Building on this finding, we propose Token-Regularized Finetuning (TReFT), which regularizes specific token representations during training to mitigate EM. Across different models and multiple EM-inducing datasets, TReFT reduces EM while preserving in-domain learning. On Llama-3.1-8B finetuned on the legal domain, TReFT achieves 33.5

Many multimodal tasks, such as image captioning and visual question answering, require vision-language models (VLMs) to bind objects with their properties and spatial relations. Yet it remains unclear where and how such associations are computed within VLMs. In this work, we show that VLMs rely on two concurrent mechanisms to represent spatial variable binding. In the language model backbone, intermediate layers represent content-independent spatial relations on top of visual tokens corresponding to objects. However, this mechanism plays only a secondary role in shaping model predictions. Instead, the dominant source of spatial information originates in the vision encoder, whose representations encode the layout of objects and are directly exploited by the language model backbone. Notably, this spatial signal is distributed globally across visual tokens, extending beyond object regions into surrounding background areas. We show that enhancing these vision-derived spatial representations globally across all image tokens improves spatial variable binding performance across models of various sizes on complex natural images from the COCO datasets. Together, our results clarify how spatial variable binding is computed within VLMs and highlight the central role of vision encoders in enabling it.

Recent work has shown that large language models (LLMs) exhibit strong numerical sequence modeling capabilities and show promise in time-series prediction. While LLMs display in-context learning capabilities, the mechanisms with which they accomplish time-series prediction remain unclear. Specifically, whether they truly understand the underlying structure, which at a minimum requires reasoning over first differences in the sequence of numbers. To study this, we investigate Llama 3.1-8B from a mechanistic interpretability point of view. Mechanistic interpretability is an emerging field concerned with the reverse engineering of the algorithms learned by neural networks such as LLMs. To assess Llamas' numerical sequence modeling capabilities and to facilitate our mechanistic interpretability analysis, we create a sequence modeling task that cannot be solved without picking up structural cues. Specifically, we sample n random numbers and repeat them with an offset. We find that Llama displays strong performance on our tasks suggesting that it can pick up on the underlying structure. To understand the mechanisms that allow it to do so, we perform probing experiments and activation patching based counterfactual analysis. Probing reveals that the model computes and stores first differences in its internal representations without explicit supervision, indicating that it tracks structural information about the sequence. Activation patching reveals that Llama retrieves the relevant first-difference with a mechanism similar to an induction circuit and subsequently adds it to the current value. Notably, our work represents one of the first studies to identify this form of concept induction in LLMs.

How do language models (LMs) represent characters’ beliefs, especially when those beliefs may differ from reality? This question lies at the heart of understanding the Theory of Mind (ToM) capabilities of LMs. We analyze LMs' ability to reason about characters’ beliefs using causal mediation and abstraction. We construct a dataset, CausalToM, consisting of simple stories where two characters independently change the state of two objects, potentially unaware of each other's actions. Our investigation uncovered a pervasive algorithmic pattern that we call a lookback mechanism, which enables the LM to recall important information when it becomes necessary. The LM binds each character-object-state triple together by co-locating their reference information, represented as Ordering IDs (OIs), in low-rank subspaces of the state token's residual stream. When asked about a character's beliefs regarding the state of an object, the binding lookback retrieves the correct state OI and then the answer lookback retrieves the corresponding state token. When we introduce text specifying that one character is (not) visible to the other, we find that the LM first generates a visibility ID encoding the relation between the observing and the observed character OIs. In a visibility lookback, this ID is used to retrieve information about the observed character and update the observing character's beliefs. Our work provides insights into belief tracking mechanisms, taking a step toward reverse-engineering ToM reasoning in LMs.

We report an exploratory red-teaming study of autonomous language-model-powered agents deployed in a live laboratory environment with persistent memory, email accounts, Discord access, file systems, and shell execution. Over a two-week period, twenty AI researchers interacted with the agents under benign and adversarial conditions. Focusing on failures emerging from the integration of language models with autonomy, tool use, and multi-party communication, we document eleven representative case studies. Observed behaviors include unauthorized compliance with non-owners, disclosure of sensitive information, execution of destructive system-level actions, denial-of-service conditions, uncontrolled resource consumption, identity spoofing vulnerabilities, cross-agent propagation of unsafe practices, and partial system takeover. In several cases, agents reported task completion while the underlying system state contradicted those reports. We also report on some of the failed attempts. Our findings establish the existence of security-, privacy-, and governance-relevant vulnerabilities in realistic deployment settings. These behaviors raise unresolved questions regarding accountability, delegated authority, and responsibility for downstream harms, and warrant urgent attention from legal scholars, policymakers, and researchers across disciplines. This report serves as an initial empirical contribution to that broader conversation.

