arXiv subjects

Jack Merullo

Publications and source records attributed to Jack Merullo.

At least 19 recordsLinked to original sources

arXiv2026

Forking Fast: Efficiently Estimating Uncertainty Dynamics in Text Generation

LLM reasoning is stochastic, and so understanding a model requires grappling with the distribution of reasoning chains that it might produce for a given question, i.e., its uncertainty. Resampling-based analyses characterize this distribution, revealing which steps of a rollout determine how the model arrives at its answer. However, a major limitation of these approaches is that resampling text sequences at every token or sentence in a reasoning chain is very costly. Our work strives to make resampling analysis more computationally efficient, while also shedding light on an important scientific question: what is the right statistical model for explaining uncertainty dynamics in text generation? We show that when resampling many reasoning chains, uncertainty dynamics converge to stable patterns, and noise is largely an artifact of sampling rather than an LLM's sensitivity to each individual token or reasoning step. We develop a statistical model for smoothing noisy low-sample rollout data to better approximate high-sample data, allowing us to significantly cut sampling costs.

cs.CL↗

arXiv2026

Structuring Sparsity: Block-Sparse Featurizers Capture Visual Concept Manifolds

What is the geometry of a visual percept? The most widely used protocols for decomposing neural network representations into interpretable parts treat concepts as isolated directions, yet recent work shows that concepts are often realized as geometric structures in low dimensional regions of activation space. We turn to the literature of Structured sparsity to close this gap, and show that block sparsity, which groups directions into blocks, is the prior matched to a generative model in which a representation is a sparse sum of low-dimensional manifolds: the modern, learned form of a classical idea in visual neuroscience, where a visual feature is carried by a coordinated group of neurons rather than a single tuned one. We implement three variants of block-sparse featurizers (BSFs) and, through a minimum-description-length analysis, show that all three describe activations more compactly than direction-based featurizers, with the recovered concepts typically two- to four-dimensional. We then use BSFs to (i) recontextualize prior work, showing that curve detectors in InceptionV1 actually read from a single continuous curve manifold, (ii) discover novel manifolds including shadows and lighting in DINOv3, and (iii) support interpretable control of image generation in diffusion models (SDXL) via manifold steering.

cs.CV↗

arXiv2026

Anatomy of Post-Training: Using Interpretability to Characterize Data and Shape the Learning Signal

Language-model post-training is the main stage at which model behavior is shaped, yet it still largely involves optimization of scalar rewards that summarize diverse desiderata. This abstraction gives practitioners little visibility into what their data actually teaches models, allowing spurious correlations to be learned by a model and inducing undesirable behaviors such as over-stylization and sycophancy. To address this problem, we ask: can we inspect a preference dataset before optimization and decide, at the level of concepts, which behaviors a model should be allowed to learn? Motivated by this, we introduce a data-centric post-training pipeline that uses interpretability protocols to develop statistical hypotheses for the latent concepts separating preferred from dispreferred generations, making them explicit for fine-grained user feedback. Building on this view, we unify several interpretability-based training protocols as ways of shaping rewards via feature or data interventions. Empirically, we show that our pipeline diagnoses undesirable signals in existing preference data, mitigates off-target learning, and can also help amplify or shape desired properties such as safeguards and model personality. More broadly, our results suggest that interpretability can turn post-training from optimizing opaque proxy rewards into a process of auditing and sculpting the learning signal itself.

cs.LG↗

arXiv2026

Stories in Space: In-Context Learning Trajectories in Conceptual Belief Space

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.

cs.CL↗

arXiv2026

Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior

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.

cs.LG↗

arXiv2026

Arithmetic in the Wild: Llama uses Base-10 Addition to Reason About Cyclic Concepts

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.

cs.AI↗

arXiv2026

Do Sparse Autoencoders Capture Concept Manifolds?

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.

cs.LG↗

arXiv2026

Reasoning Theater: Disentangling Model Beliefs from Chain-of-Thought

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.

cs.CL↗

arXiv2026

Features as Rewards: Scalable Supervision for Open-Ended Tasks via Interpretability

Language models trained on large-scale datasets have been shown to learn features that encode abstract concepts such as factuality or intent. Such features are traditionally used for test-time monitoring or steering. We present an alternative affordance: features as scalable supervision for open-ended tasks. We consider the case of hallucination-reduction as a desirable, yet open-ended behavior and design a reinforcement learning (RL) pipeline, titled RLFR (Reinforcement Learning from Feature Rewards), that uses features as reward functions. Grounded in a novel probing framework that identifies candidate hallucinated claims, our pipeline teaches a model to intervene and correct its completions when it is uncertain of their factuality. Furthermore, the pipeline enables scalable test-time compute, guided once more by our reward features. This end-to-end process operationalized on Gemma-3-12B-IT results in a policy that is 58% less likely to hallucinate compared to the original model (when run in tandem with our probing harness), while preserving performance on standard benchmarks. Taken together, by grounding supervision in the language of features, this paper introduces a novel paradigm in the use of interpretability for learning open-ended tasks.

