This Looks Distinctly Like That: Grounding Interpretable Recognition in Stiefel Geometry against Neural Collapse

2026-03-09

AI Summary

This work addresses the issue of prototype collapse in prototypical networks for interpretable recognition, which often leads to redundant evidence and diminished explanatory power. To mitigate this, the authors introduce the Stiefel manifold into the learning framework, leveraging Riemannian optimization to constrain class prototypes to form an orthonormal basis, thereby structurally preventing rank-one collapse. By integrating proximal gradient updates with a spatial regularization term, the method effectively learns class-specific optimal effective ranks, alleviating rotational ambiguity and enhancing discriminative evidence from non-overlapping local parts. Evaluated on fine-grained classification benchmarks, the proposed approach achieves state-of-the-art accuracy while significantly outperforming existing interpretable models in terms of causal fidelity.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Interpretability, Explainability, and Transparency
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Prototype networks provide an intrinsic case based explanation mechanism, but their interpretability is often undermined by prototype collapse, where multiple prototypes degenerate to highly redundant evidence. We attribute this failure mode to the terminal dynamics of Neural Collapse, where cross entropy optimization suppresses intra class variance and drives class conditional features toward a low dimensional limit. To mitigate this, we propose Adaptive Manifold Prototypes (AMP), a framework that leverages Riemannian optimization on the Stiefel manifold to represent class prototypes as orthonormal bases and make rank one prototype collapse infeasible by construction. AMP further learns class specific effective rank via a proximal gradient update on a nonnegative capacity vector, and introduces spatial regularizers that reduce rotational ambiguity and encourage localized, non overlapping part evidence. Extensive experiments on fine-grained benchmarks demonstrate that AMP achieves state-of-the-art classification accuracy while significantly improving causal faithfulness over prior interpretable models.

Problem

• prototype collapse
• neural collapse
• interpretable recognition
• class prototypes
• intra-class variance

Innovation

• Stiefel manifold
• prototype collapse
• Riemannian optimization
• interpretable recognition
• neural collapse