# Evaluating Sparse Autoencoders: From Shallow Design to Matching Pursuit

arXiv: https://arxiv.org/abs/2506.05239 · HTML: https://mlsanity.com/paper/2506.05239/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 26 of its 57 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Placed in

- Mechanistic interpretability / [Sparse autoencoder training and evaluation](https://mlsanity.com/mechinterp/sparse-autoencoder-training-and-evaluation/)

## Builds on (most cited first, 26 of 26)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Learning Multi-Level Features with Matryoshka Sparse Autoencoders](https://mlsanity.com/paper/2503.17547/) (2025)
- [BatchTopK Sparse Autoencoders](https://mlsanity.com/paper/2412.06410/) (2024)
- [A Holistic Approach to Unifying Automatic Concept Extraction and Concept Importance Estimation](https://mlsanity.com/paper/2306.07304/) (2023)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [Projecting Assumptions: The Duality Between Sparse Autoencoders and Concept Geometry](https://mlsanity.com/paper/2503.01822/) (2025)
- [Sparse Modeling for Image and Vision Processing](https://mlsanity.com/paper/1411.3230/) (2014)
- [Simple, Efficient, and Neural Algorithms for Sparse Coding](https://mlsanity.com/paper/1503.00778/) (2015)
- [Learning step sizes for unfolded sparse coding](https://mlsanity.com/paper/1905.11071/) (2019)
- [Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization](https://mlsanity.com/paper/1310.7991/) (2013)
- [Stable and Interpretable Unrolled Dictionary Learning](https://mlsanity.com/paper/2106.00058/) (2021)
- [Understanding Trainable Sparse Coding via Matrix Factorization](https://mlsanity.com/paper/1609.00285/) (2016)
- [Understanding approximate and unrolled dictionary learning for pattern recovery](https://mlsanity.com/paper/2106.06338/) (2021)
- [Learned Greedy Method (LGM): A Novel Neural Architecture for Sparse Coding and Beyond](https://mlsanity.com/paper/2010.07069/) (2020)
- [NOODL: Provable Online Dictionary Learning and Sparse Coding](https://mlsanity.com/paper/1902.11261/) (2019)

## Built on by (most cited first, 1 of 1)

- [WriteSAE: Sparse Autoencoders for Recurrent State](https://mlsanity.com/paper/2605.12770/) (2026)

## Abstract (arXiv)

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.