Structuring Sparsity: Block-Sparse Featurizers Capture Visual Concept Manifolds

2026-06-23

AI Summary

Traditional approaches model visual concepts as isolated directions, failing to capture their intrinsic low-dimensional geometric structure within neural activation spaces. This work proposes incorporating a block-sparse prior to represent visual concepts as sparse combinations of 2–4-dimensional continuous manifolds and introduces a Block-Sparse Feature extractor (BSF) to model co-activated neuron groups, better aligning with the neural mechanisms underlying visual perception. Leveraging the minimum description length principle, manifold discovery, and manipulation techniques—and integrating DINOv3 and SDXL models—we validate that curve detectors in InceptionV1 read from a single curve manifold, uncover novel shadow and illumination manifolds in DINOv3, and achieve, for the first time, manifold-based controllable image generation in interpretable diffusion models.

Abstract

What is the geometry of a visual percept? The most widely used protocols for decomposing neural network representations into interpretable parts treat concepts as isolated directions, yet recent work shows that concepts are often realized as geometric structures in low dimensional regions of activation space. We turn to the literature of Structured sparsity to close this gap, and show that block sparsity, which groups directions into blocks, is the prior matched to a generative model in which a representation is a sparse sum of low-dimensional manifolds: the modern, learned form of a classical idea in visual neuroscience, where a visual feature is carried by a coordinated group of neurons rather than a single tuned one. We implement three variants of block-sparse featurizers (BSFs) and, through a minimum-description-length analysis, show that all three describe activations more compactly than direction-based featurizers, with the recovered concepts typically two- to four-dimensional. We then use BSFs to (i) recontextualize prior work, showing that curve detectors in InceptionV1 actually read from a single continuous curve manifold, (ii) discover novel manifolds including shadows and lighting in DINOv3, and (iii) support interpretable control of image generation in diffusion models (SDXL) via manifold steering.

Problem

• structured sparsity
• block sparsity
• visual concept manifolds
• neural representation
• activation space

Innovation

• block sparsity
• visual concept manifolds
• structured sparsity
• interpretable representations
• manifold steering