One of the most common complaints about large language models (LLMs) is their prompt sensitivity – that is, the fact that their ability to perform a task or provide a correct answer to a question can depend unpredictably on the way the question is posed. We investigate this variation by comparing two very different but commonly-used styles of prompting: instruction-based prompts, which describe the task in natural language, and example-based prompts, which provide in-context few-shot demonstration pairs to illustrate the task. We find that, despite large variation in performance as a function of the prompt, the model engages some common underlying mechanisms across different prompts of a task. Specifically, we identify task-specific attention heads whose outputs literally describe the task – which we dub lexical task heads – and show that these heads are shared across prompting styles and trigger subsequent answer production. We further find that behavioral variation between prompts can be explained by the degree to which these heads are activated, and that failures are at least sometimes due to competing task representations that dilute the signal of the target task. Our results together present an increasingly clear picture of how LLMs' internal representations can explain behavior that otherwise seems idiosyncratic to users and developers.

In order to predict the next token, LLMs must represent semantic and surface-level information about the current word. Previous work identified two types of attention heads that disentangle this information: (i) Concept induction heads, which copy word meanings, and (ii) Token induction heads, which copy literal token representations (Feucht et al., 2025). We show that these heads can be used to identify subspaces of model activations that exhibit coherent semantic structure in Llama-2-7b. Specifically, when we transform hidden states using the attention weights of concept heads, we are able to more accurately perform parallelogram arithmetic (Mikolov et al., 2013) on the resulting hidden states, e.g., showing that "Athens" - "Greece" + "China" = "Beijing". This transformation allows for much higher nearest-neighbor accuracy (80

A widely used strategy to discover and understand language model mechanisms is circuit analysis. A circuit is a minimal subgraph of a model's computation graph that executes a specific task. We identify a gap in existing circuit discovery methods: they assume circuits are position-invariant, treating model components as equally relevant across input positions. This limits their ability to capture cross-positional interactions or mechanisms that vary across positions. To address this gap, we propose two improvements to incorporate positionality into circuits, even on tasks containing variable-length examples. First, we extend edge attribution patching, a gradient-based method for circuit discovery, to differentiate between token positions. Second, we introduce the concept of a dataset schema, which defines token spans with similar semantics across examples, enabling position-aware circuit discovery in datasets with variable length examples. We additionally develop an automated pipeline for schema generation and application using large language models. Our approach enables fully automated discovery of position-sensitive circuits, yielding better trade-offs between circuit size and faithfulness compared to prior work.

Induction heads are attention heads that perform inductive copying by matching patterns from earlier context and copying their continuations verbatim. As models develop induction heads, they often experience a sharp drop in training loss, a phenomenon cited as evidence that induction heads may serve as a prerequisite for more complex in-context learning (ICL) capabilities. In this work, we ask whether transformers can still acquire ICL capabilities when inductive copying is suppressed. We propose Hapax, a setting where we omit the loss contribution of any token that can be correctly predicted by induction heads. Despite a significant reduction in inductive copying, performance on abstractive ICL tasks (i.e., tasks where the answer is not contained in the input context) remains comparable and surpasses the vanilla model on 13 of 21 tasks, even though 31.7% of tokens are omitted from the loss. Furthermore, our model achieves lower loss values on token positions that cannot be predicted correctly by induction heads. Mechanistic analysis further shows that models trained with Hapax develop fewer and weaker induction heads but still preserve ICL capabilities. Taken together, our findings indicate that inductive copying is not essential for learning abstractive ICL mechanisms.

We discuss the challenges and propose research directions for using AI to revolutionize the development of high-performance computing (HPC) software. AI technologies, in particular large language models, have transformed every aspect of software development. For its part, HPC software is recognized as a highly specialized scientific field of its own. We discuss the challenges associated with leveraging state-of-the-art AI technologies to develop such a unique and niche class of software and outline our research directions in the two US Department of Energy–funded projects for advancing HPC Software via AI: Ellora and Durban.

Refusal discovery is the task of identifying the full set of topics that a language model refuses to discuss. We introduce this new problem setting and develop a refusal discovery method, LLM-crawler, that uses token prefilling to find forbidden topics. We benchmark the LLM-crawler on Tulu-3-8B, an open-source model with public safety tuning data. Our crawler manages to retrieve 31 out of 36 topics within a budget of 1000 prompts. Next, we scale the crawl to a frontier model using the prefilling option of Claude-Haiku. Finally, we crawl three widely used open-weight models: Llama-3.3-70B and two of its variants finetuned for reasoning: DeepSeek-R1-70B and Perplexity-R1-1776-70B. DeepSeek-R1-70B reveals patterns consistent with censorship tuning: The model exhibits "thought suppression" behavior that indicates memorization of CCP-aligned responses. Although Perplexity-R1-1776-70B is robust to censorship, LLM-crawler elicits CCP-aligned refusals answers in the quantized model. Our findings highlight the critical need for refusal discovery methods to detect biases, boundaries, and alignment failures of AI systems.