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Atticus Geiger

Publications and source records attributed to Atticus Geiger.

At least 19 recordsLinked to original sources
arXiv2026

Shaping & Monitoring Models through their Internal Representations

We propose Mechanistic Shaping, a unified framework for shaping models through their internal representations. Mechanistic Shaping is applied during training so that models follow specifications (rules) about which concepts they express, measured via their outputs or internal representations (e.g., no harmful content), and also which concepts they rely on, i.e., what they use to make their decisions (e.g., not a candidate's gender when screening a résumé). Across multiple domains (vision, medical imaging, language), scales (up to 32B parameters), and training paradigms (classification, SFT, DPO, GRPO), we find that Mechanistic Shaping substantially reduces targeted behaviors while preserving task performance. Since training against a representation can also modify it, we ask whether shaped concepts remain monitorable, a question that depends on the class of monitors considered. We therefore introduce a hierarchy of such classes, which separates a concept that escapes one probe from a concept that is truly gone. We characterize three geometric mechanisms of circumvention: the concept can drift away from the monitor, be erased from the layer, or persist in higher-order statistics as a nonlinear encoding, which we explain through a product-code construction. Although other mechanisms may arise in different settings or at larger scales, these three account for all of our observations, and each can be detected by a matching monitor. In practice, we find that shaped concepts largely remain monitorable: refitted linear probes recover the concept in most settings, and the original probe remains reliable whenever gradients do not flow through it. Taken together, these results point to the potential of using interpretability as a tool for training, and call for a correspondingly rigorous science of interpretability-based training.

cs.LG↗
arXiv2026

A Phenomenology of Neural Geometry in Vision-Language-Action Models

Robotic manipulation is inherently geometric, but what shape does the world take inside the policy that performs it? Prior work on vision-language-action (VLA) policies establishes that task-relevant variables are linearly readable from activations, yet readability certifies only that a variable is present and says nothing about the shape its values trace, which may be curved and multi-dimensional. Using controlled sweeps, natural rollouts, linear probes, and activation interventions, we build a taxonomy of seven task-relevant concepts in VLA models. We find that realized geometry is predominantly multi-dimensional and is shaped by the constraints under which the policy acts. Physical joint limits, for example, leave wrist orientation an open arc rather than a circle, and distance to the target, a single scalar, is realized in two orthogonal subspaces, a coarse ruler for the approach and a fine ruler for the grasp. The same geometries reappear in two further VLA models on real-world robot data, indicating that they are neither model-specific nor artifacts of simulation. We demonstrate how the findings are actionable by steering along the geometry a concept realizes. Overall, this work lays out an initial phenomenology of realized geometry in VLA policies and demonstrates that a concept's shape carries as much importance as its readability.

cs.RO↗
arXiv2026

Causal Analysis of Robot Foundation Models Enables Efficiency Gains

Vision-language-action (VLA) models are a promising approach to general purpose robot manipulation. While the internal computation of vision-language models, which compose the backbone of VLAs, has been studied extensively, less is known about how their perceptual and semantic representations are transformed into action in VLA models. We study this question mechanistically in three frontier VLA models ($π_{0.5}$, MolmoAct2, and MolmoBot) by analyzing the causal pathways through which the input image and the instruction shape actions. Across the three models, activation patching shows that causally relevant information influences the action expert (AE) through a narrow band of mid-to-late cross-attention layers, which we term the action-conditioning interface. The content of this information changes with token and layer within the model. Early-to-mid layer representations of the target noun token determine which object is selected, whereas mid-to-late layers carry the spatial information in text tokens that redirects the movement when patched. Where spatial information is stored in prompt tokens various based on the architecture. In MolmoAct2 the model forms task-conditioned representations at the text positions that follow the instruction, whereas $π_{0.5}$ additionally stores this information at image token positions. We show that these findings can be translated directly into improving model efficiency. We find that restricting MolmoBot's action expert conditioning to only 3 out of 36 layers reduces inference FLOPs by up to $33\%$ while maintaining comparable task success with the default model across 3,000 evaluation episodes ($46.7\%$ vs. $46.9\%$), and the same principle carries over to real-robot deployment of $π_{0.5}$.

cs.RO↗
arXiv2026

Multi-Dimensional Featurizers Yield Fine-Grained Steering and Data Shaping in Robot Foundation Models

