Eric Bigelow

Amir Zur, Atticus Geiger, Ekdeep Singh Lubana et al.

When a language model generates text, the selection of individual tokens might lead it down very different reasoning paths, making uncertainty difficult to quantify. In this work, we consider whether reasoning language models represent the alternate paths that they could take during generation. To test this hypothesis, we use hidden activations to control and predict a language model's uncertainty during chain-of-thought reasoning. In our experiments, we find a clear correlation between how uncertain a model is at different tokens, and how easily the model can be steered by controlling its activations. This suggests that activation interventions are most effective when there are alternate paths available to the model -- in other words, when it has not yet committed to a particular final answer. We also find that hidden activations can predict a model's future outcome distribution, demonstrating that models implicitly represent the space of possible paths.

Raphaël Sarfati, Eric Bigelow, Daniel Wurgaft et al.

Large language models (LLMs) represent prompt-conditioned beliefs (posteriors over answers and claims), but we lack a mechanistic account of how these beliefs are encoded in representation space, how they update with new evidence, and how interventions reshape them. We study a controlled setting in which Llama-3.2 generates samples from a normal distribution by implicitly inferring its parameters (mean and standard deviation) given only samples from the distribution in context. We find representations of curved "belief manifolds" for these parameters form with sufficient in-context learning and study how the model adapts when the distribution suddenly changes. While standard linear steering often pushes the model off-manifold and induces coupled, out-of-distribution shifts, geometry and field-aware steering better preserves the intended belief family. Our work demonstrates an example of linear field probing (LFP) as a simple approach to tile the data manifold and make interventions that respect the underlying geometry. We conclude that rich structure emerges naturally in LLMs and that purely linear concept representations are often an inadequate abstraction.

Eric Bigelow, Daniel Wurgaft, YingQiao Wang et al.

Large language models (LLMs) can be controlled at inference time through prompts (in-context learning) and internal activations (activation steering). Different accounts have been proposed to explain these methods, yet their common goal of controlling model behavior raises the question of whether these seemingly disparate methodologies can be seen as specific instances of a broader framework. Motivated by this, we develop a unifying, predictive account of LLM control from a Bayesian perspective. Specifically, we posit that both context- and activation-based interventions impact model behavior by altering its belief in latent concepts: steering operates by changing concept priors, while in-context learning leads to an accumulation of evidence. This results in a closed-form Bayesian model that is highly predictive of LLM behavior across context- and activation-based interventions in a set of domains inspired by prior work on many-shot in-context learning. This model helps us explain prior empirical phenomena - e.g., sigmoidal learning curves as in-context evidence accumulates - while predicting novel ones - e.g., additivity of both interventions in log-belief space, which results in distinct phases such that sudden and dramatic behavioral shifts can be induced by slightly changing intervention controls. Taken together, this work offers a unified account of prompt-based and activation-based control of LLM behavior, and a methodology for empirically predicting the effects of these interventions.

Usman Anwar, Abulhair Saparov, Javier Rando et al. · cambridge, eth-zurich

This work identifies 18 foundational challenges in assuring the alignment and safety of large language models (LLMs). These challenges are organized into three different categories: scientific understanding of LLMs, development and deployment methods, and sociotechnical challenges. Based on the identified challenges, we pose $200+$ concrete research questions.

Eric Bigelow, Raphaël Sarfati, Daniel Wurgaft et al.

Large Language Models (LLMs) update their behavior in context, which can be viewed as a form of Bayesian inference. However, the structure of the latent hypothesis space over which this inference operates remains unclear. In this work, we propose that LLMs assign beliefs over a low-dimensional geometric space - a conceptual belief space - and that in-context learning corresponds to a trajectory through this space as beliefs are updated over time. Using story understanding as a natural setting for dynamic belief updating, we combine behavioral and representational analyses to study these trajectories. We find that (1) belief updates are well-described as trajectories on low-dimensional, structured manifolds; (2) this structure is reflected consistently in both model behavior and internal representations and can be decoded with simple linear probes to predict behavior; and (3) interventions on these representations causally steer belief trajectories, with effects that can be predicted from the geometry of the conceptual space. Together, our results provide a geometric account of belief dynamics in LLMs, grounding Bayesian interpretations of in-context learning in structured conceptual representations.

Daniel Wurgaft, Can Rager, Matthew Kowal et al.