cs.LG↗

arXiv2026

The Shape of Beliefs: Geometry, Dynamics, and Interventions along Representation Manifolds of Language Models' Posteriors

Large language models (LLMs) form implicit beliefs (posteriors over latent variables) from prompts, 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 infers the parameters of a normal distribution from in-context samples. We show that parameter posteriors are encoded as curved manifolds in representation space, and trace how they evolve along the prompt. Standard linear steering moves representations off-manifold, inducing unintended, coupled changes, whereas geometry-aware methods preserve the target belief family. Our work demonstrates an example of linear field probing (LFP) as a principled approach to tile the data manifold and make interventions that respect the underlying geometry. Our results suggest that LLM beliefs are inherently geometric objects, and that globally linear representations are often inadequate abstractions.

cs.CL↗

arXiv2025

From Memorization to Reasoning in the Spectrum of Loss Curvature

We characterize how memorization is represented in transformer models and show that it can be disentangled in the weights of both language models (LMs) and vision transformers (ViTs) using a decomposition based on the loss landscape curvature. This insight is based on prior theoretical and empirical work showing that the curvature for memorized training points is much sharper than non memorized, meaning ordering weight components from high to low curvature can reveal a distinction without explicit labels. This motivates a weight editing procedure that suppresses far more recitation of untargeted memorized data more effectively than a recent unlearning method (BalancedSubnet), while maintaining lower perplexity. Since the basis of curvature has a natural interpretation for shared structure in model weights, we analyze the editing procedure extensively on its effect on downstream tasks in LMs, and find that fact retrieval and arithmetic are specifically and consistently negatively affected, even though open book fact retrieval and general logical reasoning is conserved. We posit these tasks rely heavily on specialized directions in weight space rather than general purpose mechanisms, regardless of whether those individual datapoints are memorized. We support this by showing a correspondence between task data's activation strength with low curvature components that we edit out, and the drop in task performance after the edit. Our work enhances the understanding of memorization in neural networks with practical applications towards removing it, and provides evidence for idiosyncratic, narrowly-used structures involved in solving tasks like math and fact retrieval.

cs.CL↗

arXiv2025

I Have No Mouth, and I Must Rhyme: Uncovering Internal Phonetic Representations in LLaMA 3.2

Large language models demonstrate proficiency on phonetic tasks, such as rhyming, without explicit phonetic or auditory grounding. In this work, we investigate how \verb|Llama-3.2-1B-Instruct| represents token-level phonetic information. Our results suggest that Llama uses a rich internal model of phonemes to complete phonetic tasks. We provide evidence for high-level organization of phoneme representations in its latent space. In doing so, we also identify a ``phoneme mover head" which promotes phonetic information during rhyming tasks. We visualize the output space of this head and find that, while notable differences exist, Llama learns a model of vowels similar to the standard IPA vowel chart for humans, despite receiving no direct supervision to do so.

cs.CL↗

arXiv2025

Transferring Linear Features Across Language Models With Model Stitching

In this work, we demonstrate that affine mappings between residual streams of language models is a cheap way to effectively transfer represented features between models. We apply this technique to transfer the weights of Sparse Autoencoders (SAEs) between models of different sizes to compare their representations. We find that small and large models learn similar representation spaces, which motivates training expensive components like SAEs on a smaller model and transferring to a larger model at a FLOPs savings. In particular, using a small-to-large transferred SAE as initialization can lead to 50% cheaper training runs when training SAEs on larger models. Next, we show that transferred probes and steering vectors can effectively recover ground truth performance. Finally, we dive deeper into feature-level transferability, finding that semantic and structural features transfer noticeably differently while specific classes of functional features have their roles faithfully mapped. Overall, our findings illustrate similarities and differences in the linear representation spaces of small and large models and demonstrate a method for improving the training efficiency of SAEs.

cs.CL↗

arXiv2025

On Linear Representations and Pretraining Data Frequency in Language Models

Pretraining data has a direct impact on the behaviors and quality of language models (LMs), but we only understand the most basic principles of this relationship. While most work focuses on pretraining data's effect on downstream task behavior, we investigate its relationship to LM representations. Previous work has discovered that, in language models, some concepts are encoded `linearly' in the representations, but what factors cause these representations to form? We study the connection between pretraining data frequency and models' linear representations of factual relations. We find evidence that the formation of linear representations is strongly connected to pretraining term frequencies; specifically for subject-relation-object fact triplets, both subject-object co-occurrence frequency and in-context learning accuracy for the relation are highly correlated with linear representations. This is the case across all phases of pretraining. In OLMo-7B and GPT-J, we discover that a linear representation consistently (but not exclusively) forms when the subjects and objects within a relation co-occur at least 1k and 2k times, respectively, regardless of when these occurrences happen during pretraining. Finally, we train a regression model on measurements of linear representation quality in fully-trained LMs that can predict how often a term was seen in pretraining. Our model achieves low error even on inputs from a different model with a different pretraining dataset, providing a new method for estimating properties of the otherwise-unknown training data of closed-data models. We conclude that the strength of linear representations in LMs contains signal about the models' pretraining corpora that may provide new avenues for controlling and improving model behavior: particularly, manipulating the models' training data to meet specific frequency thresholds.

