Kronecker Factorization Improves Efficiency and Interpretability of Sparse Autoencoders

Abstract:Sparse Autoencoders (SAEs) decompose language-model activations into sparse, interpretable features, but standard encoders usually treat the latent dictionary as a flat set of independent coordinates, leaving hierarchy and feature interactions to emerge only implicitly. We propose KronSAE, a design that factorizes the latent space into heads and forms post-latent features as pairwise compositions of lower-dimensional pre-latents using mAND, a differentiable AND-like interaction. This imposes a compositional co-activation prior while remaining compatible with standard SAE objectives and variants such as TopK, Matryoshka, and Switch SAEs. KronSAE matches strong baselines on the EV-FLOPs frontier, improves interpretability of the latents, better captures the underlying correlated feature structure, and reduces encoder computational cost as an additional benefit. Code is available at this https URL.

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2505.22255 [cs.LG]

(or arXiv:2505.22255v4 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2505.22255 Focus to learn more arXiv-issued DOI via DataCite

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