Do Sparse Autoencoders Capture Concept Manifolds?
Sparse autoencoders (SAEs) are widely used to extract interpretable features from neural network representations, often under the implicit assumption that concepts correspond to independent linear directions. However, a growing body of evidence suggests that many concepts are instead organized along low-dimensional manifolds encoding continuous geometric relationships. This raises three basic questions: what does it mean for an SAE to capture a manifold, when do existing SAE architectures do so, and how? We develop a theoretical framework that answers these questions and show that SAEs can capture manifolds in two fundamentally different ways: globally, by allocating a compact group of at...
| Authors | Usha Bhalla, Thomas Fel, Can Rager et al. |
|---|---|
| Primary category | cs.LG |
| Published | 30 April 2026 |
| Last updated at source | 30 April 2026 |
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