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Thomas Fel

Publications and source records attributed to Thomas Fel.

At least 19 recordsLinked to original sources
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

A Unifying Framework for Concept-Based Representational Similarity

Learned representations across models and modalities often exhibit striking structural similarities, suggesting shared underlying concept decompositions. However, concept alignment remains poorly defined: existing approaches optimize different objectives under the same terminology, obscuring what is actually aligned. We propose a unifying framework that decomposes alignment along two axes: what is aligned (representations vs. concepts) and at what level (instance-wise vs. distributional). This induces four corresponding properties -- instance-wise and distributional variants of translation and concept consistency -- and reveals precisely which of these guarantees existing methods provide. We further introduce \InterVenchA, an intervention-based benchmark that separately measures extraction quality, translation quality, and concept consistency. Through theory and experiments, we show that commonly assumed equivalences between alignment objectives fail in practice: optimizing one property does not reliably recover the others, and purely unsupervised objectives fail to recover meaningful instance-level alignment. We then propose the Coupled Sparse Autoencoder (CoSAE), which jointly enforces complementary alignment objectives. Strong alignment emerges only in this regime. Surprisingly, as little as 0.1\% paired data is sufficient to recover instance-level alignment when anchoring distributional objectives. Overall, our results show that concept alignment is fundamentally multi-objective: it must be defined, measured, and optimized as such.

cs.LG↗
arXiv2026

A Unifying View of Attention Sinks: Two Algorithms, Two Solutions

When attention concentrates on a single token, a sink, what is the model actually computing? Attention sinks are ubiquitous in softmax transformers, yet this shared visual signature can hide fundamentally different algorithms. We show that visually similar sink patterns can reflect two distinct mechanisms: {i} adaptive nop, where a head suppresses its update by routing to a null token, and {ii} broadcast, where a sink aggregates and redistributes global information. In that case, sinks serve an analogous role: a safe destination when there is nothing useful to compute. Proposed interventions like gating or registers work because they implicitly target one or the other, revealing a duality between method and assumed mechanism: gating implicitly assumes nop; registers implicitly assume broadcast. Each mechanism leaves distinct traces (nop sinks exhibit negligible value norms; broadcast sinks induce low-rank outputs) which we formalize on synthetic tasks and use to derive practical diagnostics. Applied to pretrained vision transformers, these diagnostics reveal that both mechanisms exist at scale: sinks transition from CLS in early layers to patches in deeper layers, and concentrate in specialized heads. Strikingly, register tokens, designed for broadcast, are repurposed to also serve nop, confirming that neither intervention alone suffices. Combining gating with registers yields complementary gains in stability and performance. Overall, we find that the same attention pattern can reflect two very different computations and effective intervention requires first asking what the model is actually computing.

cs.LG↗
arXiv2026

The Case for Model Science: Verify, Explore, Steer, Refine

We argue that the AI community is now ready to move beyond benchmarking and consolidate scattered efforts in model analysis into a systematic discipline, a direction we term Model Science. Complex AI models now serve billions of users, yet our understanding of how they work lags far behind our ability to deploy them. Decades of benchmark-driven research have delivered remarkable progress: extensive leaderboards, a wide range of performance metrics, tracking capability gains across diverse tasks; yet this success has also revealed the limits of benchmarks as they tell us whether models perform but not why they succeed or fail, they miss critical failure modes, such as hallucinations or shortcuts. Precedents from established sciences point the way forward: cognitive science shows that understanding complex systems requires complementary levels of analysis; neuroscience demonstrates that deep study of single cases reveals what population studies miss; medicine teaches that specialised training must develop alongside research practice; and agriculture models how shared infrastructure and principles enable cumulative progress. These lessons inform three foundations for Model Science. First, we propose to consolidate research around four functional perspectives: Verify, Explore, Steer, and Refine that address complementary questions about model behaviour. Second, we discuss the required infrastructure for cumulative knowledge: catalogues of datasets, models and findings. Third, we highlight the need for deep analysis of individual model instances, not just model families, because single cases can reveal what population studies miss.

