# A Distributional View for Visual Mechanistic Interpretability: KL-Minimal Soft-Constraint Principle

arXiv: https://arxiv.org/abs/2605.17504 · HTML: https://mlsanity.com/paper/2605.17504/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Interpreting vision and multimodal models, one of 13 directions in Mechanistic interpretability.
- Builds on 32 of its 38 references that are in the map.
- First posted on arXiv 17 May 2026.

## Placed in

- Mechanistic interpretability / [Interpreting vision and multimodal models](https://mlsanity.com/mechinterp/interpreting-vision-and-multimodal-models/)

## Builds on (most cited first, 30 of 32)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Understanding Neural Networks Through Deep Visualization](https://mlsanity.com/paper/1506.06579/) (2015)
- [Transcoders Find Interpretable LLM Feature Circuits](https://mlsanity.com/paper/2406.11944/) (2024)
- [Fundamental Limitations of Alignment in Large Language Models](https://mlsanity.com/paper/2304.11082/) (2023)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)
- [Learning a No-Reference Quality Metric for Single-Image Super-Resolution](https://mlsanity.com/paper/1612.05890/) (2016)
- [SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretability](https://mlsanity.com/paper/2503.09532/) (2025)
- [A Holistic Approach to Unifying Automatic Concept Extraction and Concept Importance Estimation](https://mlsanity.com/paper/2306.07304/) (2023)
- [Concept-based Explainable Artificial Intelligence: A Survey](https://mlsanity.com/paper/2312.12936/) (2023)
- [Visualizing Deep Convolutional Neural Networks Using Natural Pre-Images](https://mlsanity.com/paper/1512.02017/) (2015)
- [Discover-then-Name: Task-Agnostic Concept Bottlenecks via Automated Concept Discovery](https://mlsanity.com/paper/2407.14499/) (2024)
- [Sparse autoencoders reveal selective remapping of visual concepts during adaptation](https://mlsanity.com/paper/2412.05276/) (2024)
- [Universal Sparse Autoencoders: Interpretable Cross-Model Concept Alignment](https://mlsanity.com/paper/2502.03714/) (2025)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Into the Rabbit Hull: From Task-Relevant Concepts in DINO to Minkowski Geometry](https://mlsanity.com/paper/2510.08638/) (2025)
- [Making Sense of Dependence: Efficient Black-box Explanations Using Dependence Measure](https://mlsanity.com/paper/2206.06219/) (2022)
- [Quality-Aware Image-Text Alignment for Opinion-Unaware Image Quality Assessment](https://mlsanity.com/paper/2403.11176/) (2024)
- [Advancing LLM Safe Alignment with Safety Representation Ranking](https://mlsanity.com/paper/2505.15710/) (2025)
- [Towards Understanding the Nature of Attention with Low-Rank Sparse Decomposition](https://mlsanity.com/paper/2504.20938/) (2025)
- [Diffexplainer: Towards Cross-modal Global Explanations with Diffusion Models](https://mlsanity.com/paper/2404.02618/) (2024)
- [DEXTER: Diffusion-Guided EXplanations with TExtual Reasoning for Vision Models](https://mlsanity.com/paper/2510.14741/) (2025)

## Built on by (most cited first, 1 of 1)

- [DiffuseAgent-MI: Distributionally-Grounded,Tool-Integrated Self-Evolving Agents for Faithful Visual Reasoning](https://mlsanity.com/paper/2608.00540/) (2026)

## Abstract (arXiv)

Most current paradigms in visual mechanistic interpretability (MI) remain confined to interpreting internal units of the vision model via heuristic methods (e.g., top-K activation retrieval or optimization with regularization). In this work, we establish a theoretical distributional view for visual MI, which models the influence of a feature activation on the natural image distribution, thereby formulating a Kullback-Leibler (KL)-minimal optimization problem to model the MI task. Under this framework, statistical biases are identified within previous MI paradigms, which reveal that they may either be perceptually uninterpretable to humans (i.e., deviate from the natural image distribution), or mechanistically unfaithful to the vision models (i.e., unable to activate model features). To resolve the biases under the distributional view, we propose a model with a KL-minimal soft-constraint principle for visual MI that theoretically balances interpretability and faithfulness. We realize this principle via energy-guided diffusion posterior sampling. Extensive experiments validate the theoretical soundness of the proposed distributional view and demonstrate the practical effectiveness of our paradigm on the DINOv3 vision model.