Can better feature discovery improve control over robot behavior through internal interventions and training data? Recent work in vision and language models reveals multidimensional features, motivating block-sparse featurizers (BSFs), which represent each feature in a low-dimensional subspace. We investigate whether recovering this structure provides an interpretable interface for steering vision-language-action models and shaping the data from which they learn. We show that BSFs recover several multi-dimensional task-relevant features underlying the model's computation (e.g., perception, language, proprioceptive state, episode phase, and control variables). We causally validate these features through fine-grained steering: targeted changes in visual perception, semantic representation, and spatial localization produce predictable changes in downstream action prediction. Finally, we use feature-based data attribution to isolate where a specific behavior (failure recovery) arises in the training dataset, identifying fewer than $1.4\%$ of training tokens whose masking is sufficient to remove the targeted behavior. Overall, our results show how matching featurizers to representation geometry can provide more effective tools for understanding and changing robot behavior.

cs.RO↗
arXiv2026

Monitoring and Discovering Reward Hacking with Internal Representations during LLM Evaluations

As models scale, reward hacking becomes more frequent, more sophisticated, and more consequential. Does it leave a telltale signature in model representations? This work analyzes how reward hacking is represented internally in frontier open source LLMs, and how those representations can be used to understand and discover the range of hacking behaviors a model displays. In particular, we find that simple difference of means vectors coherently represent reward hacking in Kimi K3, GLM 5.2, and Qwen 3.8 Max across a variety of behaviors in common evaluations. Despite their simplicity, these vectors are both generalizable and interpretable, and we can use them to reliably detect reward hacking. We first evaluate reward hacking in commonly reported benchmarks like DeepSWE and SWE-bench, finding that models reward hack excessively in these environments; GLM 5.2 hacks in 57.2% of rollouts on DeepSWE and in 73% of rollouts on SWE-bench. Catching these requires monitors; LLM monitors are effective, but expensive detectors. We show that DoM vectors are similarly effective but virtually free, catching 3.1% more hacks in Kimi K3 and 7.9% fewer hacks in GLM 5.2 on DeepSWE at a monitor matched false positive rate. DoM vectors run on the chain-of-thought also predict reward hacks in the model's subsequent actions, meaning we can run them online and catch potential hacks before they occur. Finally, we analyze probe-hits that LLM monitors do not catch and discover other undesirable behaviors, as well as show transfer to finding hacks in non-SWE evaluations. Together, these results provide evidence that simple, white-box methods can be used to scalably study and monitor reward hacking behaviors in frontier open source models

cs.CL↗
arXiv2026

Language Model Activations Inhabit Privileged Error-Correcting Basins

Language models exhibit remarkable robustness, continuing to produce coherent text even when their activations are perturbed by interventions like linear steering. We hypothesize that this robustness is a result of passive dynamics, i.e., constraining mechanisms in the forward pass that funnel activations toward "good" regions that produce coherent outputs. To investigate these hypothesized error-correcting mechanisms, we probe the geometry of language model activation space by observing the action of model layers on low-dimensional curves. In doing so, we discover that model activations occur within a cluster of distinct attracting basins, which differentiate natural activations geometrically from distributionally similar synthetic activations. Applying this lens to language model steering, we observe feature-specific basins along semantic steering directions, and find that steering moves activations between these basins. To demonstrate the active role of this geometry in neural computation, we show that adaptively modulating steering strength to transport activations across basins improves inter-language steering, significantly increasing the probability of sampling tokens from the target language compared to fixed-strength steering. Our findings establish analysis of activation space geometry as a promising approach to interpreting and controlling language models.

cs.AI↗
arXiv2026

From Directions to Regions: Decomposing Activations in Language Models via Local Geometry

Activation decomposition methods in language models are tightly coupled to geometric assumptions on how concepts are realized in activation space. Existing approaches search for individual global directions, implicitly assuming linear separability, which overlooks concepts with nonlinear or multi-dimensional structure. In this work, we leverage Mixture of Factor Analyzers (MFA) as a scalable, unsupervised alternative that models the activation space as a collection of Gaussian regions with their local covariance structure. MFA decomposes activations into two compositional geometric objects: the region's centroid in activation space, and the local variation from the centroid. We train large-scale MFAs for Llama-3.1-8B and Gemma-2-2B, and show they capture complex, nonlinear structures in activation space. Moreover, evaluations on localization and steering benchmarks show that MFA outperforms unsupervised baselines, is competitive with supervised localization methods, and often achieves stronger steering performance than sparse autoencoders. Together, our findings position local geometry, expressed through subspaces, as a promising unit of analysis for scalable concept discovery and model control, accounting for complex structures that isolated directions fail to capture.

