# Beyond a Bag of Features: Set-Level Instability in Sparse Autoencoders

arXiv: https://arxiv.org/abs/2608.11197 · HTML: https://mlsanity.com/paper/2608.11197/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in SAE features and their applications, one of 13 directions in Mechanistic interpretability.
- Builds on 16 of its 41 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [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)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [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)
- [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)
- [Llama Scope: Extracting Millions of Features from Llama-3.1-8B with Sparse Autoencoders](https://mlsanity.com/paper/2410.20526/) (2024)
- [SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretability](https://mlsanity.com/paper/2503.09532/) (2025)
- [Sparse Autoencoders Do Not Find Canonical Units of Analysis](https://mlsanity.com/paper/2502.04878/) (2025)
- [Language Models Use Trigonometry to Do Addition](https://mlsanity.com/paper/2502.00873/) (2025)
- [From Tokens to Thoughts: How LLMs and Humans Trade Compression for Meaning](https://mlsanity.com/paper/2505.17117/) (2025)
- [Mechanistic Permutability: Match Features Across Layers](https://mlsanity.com/paper/2410.07656/) (2024)
- [Can sparse autoencoders be used to decompose and interpret steering vectors?](https://mlsanity.com/paper/2411.08790/) (2024)
- [Feature Hedging: Correlated Features Break Narrow Sparse Autoencoders](https://mlsanity.com/paper/2505.11756/) (2025)
- [Probing the Representational Power of Sparse Autoencoders in Vision Models](https://mlsanity.com/paper/2508.11277/) (2025)

## Abstract (arXiv)

Shani et al. (2026) show that LLM representations broadly recover human category boundaries, while failing to reflect fine-grained typicality structure. Their analysis uses cosine similarity over dense model representations. We revisit their approach using overlap over active sparse autoencoder (SAE) latent sets as a more interpretable similarity measure. We first verify that this set-level measure is meaningful: SAE latent sets can recover union-like compositional structure in controlled toy models and induce semantically coherent neighborhoods in natural text. Extending the human-concepts analysis to SAE set similarities, we find that SAE activation sets do not recover human category boundaries or within-category typicality more faithfully than dense embeddings or residual-stream states, but instead track model-internal similarity structure. To probe this gap further, we study active latent sets under well-controlled semantic modifications, revealing a substantial mismatch between human judgements of conceptual change and change in the SAE active set. We interpret this as evidence that, outside idealised settings, SAE features do not compose via simple bag-of-features semantics.