# Geodesic Prototype Matching via Diffusion Maps for Interpretable Fine-Grained Recognition

arXiv: https://arxiv.org/abs/2509.17050 · HTML: https://mlsanity.com/paper/2509.17050/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 21 Sep 2025.

## Builds on (most cited first, 10 of 10)

- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Interpretable Image Classification with Differentiable Prototypes Assignment](https://mlsanity.com/paper/2112.02902/) (2021)
- [This Looks Like That... Does it? Shortcomings of Latent Space Prototype Interpretability in Deep Networks](https://mlsanity.com/paper/2105.02968/) (2021)
- [Learning Support and Trivial Prototypes for Interpretable Image Classification](https://mlsanity.com/paper/2301.04011/) (2023)
- [Evaluation and Improvement of Interpretability for Self-Explainable Part-Prototype Networks](https://mlsanity.com/paper/2212.05946/) (2022)
- [This Looks Like Those: Illuminating Prototypical Concepts Using Multiple Visualizations](https://mlsanity.com/paper/2310.18589/) (2023)
- [Mixture of Gaussian-distributed Prototypes with Generative Modelling for Interpretable and Trustworthy Image Recognition](https://mlsanity.com/paper/2312.00092/) (2023)
- [ProtoArgNet: Interpretable Image Classification with Super-Prototypes and Argumentation [Technical Report]](https://mlsanity.com/paper/2311.15438/) (2023)
- [A Robust Prototype-Based Network with Interpretable RBF Classifier Foundations](https://mlsanity.com/paper/2412.15499/) (2024)
- [Brain-HGCN: A Hyperbolic Graph Convolutional Network for Brain Functional Network Analysis](https://mlsanity.com/paper/2509.14965/) (2025)

## Built on by (most cited first, 6 of 6)

- [MedSynapse-V: Bridging Visual Perception and Clinical Intuition via Latent Memory Evolution](https://mlsanity.com/paper/2604.26283/) (2026)
- [Unsupervised Causal Prototypical Networks for De-biased Interpretable Dermoscopy Diagnosis](https://mlsanity.com/paper/2602.23752/) (2026)
- [This Looks Distinctly Like That: Grounding Interpretable Recognition in Stiefel Geometry against Neural Collapse](https://mlsanity.com/paper/2603.08374/) (2026)
- [Multimodal Feature Prototype Learning for Interpretable and Discriminative Cancer Survival Prediction](https://mlsanity.com/paper/2510.06113/) (2025)
- [Effective Attention-Guided Multi-Scale Medical Network for Skin Lesion Segmentation](https://mlsanity.com/paper/2512.07275/) (2025)
- [Directed Ordinal Diffusion Regularization for Progression-Aware Diabetic Retinopathy Grading](https://mlsanity.com/paper/2602.21942/) (2026)

## Abstract (arXiv)

Nonlinear manifolds are pervasive in deep visual features, where Euclidean distances can misrepresent true similarity. This mismatch is particularly detrimental to prototype-based interpretable fine-grained recognition, where even subtle semantic distinctions are crucial. To mitigate this issue, this work presents a novel paradigm for prototype-based recognition by grounding similarity in the intrinsic geometry of deep features. Concretely, we distill the latent manifold structure of each class into a diffusion space and, critically, devise a differentiable Nystr"om interpolation to make this geometry accessible to both unseen samples and learnable prototypes. To maintain efficiency, we employ compact per-class landmark sets with periodic updates. This strategy keeps the embedding synchronized with the evolving backbone, enabling fast inference at scale. Comprehensive experiments on two benchmark datasets demonstrate that our GeoProto yields prototypes focusing on semantically corresponding parts, significantly outperforming Euclidean prototype networks.