# Into the Rabbit Hull: From Task-Relevant Concepts in DINO to Minkowski Geometry

arXiv: https://arxiv.org/abs/2510.08638 · HTML: https://mlsanity.com/paper/2510.08638/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2025.

## Built on by (most cited first, 30 of 34)

- [Do Sparse Autoencoders Capture Concept Manifolds?](https://mlsanity.com/paper/2604.28119/) (2026)
- [Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior](https://mlsanity.com/paper/2605.05115/) (2026)
- [The Shape of Beliefs: Geometry, Dynamics, and Interventions along Representation Manifolds of Language Models' Posteriors](https://mlsanity.com/paper/2602.02315/) (2026)
- [SynthSAEBench: Evaluating Sparse Autoencoders on Scalable Realistic Synthetic Data](https://mlsanity.com/paper/2602.14687/) (2026)
- [Arithmetic in the Wild: Llama uses Base-10 Addition to Reason About Cyclic Concepts](https://mlsanity.com/paper/2605.01148/) (2026)
- [Structuring Sparsity: Block-Sparse Featurizers Capture Visual Concept Manifolds](https://mlsanity.com/paper/2606.25234/) (2026)
- [Circuit Mechanisms for Spatial Relation Generation in Diffusion Transformers](https://mlsanity.com/paper/2601.06338/) (2026)
- [Language Models Can Explain Visual Features via Steering](https://mlsanity.com/paper/2603.22593/) (2026)
- [Anatomy of Post-Training: Using Interpretability to Characterize Data and Shape the Learning Signal](https://mlsanity.com/paper/2606.12360/) (2026)
- [What Does a Chemical Language Model Know About Molecules?](https://mlsanity.com/paper/2606.23443/) (2026)
- [Evaluating the Interpretability of Sparse Autoencoders with Concept Annotations](https://mlsanity.com/paper/2606.24716/) (2026)
- [Understanding Geometric Representations in Self-Supervised Vision Transformers via Subspace Intervention](https://mlsanity.com/paper/2607.01987/) (2026)
- [What DINO saw: ALiBi positional encoding reduces positional bias in Vision Transformers](https://mlsanity.com/paper/2603.16840/) (2026)
- [Bilinear autoencoders find interpretable manifolds](https://mlsanity.com/paper/2605.08891/) (2026)
- [A Distributional View for Visual Mechanistic Interpretability: KL-Minimal Soft-Constraint Principle](https://mlsanity.com/paper/2605.17504/) (2026)
- [Representation Alignment Rests on Linear Structure](https://mlsanity.com/paper/2605.28870/) (2026)
- [A Unifying Framework for Concept-Based Representational Similarity](https://mlsanity.com/paper/2606.09653/) (2026)
- [DiMaS: Distribution Matching for Steering Vision-Language-Action Models](https://mlsanity.com/paper/2607.14280/) (2026)
- [From Measurement to Mitigation: Quantifying and Reducing Identity Leakage in Image Representation Encoders with Linear Subspace Removal](https://mlsanity.com/paper/2604.05296/) (2026)
- [Zero-Ablation Overstates Register Content Dependence in DINO Vision Transformers](https://mlsanity.com/paper/2604.14433/) (2026)
- [How Far Does a Shared Linear Map Go? Probing Feature-Space Manipulability for Image Editing](https://mlsanity.com/paper/2605.11203/) (2026)
- [Interpretability-Guided Layer Selection over Subspace Projection: SAEs as Stethoscopes, Not Scalpels, for Raw Task Vector Model Editing](https://mlsanity.com/paper/2605.28649/) (2026)
- [Driving the Wrong Way: Leveraging Interpretability in End2End Autonomous Driving Models](https://mlsanity.com/paper/2607.06328/) (2026)
- [Explaining Image Similarity with Automatically Extracted Concept Activation Vectors](https://mlsanity.com/paper/2607.28386/) (2026)
- [Concept-based explanation of gene expression prediction from H&E images](https://mlsanity.com/paper/2608.16669/) (2026)
- [What, Where, and How: Probing Spatiotemporal Representations in Video Foundation Models](https://mlsanity.com/paper/2609.01551/) (2026)
- [From Interpretability Methods to Interpretable Models](https://mlsanity.com/paper/2609.05399/) (2026)
- [MAxBench: A Multinomial Concept Recovery Benchmark](https://mlsanity.com/paper/2609.13072/) (2026)
- [Intuition vectors](https://mlsanity.com/paper/2609.32619/) (2026)
- [Interference Beyond Geometry in Concept Extraction](https://mlsanity.com/paper/2609.35351/) (2026)

## Abstract (arXiv)

DINOv2 is routinely deployed to recognize objects, scenes, and actions; yet the nature of what it perceives remains unknown. As a working baseline, we adopt the Linear Representation Hypothesis (LRH) and operationalize it using SAEs, producing a 32,000-unit dictionary that serves as the interpretability backbone of our study, which unfolds in three parts. In the first part, we analyze how different downstream tasks recruit concepts from our learned dictionary, revealing functional specialization: classification exploits "Elsewhere" concepts that fire everywhere except on target objects, implementing learned negations; segmentation relies on boundary detectors forming coherent subspaces; depth estimation draws on three distinct monocular depth cues matching visual neuroscience principles. Following these functional results, we analyze the geometry and statistics of the concepts learned by the SAE. We found that representations are partly dense rather than strictly sparse. The dictionary evolves toward greater coherence and departs from maximally orthogonal ideals (Grassmannian frames). Within an image, tokens occupy a low dimensional, locally connected set persisting after removing position. These signs suggest representations are organized beyond linear sparsity alone. Synthesizing these observations, we propose a refined view: tokens are formed by combining convex mixtures of archetypes (e.g., a rabbit among animals, brown among colors, fluffy among textures). This structure is grounded in Gardenfors' conceptual spaces and in the model's mechanism as multi-head attention produces sums of convex mixtures, defining regions bounded by archetypes. We introduce the Minkowski Representation Hypothesis (MRH) and examine its empirical signatures and implications for interpreting vision-transformer representations.