Subspace-Aware Sparse Autoencoders for Effective Mechanistic Interpretability
Sparse Autoencoders (SAEs) are widely used for mechanistic interpretability in large language models, yet their formulation assigns each latent feature a single decoder direction, implicitly assuming features to be one-dimensional. We show that this assumption mismatches with the multi-dimensional structure of model features, provably inducing feature splitting through two distinct mechanisms. Geometrically, reconstructing a feature of intrinsic dimension $d_i \ge 2$ to error $\varepsilon$ with single-direction decoders forces a number of atoms that is exponential in $d_i$. From an end-to-end optimization perspective, this splitting is not merely possible but actively preferred. We prove ...
| Authors | Seyed Arshan Dalili, Mehrdad Mahdavi |
|---|---|
| Primary category | cs.LG |
| Published | 4 June 2026 |
| Last updated at source | 4 June 2026 |
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