Evaluating Sparse Autoencoders: From Shallow Design to Matching Pursuit

TL;DR

This paper critically evaluates sparse autoencoders (SAEs) on MNIST, revealing limitations of shallow architectures and proposing an iterative SAE with Matching Pursuit to better extract correlated features in hierarchical data.

Contribution

It introduces an iterative SAE unrolled from Matching Pursuit, improving feature extraction beyond shallow SAE limitations and ensuring monotonic reconstruction improvement.

Findings

Shallow SAEs rely on quasi-orthogonality, limiting correlated feature extraction.

Iterative MP-SAE effectively captures correlated features in hierarchical data.

MP-SAE guarantees monotonic reconstruction improvement.

Abstract

Sparse autoencoders (SAEs) have recently become central tools for interpretability, leveraging dictionary learning principles to extract sparse, interpretable features from neural representations whose underlying structure is typically unknown. This paper evaluates SAEs in a controlled setting using MNIST, which reveals that current shallow architectures implicitly rely on a quasi-orthogonality assumption that limits the ability to extract correlated features. To move beyond this, we compare them with an iterative SAE that unrolls Matching Pursuit (MP-SAE), enabling the residual-guided extraction of correlated features that arise in hierarchical settings such as handwritten digit generation while guaranteeing monotonic improvement of the reconstruction as more atoms are selected.