cs.CL↗

arXiv2024

$100K or 100 Days: Trade-offs when Pre-Training with Academic Resources

Pre-training is notoriously compute-intensive and academic researchers are notoriously under-resourced. It is, therefore, commonly assumed that academics can't pre-train models. In this paper, we seek to clarify this assumption. We first survey academic researchers to learn about their available compute and then empirically measure the time to replicate models on such resources. We introduce a benchmark to measure the time to pre-train models on given GPUs and also identify ideal settings for maximizing training speed. We run our benchmark on a range of models and academic GPUs, spending 2,000 GPU-hours on our experiments. Our results reveal a brighter picture for academic pre-training: for example, although Pythia-1B was originally trained on 64 GPUs for 3 days, we find it is also possible to replicate this model (with the same hyper-parameters) in 3x fewer GPU-days: i.e. on 4 GPUs in 18 days. We conclude with a cost-benefit analysis to help clarify the trade-offs between price and pre-training time. We believe our benchmark will help academic researchers conduct experiments that require training larger models on more data. We fully release our codebase at: https://github.com/apoorvkh/academic-pretraining.

cs.CL↗

arXiv2024

Talking Heads: Understanding Inter-layer Communication in Transformer Language Models

Although it is known that transformer language models (LMs) pass features from early layers to later layers, it is not well understood how this information is represented and routed by the model. We analyze a mechanism used in two LMs to selectively inhibit items in a context in one task, and find that it underlies a commonly used abstraction across many context-retrieval behaviors. Specifically, we find that models write into low-rank subspaces of the residual stream to represent features which are then read out by later layers, forming low-rank communication channels (Elhage et al., 2021) between layers. A particular 3D subspace in model activations in GPT-2 can be traversed to positionally index items in lists, and we show that this mechanism can explain an otherwise arbitrary-seeming sensitivity of the model to the order of items in the prompt. That is, the model has trouble copying the correct information from context when many items ``crowd" this limited space. By decomposing attention heads with the Singular Value Decomposition (SVD), we find that previously described interactions between heads separated by one or more layers can be predicted via analysis of their weight matrices alone. We show that it is possible to manipulate the internal model representations as well as edit model weights based on the mechanism we discover in order to significantly improve performance on our synthetic Laundry List task, which requires recall from a list, often improving task accuracy by over 20%. Our analysis reveals a surprisingly intricate interpretable structure learned from language model pretraining, and helps us understand why sophisticated LMs sometimes fail in simple domains, facilitating future analysis of more complex behaviors.

cs.CL↗

arXiv2024

Dual Process Learning: Controlling Use of In-Context vs. In-Weights Strategies with Weight Forgetting

Language models have the ability to perform in-context learning (ICL), allowing them to flexibly adapt their behavior based on context. This contrasts with in-weights learning (IWL), where memorized information is encoded in model parameters after iterated observations of data. An ideal model should be able to flexibly deploy both of these abilities. Despite their apparent ability to learn in-context, language models are known to struggle when faced with unseen or rarely seen tokens (Land & Bartolo, 2024). Hence, we study $\textbf{structural in-context learning}$, which we define as the ability of a model to execute in-context learning on arbitrary novel tokens -- so called because the model must generalize on the basis of e.g. sentence structure or task structure, rather than content encoded in token embeddings. We study structural in-context algorithms on both synthetic and naturalistic tasks using toy models, masked language models, and autoregressive language models. We find that structural ICL appears before quickly disappearing early in LM pretraining. While it has been shown that ICL can diminish during training (Singh et al., 2023), we find that prior work does not account for structural ICL. Building on Chen et al. (2024) 's active forgetting method, we introduce pretraining and finetuning methods that can modulate the preference for structural ICL and IWL. Importantly, this allows us to induce a $\textit{dual process strategy}$ where in-context and in-weights solutions coexist within a single model.

cs.CL↗

arXiv2024

Axiomatic Causal Interventions for Reverse Engineering Relevance Computation in Neural Retrieval Models

Neural models have demonstrated remarkable performance across diverse ranking tasks. However, the processes and internal mechanisms along which they determine relevance are still largely unknown. Existing approaches for analyzing neural ranker behavior with respect to IR properties rely either on assessing overall model behavior or employing probing methods that may offer an incomplete understanding of causal mechanisms. To provide a more granular understanding of internal model decision-making processes, we propose the use of causal interventions to reverse engineer neural rankers, and demonstrate how mechanistic interpretability methods can be used to isolate components satisfying term-frequency axioms within a ranking model. We identify a group of attention heads that detect duplicate tokens in earlier layers of the model, then communicate with downstream heads to compute overall document relevance. More generally, we propose that this style of mechanistic analysis opens up avenues for reverse engineering the processes neural retrieval models use to compute relevance. This work aims to initiate granular interpretability efforts that will not only benefit retrieval model development and training, but ultimately ensure safer deployment of these models.

cs.IR↗