Thomas Fel
Publications
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.
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.