# Sparse but Wrong: Incorrect L0 Leads to Incorrect Features in Sparse Autoencoders

arXiv: https://arxiv.org/abs/2508.16560 · HTML: https://mlsanity.com/paper/2508.16560/

## Key facts

- Cited by 14 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 18 of its 31 references that are in the map.
- First posted on arXiv 22 Aug 2025.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [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)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [AxBench: Steering LLMs? Even Simple Baselines Outperform Sparse Autoencoders](https://mlsanity.com/paper/2501.17148/) (2025)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (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)
- [BatchTopK Sparse Autoencoders](https://mlsanity.com/paper/2412.06410/) (2024)
- [Are Sparse Autoencoders Useful? A Case Study in Sparse Probing](https://mlsanity.com/paper/2502.16681/) (2025)
- [Decomposing The Dark Matter of Sparse Autoencoders](https://mlsanity.com/paper/2410.14670/) (2024)
- [A note on the sample complexity of the Er-SpUD algorithm by Spielman, Wang and Wright for exact recovery of sparsely used dictionaries](https://mlsanity.com/paper/1601.02049/) (2016)
- [Interpretability as Compression: Reconsidering SAE Explanations of Neural Activations with MDL-SAEs](https://mlsanity.com/paper/2410.11179/) (2024)
- [Feature Hedging: Correlated Features Break Narrow Sparse Autoencoders](https://mlsanity.com/paper/2505.11756/) (2025)
- [Evaluating and Designing Sparse Autoencoders by Approximating Quasi-Orthogonality](https://mlsanity.com/paper/2503.24277/) (2025)

## Built on by (most cited first, 14 of 14)

- [Sanity Checks for Sparse Autoencoders: Do SAEs Beat Random Baselines?](https://mlsanity.com/paper/2602.14111/) (2026)
- [SynthSAEBench: Evaluating Sparse Autoencoders on Scalable Realistic Synthetic Data](https://mlsanity.com/paper/2602.14687/) (2026)
- [Learning a Generative Meta-Model of LLM Activations](https://mlsanity.com/paper/2602.06964/) (2026)
- [Stable and Steerable Sparse Autoencoders with Weight Regularization](https://mlsanity.com/paper/2603.04198/) (2026)
- [Perplexity Can Miss SAE Feature Damage Under Quantization](https://mlsanity.com/paper/2606.03002/) (2026)
- [The Rate-Distortion-Polysemanticity Tradeoff in SAEs](https://mlsanity.com/paper/2605.14694/) (2026)
- [Feature Superposition in Neural Networks: From Theory to Practice](https://mlsanity.com/paper/2609.06862/) (2026)
- [The Pain Axis: LLMs Represent Self-Directed Harm and Act on It](https://mlsanity.com/paper/2609.16247/) (2026)
- [Building Fast, Evaluating Slow: Pipeline Choices Dominate Autointerpretability Score Variance](https://mlsanity.com/paper/2607.19386/) (2026)
- [SharedSAE: One Feature Dictionary Across Language Models](https://mlsanity.com/paper/2609.04344/) (2026)
- [Verifying the Linear Representation Hypothesis: How Interpretable Are Vision SAEs?](https://mlsanity.com/paper/2609.35020/) (2026)
- [Beyond Token Scale: Chunk-Level Sparse Autoencoders for Reliable Semantic Feature Discovery](https://mlsanity.com/paper/2609.35521/) (2026)
- [A Testable Theory of Atomic Features](https://mlsanity.com/paper/2610.05794/) (2026)
- [Sparse Transformer: a Controlled Testbed for Mechanistic Interpretability](https://mlsanity.com/paper/2610.19907/) (2026)

## Abstract (arXiv)

Sparse Autoencoders (SAEs) extract features from LLM internal activations, meant to correspond to interpretable concepts. A core SAE training hyperparameter is L0: how many SAE features should fire per token on average. Existing work compares SAE algorithms using sparsity-reconstruction tradeoff plots, implying L0 is a free parameter with no inherently correct value aside from its effect on reconstruction. In this work we study the effect of L0 on SAEs, and show that if L0 is not set correctly, the SAE fails to disentangle the underlying features of the LLM. If L0 is too low, the SAE will mix correlated features to improve reconstruction. If L0 is too high, the SAE finds degenerate solutions that also mix features. Further, we present a proxy metric that can help guide the search for the correct L0 for an SAE on a given training distribution. We show that our method finds the correct L0 in toy models and coincides with peak sparse probing performance in LLM SAEs. We find that most commonly used SAEs have an L0 that is too low. Our work shows that practitioners must set L0 correctly to train SAEs with monosemantic features.