Daniel Wurgaft

Ian R. McKenzie, Alexander Lyzhov, Michael Pieler et al. · stanford, utoronto

Work on scaling laws has found that large language models (LMs) show predictable improvements to overall loss with increased scale (model size, training data, and compute). Here, we present evidence for the claim that LMs may show inverse scaling, or worse task performance with increased scale, e.g., due to flaws in the training objective and data. We present empirical evidence of inverse scaling on 11 datasets collected by running a public contest, the Inverse Scaling Prize, with a substantial prize pool. Through analysis of the datasets, along with other examples found in the literature, we identify four potential causes of inverse scaling: (i) preference to repeat memorized sequences over following in-context instructions, (ii) imitation of undesirable patterns in the training data, (iii) tasks containing an easy distractor task which LMs could focus on, rather than the harder real task, and (iv) correct but misleading few-shot demonstrations of the task. We release the winning datasets at https://inversescaling.com/data to allow for further investigation of inverse scaling. Our tasks have helped drive the discovery of U-shaped and inverted-U scaling trends, where an initial trend reverses, suggesting that scaling trends are less reliable at predicting the behavior of larger-scale models than previously understood. Overall, our results suggest that there are tasks for which increased model scale alone may not lead to progress, and that more careful thought needs to go into the data and objectives for training language models.

Sheridan Feucht, Tal Haklay, Usha Bhalla et al.

Does structure in representations imply structure in computation? We study how Llama-3.1-8B reasons over cyclic concepts (e.g., "what month is six months after August?"). Even though Llama-3.1-8B's representations for these concepts are circularly structured, we find that instead of directly computing modular addition in the period of the cyclic concept (e.g., 12 for months), the model re-uses a generic addition mechanism across tasks that operates independently of concept-specific geometry. First, it computes the sum of its two inputs using base-10 addition (six + August=14). Then, it maps this sum back to cyclic concept space (14->February). We show that Llama-3.1-8B uses task-agnostic Fourier features to compute these sums--in fact, these features have periods that respect standard base-10 addition, e.g., 2, 5, and 10, rather than the cyclic concept period (e.g., 12 for months). Furthermore, we identify a sparse set of 28 MLP neurons re-used across all tasks (approximately 0.2% of the MLP at layer 18) that can be partitioned into disjoint clusters, each computing the sum for a Fourier feature with a different period. Our work highlights how an interplay between causal abstraction and feature geometry can deepen our mechanistic understanding of LMs.

Usha Bhalla, Thomas Fel, Can Rager et al.

Sparse autoencoders (SAEs) are widely used to extract interpretable features from neural network representations, often under the implicit assumption that concepts correspond to independent linear directions. However, a growing body of evidence suggests that many concepts are instead organized along low-dimensional manifolds encoding continuous geometric relationships. This raises three basic questions: what does it mean for an SAE to capture a manifold, when do existing SAE architectures do so, and how? We develop a theoretical framework that answers these questions and show that SAEs can capture manifolds in two fundamentally different ways: globally, by allocating a compact group of atoms whose linear span contains the entire manifold, or locally, by distributing it across features that each selectively tile a restricted region of the underlying geometry. Empirically, we find that SAEs suboptimally recover continuous structures, mixing the global subspace and local tiling solutions in a fragmented regime we call dilution. This explains why manifold structure is rarely visible at the level of individual concepts and motivates post-hoc unsupervised discovery methods that search for coherent groups of atoms rather than isolated directions. More broadly, our results suggest that future representation learning methods should treat geometric objects, not just individual directions, as the basic units of interpretability.

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.

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, Ben Prystawski, Kanishk Gandhi et al.

The think-aloud method, where participants voice their thoughts as they solve a task, is a valuable source of rich data about human reasoning processes. Yet, it has declined in popularity in contemporary cognitive science, largely because labor-intensive transcription and annotation preclude large sample sizes. Here, we develop methods to automate the transcription and annotation of verbal reports of reasoning using natural language processing tools, allowing for large-scale analysis of think-aloud data. In our study, 640 participants thought aloud while playing the Game of 24, a mathematical reasoning task. We automatically transcribed the recordings and coded the transcripts as search graphs, finding moderate inter-rater reliability with humans. We analyze these graphs and characterize consistency and variation in human reasoning traces. Our work demonstrates the value of think-aloud data at scale and serves as a proof of concept for the automated analysis of verbal reports.