The Independence Prior of SAEs Fragments Visual Concepts

Abstract:Sparse Autoencoders (SAEs) decompose model activations into sparse combinations of interpretable dictionary atoms. Although SAEs are grounded in the Linear Representation Hypothesis (LRH), their objective smuggles in an additional prior: concepts across patches are treated as independent, an assumption clearly violated by natural images and by the activations they induce. We therefore specialize LRH to vision through the Markov-Field Linear Representation Hypothesis (MFLRH), which adds the missing spatial dependencies to the LRH assumptions. We thus propose Spatial-SAE as an amortized MAP estimator under the MFLRH. Spatial-SAE consistently outperforms standard SAEs in concept recovery and interpretability. Across four variants, it achieves a 96% average win rate on synthetic concept recovery and improves interpretability on DINOv2 activations, at a reconstruction cost concentrated in high spatial frequencies.

Artificial Intelligence (cs.AI)

arXiv:2610.04112 [cs.AI]

(or arXiv:2610.04112v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.04112 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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