# Interpretability as Compression: Reconsidering SAE Explanations of Neural Activations with MDL-SAEs

arXiv: https://arxiv.org/abs/2410.11179 · HTML: https://mlsanity.com/paper/2410.11179/

## Key facts

- Cited by 23 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 5 of its 23 references that are in the map.
- First posted on arXiv 15 Oct 2024.

## Placed in

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

## Builds on (most cited first, 5 of 5)

- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Compact Proofs of Model Performance via Mechanistic Interpretability](https://mlsanity.com/paper/2406.11779/) (2024)

## Built on by (most cited first, 23 of 23)

- [Projecting Assumptions: The Duality Between Sparse Autoencoders and Concept Geometry](https://mlsanity.com/paper/2503.01822/) (2025)
- [From Flat to Hierarchical: Extracting Sparse Representations with Matching Pursuit](https://mlsanity.com/paper/2506.03093/) (2025)
- [Sparse but Wrong: Incorrect L0 Leads to Incorrect Features in Sparse Autoencoders](https://mlsanity.com/paper/2508.16560/) (2025)
- [Adaptive Sparse Allocation with Mutual Choice & Feature Choice Sparse Autoencoders](https://mlsanity.com/paper/2411.02124/) (2024)
- [AbsTopK: Rethinking Sparse Autoencoders For Bidirectional Features](https://mlsanity.com/paper/2510.00404/) (2025)
- [SAFE: A Sparse Autoencoder-Based Framework for Robust Query Enrichment and Hallucination Mitigation in LLMs](https://mlsanity.com/paper/2503.03032/) (2025)
- [Superposition as Lossy Compression: Measure with Sparse Autoencoders and Connect to Adversarial Vulnerability](https://mlsanity.com/paper/2512.13568/) (2025)
- [A Mathematical Philosophy of Explanations in Mechanistic Interpretability -- The Strange Science Part I.i](https://mlsanity.com/paper/2505.00808/) (2025)
- [Evaluating SAE interpretability without explanations](https://mlsanity.com/paper/2507.08473/) (2025)
- [Finding Manifolds With Bilinear Autoencoders](https://mlsanity.com/paper/2510.16820/) (2025)
- [Stable and Steerable Sparse Autoencoders with Weight Regularization](https://mlsanity.com/paper/2603.04198/) (2026)
- [Structuring Sparsity: Block-Sparse Featurizers Capture Visual Concept Manifolds](https://mlsanity.com/paper/2606.25234/) (2026)
- [Train One Sparse Autoencoder Across Multiple Sparsity Budgets to Preserve Interpretability and Accuracy](https://mlsanity.com/paper/2505.24473/) (2025)
- [Tree SAE: Learning Hierarchical Feature Structures in Sparse Autoencoders](https://mlsanity.com/paper/2605.07922/) (2026)
- [Resurrecting the Salmon: Rethinking Mechanistic Interpretability with Domain-Specific Sparse Autoencoders](https://mlsanity.com/paper/2508.09363/) (2025)
- [Binary Sparse Coding for Interpretability](https://mlsanity.com/paper/2509.25596/) (2025)
- [The Rate-Distortion-Polysemanticity Tradeoff in SAEs](https://mlsanity.com/paper/2605.14694/) (2026)
- [Evaluating Explanations: An Explanatory Virtues Framework for Mechanistic Interpretability -- The Strange Science Part I.ii](https://mlsanity.com/paper/2505.01372/) (2025)
- [FaithfulSAE: Towards Capturing Faithful Features with Sparse Autoencoders without External Dataset Dependencies](https://mlsanity.com/paper/2506.17673/) (2025)
- [Descriptive Collision in Sparse Autoencoder Auto-Interpretability: When One Explanation Describes Many Features](https://mlsanity.com/paper/2605.12874/) (2026)
- [Bilinear autoencoders find interpretable manifolds](https://mlsanity.com/paper/2605.08891/) (2026)
- [Decoder-Preserving Sparse Autoencoders: Which Readouts Survive Sparse Compression?](https://mlsanity.com/paper/2607.17425/) (2026)
- [The Independence Prior of SAEs Fragments Visual Concepts](https://mlsanity.com/paper/2610.04112/) (2026)

## Abstract (arXiv)

Sparse Autoencoders (SAEs) have emerged as a useful tool for interpreting the internal representations of neural networks. However, naively optimising SAEs for reconstruction loss and sparsity results in a preference for SAEs that are extremely wide and sparse. We present an information-theoretic framework for interpreting SAEs as lossy compression algorithms for communicating explanations of neural activations. We appeal to the Minimal Description Length (MDL) principle to motivate explanations of activations which are both accurate and concise. We further argue that interpretable SAEs require an additional property, "independent additivity": features should be able to be understood separately. We demonstrate an example of applying our MDL-inspired framework by training SAEs on MNIST handwritten digits and find that SAE features representing significant line segments are optimal, as opposed to SAEs with features for memorised digits from the dataset or small digit fragments. We argue that using MDL rather than sparsity may avoid potential pitfalls with naively maximising sparsity such as undesirable feature splitting and that this framework naturally suggests new hierarchical SAE architectures which provide more concise explanations.