Neural representations carry rich geometric structure; but does that structure causally shape behavior? To address this question, we intervene along paths through activation space defined by different geometries, and measure the behavioral trajectories they induce. In particular, we test whether interventions that respect the geometry of activation space will yield behaviors close to those the model exhibits naturally. Concretely, we first fit an activation manifold $M_h$ to representations and a behavior manifold $M_y$ to output probability distributions. We then test the link $M_h \leftrightarrow M_y$ via interventions: we find that steering along $M_h$, which we term manifold steering, yields behavioral trajectories that follow $M_y$, while linear steering -- which assumes a Euclidean geometry -- cuts through off-manifold regions and hence produces unnatural outputs. Moreover, optimizing interventions in activation space to produce paths along $M_y$ recovers activation trajectories that trace the curvature of $M_h$. We demonstrate this bidirectional relationship between the geometry of representation and behavior across tasks and modalities. In language models, we use reasoning tasks with cyclic and sequential geometries as well as in-context learning tasks with more complex graph geometries. In a video world model, we use a task with geometry corresponding to physical dynamics. Overall, our work shows that geometry in neural representation is not merely incidental, but is in fact the proper object for enabling principled control via intervention on internals. This recasts the core problem of steering from finding the right direction to finding the right geometry.

YingQiao Wang, Eric Bigelow, Boyi Li et al.

We propose a novel cognitively-inspired method to improve and interpret physical simulation in vision-language models. Our ``Chain of Time" method involves generating a series of intermediate images during a simulation, and it is motivated by in-context reasoning in machine learning, as well as mental simulation in humans. Chain of Time is used at inference time, and requires no additional fine-tuning. We apply the Chain-of-Time method to synthetic and real-world domains, including 2-D graphics simulations and natural 3-D videos. These domains test a variety of particular physical properties, including velocity, acceleration, fluid dynamics, and conservation of momentum. We found that using Chain-of-Time simulation substantially improves the performance of a state-of-the-art image generation model. Beyond examining performance, we also analyzed the specific states of the world simulated by an image model at each time step, which sheds light on the dynamics underlying these simulations. This analysis reveals insights that are hidden from traditional evaluations of physical reasoning, including cases where an image generation model is able to simulate physical properties that unfold over time, such as velocity, gravity, and collisions. Our analysis also highlights particular cases where the image generation model struggles to infer particular physical parameters from input images, despite being capable of simulating relevant physical processes.

Siddharth Boppana, Annabel Ma, Max Loeffler et al.

We provide evidence of performative chain-of-thought (CoT) in reasoning models, where a model becomes strongly confident in its final answer, but continues generating tokens without revealing its internal belief. Our analysis compares activation probing, early forced answering, and a CoT monitor across two large models (DeepSeek-R1 671B & GPT-OSS 120B) and find task difficulty-specific differences: The model's final answer is decodable from activations far earlier in CoT than a monitor is able to say, especially for easy recall-based MMLU questions. We contrast this with genuine reasoning in difficult multihop GPQA-Diamond questions. Despite this, inflection points (e.g., backtracking, 'aha' moments) occur almost exclusively in responses where probes show large belief shifts, suggesting these behaviors track genuine uncertainty rather than learned "reasoning theater." Finally, probe-guided early exit reduces tokens by up to 80% on MMLU and 30% on GPQA-Diamond with similar accuracy, positioning attention probing as an efficient tool for detecting performative reasoning and enabling adaptive computation.

Eric Bigelow, Ari Holtzman, Hidenori Tanaka et al.

Estimating uncertainty in Large Language Models (LLMs) is important for properly evaluating LLMs, and ensuring safety for users. However, prior approaches to uncertainty estimation focus on the final answer in generated text, ignoring intermediate steps that might dramatically impact the outcome. We hypothesize that there exist key forking tokens, such that re-sampling the system at those specific tokens, but not others, leads to very different outcomes. To test this empirically, we develop a novel approach to representing uncertainty dynamics across individual tokens of text generation, and applying statistical models to test our hypothesis. Our approach is highly flexible: it can be applied to any dataset and any LLM, without fine tuning or accessing model weights. We use our method to analyze LLM responses on 7 different tasks across 4 domains, spanning a wide range of typical use cases. We find many examples of forking tokens, including surprising ones such as punctuation marks, suggesting that LLMs are often just a single token away from saying something very different.