Understanding Geometric Representations in Self-Supervised Vision Transformers via Subspace Intervention

2026-07-02

AI Summary

Existing linear probes struggle to uncover the internal encoding structure of geometric information in self-supervised vision Transformers (ViTs). This work proposes a controlled subspace intervention framework that leverages singular value decomposition (SVD) on converged linear probe weights to isolate a low-rank subspace carrying explicit geometric signals. For the first time, subspace analysis reveals distinct differences in geometric representation between DINOv2 and MAE, demonstrating that geometric information is highly compressible, peaks in accuracy at intermediate network layers, and exhibits pronounced low-rank characteristics. These findings provide both theoretical grounding and practical design guidance for lightweight decoders and efficient feature selection strategies in self-supervised vision models.

Abstract

We introduce a controlled subspace intervention framework to investigate how self-supervised Vision Transformers (ViTs) encode dense geometric information. While linear probing is widely used to assess geometric representations, it treats features as a black box, failing to disentangle the underlying topology. To address this issue, we decompose the weights of converged linear probes to isolate the low-rank subspaces containing explicit geometric signals using Singular Value Decomposition (SVD). Our perspective yields three key insights: (1) Pre-training objectives determine how features are encoded. DINOv2 aligns spatial features for efficient linear extraction, while Masked Autoencoders (MAE) tend to disperse these signals, requiring a broader spatial context. (2) Explicit geometric representations are highly compressible, suggesting dense predictive heads could potentially be constrained to low-rank subspaces with minimal performance loss. (3) The layer-wise task affinity suggests that geometric precision peaks at intermediate layers before yielding to semantic abstraction in the final layers. By connecting internal encoding mechanics with downstream performance, these findings provide a basis for effective feature selection and lightweight decoder design. The source code is available at https://github.com/Zhou-Weichen/Geosubprobe.

Problem

• geometric representations
• self-supervised Vision Transformers
• linear probing
• subspace analysis
• feature disentanglement

Innovation

• subspace intervention
• self-supervised Vision Transformers
• geometric representation
• low-rank subspace
• Singular Value Decomposition