Supervised sparse auto-encoders for interpretable and compositional representations

Ouns El Harzli; Hugo Wallner; Yoonsoo Nam; Haixuan Xavier Tao

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arXiv · 2602.00924

Supervised sparse auto-encoders for interpretable and compositional representations

Ouns El Harzli·Hugo Wallner·Yoonsoo Nam·Haixuan Xavier Tao

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Abstract

Sparse auto-encoders (SAEs) have re-emerged as a prominent method for mechanistic interpretability, yet they face two significant challenges: the non-smoothness of the $L_1$ penalty, which hinders reconstruction and scalability, and a lack of alignment between learned features and human semantics. In this paper, we address these limitations by adapting unconstrained feature models, a mathematical framework from neural collapse theory, and by supervising the task. We supervise (decoder-only) SAEs to reconstruct feature vectors by jointly learning sparse concept embeddings and decoder weights. Validated on Stable Diffusion 3.5, our approach demonstrates compositional generalization, successfully reconstructing images with concept combinations unseen during training, and enabling feature-level intervention for semantic image editing without prompt modification.

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Ouns El Harzli, Hugo Wallner, Yoonsoo Nam, Haixuan Xavier Tao. 2026-01-31. Supervised sparse auto-encoders for interpretable and compositional representations. https://arxiv.org/abs/2602.00924

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