cs.AI↗
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

Cross-Modal Redundancy and the Geometry of Vision-Language Embeddings

Vision-language models (VLMs) align images and text with remarkable success, yet the geometry of their shared embedding space remains poorly understood. To probe this geometry, we begin from the Iso-Energy Assumption, which exploits cross-modal redundancy: a concept that is truly shared should exhibit the same average energy across modalities. We operationalize this assumption with an Aligned Sparse Autoencoder (SAE) that encourages energy consistency during training while preserving reconstruction. We find that this inductive bias changes the SAE solution without harming reconstruction, giving us a representation that serves as a tool for geometric analysis. Sanity checks on controlled data with known ground truth confirm that alignment improves when Iso-Energy holds and remains neutral when it does not. Applied to foundational VLMs, our framework reveals a clear structure with practical consequences: (i) sparse bimodal atoms carry the entire cross-modal alignment signal; (ii) unimodal atoms act as modality-specific biases and fully explain the modality gap; (iii) removing unimodal atoms collapses the gap without harming performance; (iv) restricting vector arithmetic to the bimodal subspace yields in-distribution edits and improved retrieval. These findings suggest that the right inductive bias can both preserve model fidelity and render the latent geometry interpretable and actionable.

cs.CV↗
arXiv2026

Interpreting Physics in Video World Models

A long-standing question in physical reasoning is whether video-based models need to rely on factorized representations of physical variables in order to make physically accurate predictions, or whether they can implicitly represent such variables in a task-specific, distributed manner. While modern video world models achieve strong performance on intuitive physics benchmarks, it remains unclear which of these representational regimes they implement internally. Here, we present the first interpretability study to directly examine physical representations inside large-scale video encoders. Using layerwise probing, subspace geometry, patch-level decoding, and targeted attention ablations, we characterize where physical information becomes accessible and how it is organized within encoder-based video transformers. Across architectures, we identify a sharp intermediate-depth transition -- which we call the Physics Emergence Zone -- at which physical variables become accessible. Physics-related representations peak shortly after this transition and degrade toward the output layers. Decomposing motion into explicit variables, we find that scalar quantities such as speed and acceleration are available from early layers onwards, whereas motion direction becomes accessible only at the Physics Emergence Zone. Notably, we find that direction is encoded through a high-dimensional population structure with circular geometry, requiring coordinated multi-feature intervention to control. These findings suggest that modern video models do not use factorized representations of physical variables like a classical physics engine. Instead, they use a distributed representation that is nonetheless sufficient for making physical predictions.

cs.CV↗
arXiv2026

Bi-Orthogonal Factor Decomposition for Vision Transformers

Self-attention is the central computational primitive of Vision Transformers, yet we lack a principled understanding of what information attention mechanisms exchange between tokens. Attention maps describe where weight mass concentrates; they do not reveal whether queries and keys trade position, content, or both. We introduce Bi-orthogonal Factor Decomposition (BFD), a two-stage analytical framework: first, an ANOVA-based decomposition statistically disentangles token activations into orthogonal positional and content factors; second, SVD of the query-key interaction matrix QK^T exposes bi-orthogonal modes that reveal how these factors mediate communication. After validating proper isolation of position and content, we apply BFD to state-of-the-art vision models and uncover three phenomena.(i) Attention operates primarily through content. Content-content interactions dominate attention energy, followed by content-position coupling. DINOv2 allocates more energy to content-position than supervised models and distributes computation across a richer mode spectrum. (ii) Attention mechanisms exhibit specialization: heads differentiate into content-content, content-position, and position-position operators, while singular modes within heads show analogous specialization. (iii) DINOv2's superior holistic shape processing emerges from intermediate layers that simultaneously preserve positional structure while contextually enriching semantic content. Overall, BFD exposes how tokens interact through attention and which informational factors - positional or semantic - mediate their communication, yielding practical insights into vision transformer mechanisms.

cs.CV↗
arXiv2025

Block-Recurrent Dynamics in Vision Transformers

As Vision Transformers (ViTs) become standard vision backbones, a mechanistic account of their computational phenomenology is essential. Despite architectural cues that hint at dynamical structure, there is no settled framework that interprets Transformer depth as a well-characterized flow. In this work, we introduce the Block-Recurrent Hypothesis (BRH), arguing that trained ViTs admit a block-recurrent depth structure such that the computation of the original $L$ blocks can be accurately rewritten using only $k \ll L$ distinct blocks applied recurrently. Across diverse ViTs, between-layer representational similarity matrices suggest few contiguous phases. To determine whether these phases reflect genuinely reusable computation, we train block-recurrent surrogates of pretrained ViTs: Recurrent Approximations to Phase-structured TransfORmers (Raptor). In small-scale, we demonstrate that stochastic depth and training promote recurrent structure and subsequently correlate with our ability to accurately fit Raptor. We then provide an empirical existence proof for BRH by training a Raptor model to recover $96\%$ of DINOv2 ImageNet-1k linear probe accuracy in only 2 blocks at equivalent runtime. Finally, we leverage our hypothesis to develop a program of Dynamical Interpretability. We find i) directional convergence into class-dependent angular basins with self-correcting trajectories under small perturbations, ii) token-specific dynamics, where cls executes sharp late reorientations while patch tokens exhibit strong late-stage coherence toward their mean direction, and iii) a collapse to low rank updates in late depth, consistent with convergence to low-dimensional attractors. Altogether, we find a compact recurrent program emerges along ViT depth, pointing to a low-complexity normative solution that enables these models to be studied through principled dynamical systems analysis.