cs.CL↗
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

How Causal Abstraction Underpins Computational Explanation

Explanations of cognitive behavior often appeal to computations over representations. What does it take for a system to implement a given computation over suitable representational vehicles within that system? We argue that the language of causality -- and specifically the theory of causal abstraction -- provides a fruitful lens on this topic. Drawing on current discussions in deep learning with artificial neural networks, we illustrate how classical themes in the philosophy of computation and cognition resurface in contemporary machine learning. We offer an account of computational implementation grounded in causal abstraction, and examine the role for representation in the resulting picture. We argue that these issues are most profitably explored in connection with generalization and prediction.

cs.LG↗
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

Mixing Mechanisms: How Language Models Retrieve Bound Entities In-Context

A key component of in-context reasoning is the ability of language models (LMs) to bind entities for later retrieval. For example, an LM might represent "Ann loves pie" by binding "Ann" to "pie", allowing it to later retrieve "Ann" when asked "Who loves pie?" Prior research on short lists of bound entities found strong evidence that LMs implement such retrieval via a positional mechanism, where "Ann" is retrieved based on its position in context. In this work, we find that this mechanism generalizes poorly to more complex settings; as the number of bound entities in context increases, the positional mechanism becomes noisy and unreliable in middle positions. To compensate for this, we find that LMs supplement the positional mechanism with a lexical mechanism (retrieving "Ann" using its bound counterpart "pie") and a reflexive mechanism (retrieving "Ann" through a direct pointer). Through extensive experiments on nine models and ten binding tasks, we uncover a consistent pattern in how LMs mix these mechanisms to drive model behavior. We leverage these insights to develop a causal model combining all three mechanisms that estimates next token distributions with 95% agreement. Finally, we show that our model generalizes to substantially longer inputs of open-ended text interleaved with entity groups, further demonstrating the robustness of our findings in more natural settings. Overall, our study establishes a more complete picture of how LMs bind and retrieve entities in-context.

cs.CL↗
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

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

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↗
arXiv2026

Bucketing the Good Apples: A Method for Diagnosing and Improving Causal Abstraction

We present a method for diagnosing interpretation in neural networks by identifying an input subspace where a proposed interpretation is highly faithful. Our method is particularly useful for causal-abstraction-style interpretability, where a high-level causal hypothesis is evaluated by interchange interventions. Rather than treating interchange intervention accuracy as a single global summary, we refine this framework by partitioning the input space into well-interpreted and under-interpreted regions according to pairwise interchange-intervention behavior. This turns causal abstraction from a purely global evaluation into a more diagnostic tool: it not only measures whether an interpretation works, but also reveals where it works, where it fails, and what distinguishes the two cases. This diagnostic view also provides practical heuristics for improving interpretations. By analyzing the structure of the well-interpreted and under-interpreted regions, we can identify missing distinctions in a high-level hypothesis, discover previously unmodeled intermediate variables, and combine complementary partial interpretations into a stronger one. We instantiate this idea as a simple four-step recipe and show that it yields informative error analyses across multiple causal abstraction settings. In a toy logic task, recursively applying the recipe recovers a high-level hypothesis from scratch. More broadly, our results suggest that partitioning the input space is a useful step toward more precise, constructive, and scalable mechanistic interpretability.

cs.AI↗
arXiv2026

Constructing Interpretable Features from Compositional Neuron Groups

A central goal for mechanistic interpretability has been to identify the right units of analysis in large language models (LLMs) that causally explain their outputs. While early work focused on individual neurons, evidence that neurons often encode multiple concepts has motivated a shift toward analyzing directions in activation space. A key question is how to find directions that capture interpretable features in an unsupervised manner. Current methods rely on dictionary learning with sparse autoencoders (SAEs), commonly trained over residual stream activations to learn directions from scratch. However, SAEs often struggle in causal evaluations and lack intrinsic interpretability, as their learning is not explicitly tied to the computations of the model. Here, we tackle these limitations by directly decomposing MLP activations with semi-nonnegative matrix factorization (SNMF), such that the learned features are (a) sparse linear combinations of co-activated neurons, and (b) mapped to their activating inputs, making them directly interpretable. Experiments on Llama 3.1, Gemma 2 and GPT-2 show that SNMF derived features outperform SAEs and a strong supervised baseline (difference-in-means) on causal steering, while aligning with human-interpretable concepts. Further analysis reveals that specific neuron combinations are reused across semantically-related features, exposing a hierarchical structure in the MLP's activation space. Together, these results position SNMF as a simple and effective tool for identifying interpretable features and dissecting concept representations in LLMs.

cs.CL↗