# Verifying the Linear Representation Hypothesis: How Interpretable Are Vision SAEs?

arXiv: https://arxiv.org/abs/2609.35020 · HTML: https://mlsanity.com/paper/2609.35020/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 59 of its 85 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

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

## Builds on (most cited first, 30 of 59)

- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [InstructBLIP: Towards General-purpose Vision-Language Models with Instruction Tuning](https://mlsanity.com/paper/2305.06500/) (2023)
- [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [On the Robustness of Interpretability Methods](https://mlsanity.com/paper/1806.08049/) (2018)
- [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)
- [RedPajama: an Open Dataset for Training Large Language Models](https://mlsanity.com/paper/2411.12372/) (2024)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [CLIP-Dissect: Automatic Description of Neuron Representations in Deep Vision Networks](https://mlsanity.com/paper/2204.10965/) (2022)
- [Learning Multi-Level Features with Matryoshka Sparse Autoencoders](https://mlsanity.com/paper/2503.17547/) (2025)
- [Natural Language Descriptions of Deep Visual Features](https://mlsanity.com/paper/2201.11114/) (2022)
- [BatchTopK Sparse Autoencoders](https://mlsanity.com/paper/2412.06410/) (2024)
- [Explainable Artificial Intelligence (XAI) 2.0: A Manifesto of Open Challenges and Interdisciplinary Research Directions](https://mlsanity.com/paper/2310.19775/) (2023)
- [Automatically Interpreting Millions of Features in Large Language Models](https://mlsanity.com/paper/2410.13928/) (2024)
- [Neural Collapse: A Review on Modelling Principles and Generalization](https://mlsanity.com/paper/2206.04041/) (2022)
- [Sparse Autoencoders Trained on the Same Data Learn Different Features](https://mlsanity.com/paper/2501.16615/) (2025)

## Abstract (arXiv)

Vision Sparse Autoencoders (SAEs) have become a popular tool in Mechanistic Interpretability due to their presumed ability to disentangle complex features learned by a model into monosemantic concepts. Despite their growing popularity, evaluating their interpretability remains an active topic of research. The bedrock motivating the adoption of SAEs is the Linear Representation Hypothesis (LRH), which claims that polysemantic features can be projected onto a (near) orthogonal basis of sparse, human-understandable representations. Yet, most current frameworks evaluate proxies such as the sparsity of SAE features or the coherence of the inferred dictionary, implicitly assuming that these reflect alignment with human perception. In this paper, we provide empirical evidence that measuring the interpretability of SAE concepts is more difficult than these proxies suggest. To this end, we adapt the Autointerpretability Score (AIS) - previously shown to align with human judgments in Natural Language Processing - to vision tasks and validate our approach in a dedicated user study. We evaluate SAE concept quality using both standard metrics and our adapted AIS. We find that established interpretability metrics for SAEs correlate neither with one another nor with AIS, indicating that no single reference-free metric, whether grounded in the LRH or not, is sufficient for verifying the interpretability of vision SAEs. We argue these findings support recent calls for more verifiable, ground-truth-anchored design and evaluation of explanation methods.