cs.CV↗
arXiv2025

Back to the Baseline: Examining Baseline Effects on Explainability Metrics

Attribution methods are among the most prevalent techniques in Explainable Artificial Intelligence (XAI) and are usually evaluated and compared using Fidelity metrics, with Insertion and Deletion being the most popular. These metrics rely on a baseline function to alter the pixels of the input image that the attribution map deems most important. In this work, we highlight a critical problem with these metrics: the choice of a given baseline will inevitably favour certain attribution methods over others. More concerningly, even a simple linear model with commonly used baselines contradicts itself by designating different optimal methods. A question then arises: which baseline should we use? We propose to study this problem through two desirable properties of a baseline: (i) that it removes information and (ii) that it does not produce overly out-of-distribution (OOD) images. We first show that none of the tested baselines satisfy both criteria, and there appears to be a trade-off among current baselines: either they remove information or they produce a sequence of OOD images. Finally, we introduce a novel baseline by leveraging recent work in feature visualisation to artificially produce a model-dependent baseline that removes information without being overly OOD, thus improving on the trade-off when compared to other existing baselines. Our code is available at https://github.com/deel-ai-papers/Back-to-the-Baseline

cs.AI↗
arXiv2025

A Geometric Unification of Concept Learning with Concept Cones

Two traditions of interpretability have evolved side by side but seldom spoken to each other: Concept Bottleneck Models (CBMs), which prescribe what a concept should be, and Sparse Autoencoders (SAEs), which discover what concepts emerge. While CBMs use supervision to align activations with human-labeled concepts, SAEs rely on sparse coding to uncover emergent ones. We show that both paradigms instantiate the same geometric structure: each learns a set of linear directions in activation space whose nonnegative combinations form a concept cone. Supervised and unsupervised methods thus differ not in kind but in how they select this cone. Building on this view, we propose an operational bridge between the two paradigms. CBMs provide human-defined reference geometries, while SAEs can be evaluated by how well their learned cones approximate or contain those of CBMs. This containment framework yields quantitative metrics linking inductive biases -- such as SAE type, sparsity, or expansion ratio -- to emergence of plausible\footnote{We adopt the terminology of \citet{jacovi2020towards}, who distinguish between faithful explanations (accurately reflecting model computations) and plausible explanations (aligning with human intuition and domain knowledge). CBM concepts are plausible by construction -- selected or annotated by humans -- though not necessarily faithful to the true latent factors that organise the data manifold.} concepts. Using these metrics, we uncover a ``sweet spot'' in both sparsity and expansion factor that maximizes both geometric and semantic alignment with CBM concepts. Overall, our work unifies supervised and unsupervised concept discovery through a shared geometric framework, providing principled metrics to measure SAE progress and assess how well discovered concept align with plausible human concepts.

cs.AI↗
arXiv2025

Sparse, self-organizing ensembles of local kernels detect rare statistical anomalies

Modern artificial intelligence has revolutionized our ability to extract rich and versatile data representations across scientific disciplines. Yet, the statistical properties of these representations remain poorly controlled, causing misspecified anomaly detection (AD) methods to falter. Weak or rare signals can remain hidden within the apparent regularity of normal data, creating a gap in our ability to detect and interpret anomalies. We examine this gap and identify a set of structural desiderata for detection methods operating under minimal prior information: sparsity, to enforce parsimony; locality, to preserve geometric sensitivity; and competition, to promote efficient allocation of model capacity. These principles define a class of self-organizing local kernels that adaptively partition the representation space around regions of statistical imbalance. As an instantiation of these principles, we introduce SparKer, a sparse ensemble of Gaussian kernels trained within a semi-supervised Neyman--Pearson framework to locally model the likelihood ratio between a sample that may contain anomalies and a nominal, anomaly-free reference. We provide theoretical insights into the mechanisms that drive detection and self-organization in the proposed model, and demonstrate the effectiveness of this approach on realistic high-dimensional problems of scientific discovery, open-world novelty detection, intrusion detection, and generative-model validation. Our applications span both the natural- and computer-science domains. We demonstrate that ensembles containing only a handful of kernels can identify statistically significant anomalous locations within representation spaces of thousands of dimensions, underscoring both the interpretability, efficiency and scalability of the proposed approach.

