# The Independence Prior of SAEs Fragments Visual Concepts

arXiv: https://arxiv.org/abs/2610.04112 · HTML: https://mlsanity.com/paper/2610.04112/

## 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 26 of its 46 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Semantic Understanding of Scenes through the ADE20K Dataset](https://mlsanity.com/paper/1608.05442/) (2016)
- [Vision Transformers Need Registers](https://mlsanity.com/paper/2309.16588/) (2023)
- [COCO-Stuff: Thing and Stuff Classes in Context](https://mlsanity.com/paper/1612.03716/) (2016)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoders](https://mlsanity.com/paper/2409.14507/) (2024)
- [Vision Transformers provably learn spatial structure](https://mlsanity.com/paper/2210.09221/) (2022)
- [On the Origins of Linear Representations in Large Language Models](https://mlsanity.com/paper/2403.03867/) (2024)
- [Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Models](https://mlsanity.com/paper/2502.12892/) (2025)
- [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)
- [Into the Rabbit Hull: From Task-Relevant Concepts in DINO to Minkowski Geometry](https://mlsanity.com/paper/2510.08638/) (2025)
- [Do Sparse Autoencoders Capture Concept Manifolds?](https://mlsanity.com/paper/2604.28119/) (2026)
- [Amortized Variational Inference: When and Why?](https://mlsanity.com/paper/2307.11018/) (2023)
- [Submodular Functions: from Discrete to Continous Domains](https://mlsanity.com/paper/1511.00394/) (2015)
- [Interpretable and Testable Vision Features via Sparse Autoencoders](https://mlsanity.com/paper/2502.06755/) (2025)
- [Priors in Time: Missing Inductive Biases for Language Model Interpretability](https://mlsanity.com/paper/2511.01836/) (2025)
- [Interpretability as Compression: Reconsidering SAE Explanations of Neural Activations with MDL-SAEs](https://mlsanity.com/paper/2410.11179/) (2024)
- [Qwen-Scope: Turning Sparse Features into Development Tools for Large Language Models](https://mlsanity.com/paper/2605.11887/) (2026)
- [Compute Optimal Inference and Provable Amortisation Gap in Sparse Autoencoders](https://mlsanity.com/paper/2411.13117/) (2024)
- [Feature Hedging: Correlated Features Break Narrow Sparse Autoencoders](https://mlsanity.com/paper/2505.11756/) (2025)
- [SynthSAEBench: Evaluating Sparse Autoencoders on Scalable Realistic Synthetic Data](https://mlsanity.com/paper/2602.14687/) (2026)
- [The Rate-Distortion-Polysemanticity Tradeoff in SAEs](https://mlsanity.com/paper/2605.14694/) (2026)

## Abstract (arXiv)

Sparse Autoencoders (SAEs) decompose model activations into sparse combinations of interpretable dictionary atoms. Although SAEs are grounded in the Linear Representation Hypothesis (LRH), their objective smuggles in an additional prior: concepts across patches are treated as independent, an assumption clearly violated by natural images and by the activations they induce. We therefore specialize LRH to vision through the Markov-Field Linear Representation Hypothesis (MFLRH), which adds the missing spatial dependencies to the LRH assumptions. We thus propose Spatial-SAE as an amortized MAP estimator under the MFLRH. Spatial-SAE consistently outperforms standard SAEs in concept recovery and interpretability. Across four variants, it achieves a 96% average win rate on synthetic concept recovery and improves interpretability on DINOv2 activations, at a reconstruction cost concentrated in high spatial frequencies.