# The Rate-Distortion-Polysemanticity Tradeoff in SAEs

arXiv: https://arxiv.org/abs/2605.14694 · HTML: https://mlsanity.com/paper/2605.14694/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in SAE features and their applications, one of 13 directions in Mechanistic interpretability.
- Builds on 22 of its 30 references that are in the map.
- First posted on arXiv 14 May 2026.

## Placed in

- Mechanistic interpretability / [SAE features and their applications](https://mlsanity.com/mechinterp/sae-features-and-their-applications/)

## Builds on (most cited first, 22 of 22)

- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [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)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoders](https://mlsanity.com/paper/2409.14507/) (2024)
- [Learning Multi-Level Features with Matryoshka Sparse Autoencoders](https://mlsanity.com/paper/2503.17547/) (2025)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)
- [SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretability](https://mlsanity.com/paper/2503.09532/) (2025)
- [Automatically Interpreting Millions of Features in Large Language Models](https://mlsanity.com/paper/2410.13928/) (2024)
- [Polysemanticity and Capacity in Neural Networks](https://mlsanity.com/paper/2210.01892/) (2022)
- [Projecting Assumptions: The Duality Between Sparse Autoencoders and Concept Geometry](https://mlsanity.com/paper/2503.01822/) (2025)
- [Interpretability as Compression: Reconsidering SAE Explanations of Neural Activations with MDL-SAEs](https://mlsanity.com/paper/2410.11179/) (2024)
- [Compute Optimal Inference and Provable Amortisation Gap in Sparse Autoencoders](https://mlsanity.com/paper/2411.13117/) (2024)
- [Rethinking Evaluation of Sparse Autoencoders through the Representation of Polysemous Words](https://mlsanity.com/paper/2501.06254/) (2025)
- [Feature Hedging: Correlated Features Break Narrow Sparse Autoencoders](https://mlsanity.com/paper/2505.11756/) (2025)
- [Sparse but Wrong: Incorrect L0 Leads to Incorrect Features in Sparse Autoencoders](https://mlsanity.com/paper/2508.16560/) (2025)
- [SynthSAEBench: Evaluating Sparse Autoencoders on Scalable Realistic Synthetic Data](https://mlsanity.com/paper/2602.14687/) (2026)
- [Information Theory: A Tutorial Introduction](https://mlsanity.com/paper/1802.05968/) (2018)

## Built on by (most cited first, 3 of 3)

- [Sparse Autoencoders Encode Both Concepts and Functions: The Downstream Geometry of Feature Effects](https://mlsanity.com/paper/2607.24645/) (2026)
- [The Independence Prior of SAEs Fragments Visual Concepts](https://mlsanity.com/paper/2610.04112/) (2026)
- [Sparse Autoencoders for Mechanistic Interpretability in NLP: A Critical Survey of Recoverability, Interpretability, and Utility](https://mlsanity.com/paper/2610.20139/) (2026)

## Abstract (arXiv)

Sparse Autoencoders (SAEs) that can accurately reconstruct their input (minimizing distortion) by making efficient use of few features (minimizing the rate) often fail to learn monosemantic representations (highly interpretable), limiting their usefulness for mechanistic interpretability. In this paper, we characterise this tension in learning faithful, efficient, and interpretable explanations, introducing the Rate-Distortion-Polysemanticity tradeoff in SAEs. Under toy-modeling assumptions, we theoretically and empirically show that restricting the SAE to be monosemantic necessarily comes with an increase in rate and distortion. Assuming a generative model behind the input observations, we further demonstrate that the degree of polysemanticity of optimal SAEs is determined by the training data distribution, especially by the probability of features to co-occur. Finally, we extend the analysis to real-world settings by deriving necessary conditions that a polysemanticity measure should satisfy when the data-generating process is unknown, and we benchmark existing proxy metrics on SAEs trained on Large Language Models. Taken together, our findings show that polysemanticity is a data problem that should be accounted for when addressing it at the architectural and optimization level.