cs.LG↗
arXiv2025

Priors in Time: Missing Inductive Biases for Language Model Interpretability

Recovering meaningful concepts from language model activations is a central aim of interpretability. While existing feature extraction methods aim to identify concepts that are independent directions, it is unclear if this assumption can capture the rich temporal structure of language. Specifically, via a Bayesian lens, we demonstrate that Sparse Autoencoders (SAEs) impose priors that assume independence of concepts across time, implying stationarity. Meanwhile, language model representations exhibit rich temporal dynamics, including systematic growth in conceptual dimensionality, context-dependent correlations, and pronounced non-stationarity, in direct conflict with the priors of SAEs. Taking inspiration from computational neuroscience, we introduce a new interpretability objective -- Temporal Feature Analysis -- which possesses a temporal inductive bias to decompose representations at a given time into two parts: a predictable component, which can be inferred from the context, and a residual component, which captures novel information unexplained by the context. Temporal Feature Analyzers correctly parse garden path sentences, identify event boundaries, and more broadly delineate abstract, slow-moving information from novel, fast-moving information, while existing SAEs show significant pitfalls in all the above tasks. Overall, our results underscore the need for inductive biases that match the data in designing robust interpretability tools.

cs.LG↗
arXiv2025

Into the Rabbit Hull: From Task-Relevant Concepts in DINO to Minkowski Geometry

DINOv2 is routinely deployed to recognize objects, scenes, and actions; yet the nature of what it perceives remains unknown. As a working baseline, we adopt the Linear Representation Hypothesis (LRH) and operationalize it using SAEs, producing a 32,000-unit dictionary that serves as the interpretability backbone of our study, which unfolds in three parts. In the first part, we analyze how different downstream tasks recruit concepts from our learned dictionary, revealing functional specialization: classification exploits "Elsewhere" concepts that fire everywhere except on target objects, implementing learned negations; segmentation relies on boundary detectors forming coherent subspaces; depth estimation draws on three distinct monocular depth cues matching visual neuroscience principles. Following these functional results, we analyze the geometry and statistics of the concepts learned by the SAE. We found that representations are partly dense rather than strictly sparse. The dictionary evolves toward greater coherence and departs from maximally orthogonal ideals (Grassmannian frames). Within an image, tokens occupy a low dimensional, locally connected set persisting after removing position. These signs suggest representations are organized beyond linear sparsity alone. Synthesizing these observations, we propose a refined view: tokens are formed by combining convex mixtures of archetypes (e.g., a rabbit among animals, brown among colors, fluffy among textures). This structure is grounded in Gardenfors' conceptual spaces and in the model's mechanism as multi-head attention produces sums of convex mixtures, defining regions bounded by archetypes. We introduce the Minkowski Representation Hypothesis (MRH) and examine its empirical signatures and implications for interpreting vision-transformer representations.

cs.CV↗
arXiv2025

Visual Anagrams Reveal Hidden Differences in Holistic Shape Processing Across Vision Models

Humans are able to recognize objects based on both local texture cues and the configuration of object parts, yet contemporary vision models primarily harvest local texture cues, yielding brittle, non-compositional features. Work on shape-vs-texture bias has pitted shape and texture representations in opposition, measuring shape relative to texture, ignoring the possibility that models (and humans) can simultaneously rely on both types of cues, and obscuring the absolute quality of both types of representation. We therefore recast shape evaluation as a matter of absolute configural competence, operationalized by the Configural Shape Score (CSS), which (i) measures the ability to recognize both images in Object-Anagram pairs that preserve local texture while permuting global part arrangement to depict different object categories. Across 86 convolutional, transformer, and hybrid models, CSS (ii) uncovers a broad spectrum of configural sensitivity with fully self-supervised and language-aligned transformers -- exemplified by DINOv2, SigLIP2 and EVA-CLIP -- occupying the top end of the CSS spectrum. Mechanistic probes reveal that (iii) high-CSS networks depend on long-range interactions: radius-controlled attention masks abolish performance showing a distinctive U-shaped integration profile, and representational-similarity analyses expose a mid-depth transition from local to global coding. A BagNet control remains at chance (iv), ruling out "border-hacking" strategies. Finally, (v) we show that configural shape score also predicts other shape-dependent evals. Overall, we propose that the path toward truly robust, generalizable, and human-like vision systems may not lie in forcing an artificial choice between shape and texture, but rather in architectural and learning frameworks that seamlessly integrate both local-texture and global configural shape.

cs.CV↗