# Beyond Points: Spherical Distributional Part Prototypes for Interpretable Classification

arXiv: https://arxiv.org/abs/2606.27582 · HTML: https://mlsanity.com/paper/2606.27582/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 32 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Localizing Objects with Self-Supervised Transformers and no Labels](https://mlsanity.com/paper/2109.14279/) (2021)
- [Neural Prototype Trees for Interpretable Fine-grained Image Recognition](https://mlsanity.com/paper/2012.02046/) (2020)
- [Deformable ProtoPNet: An Interpretable Image Classifier Using Deformable Prototypes](https://mlsanity.com/paper/2111.15000/) (2021)
- [Interpretable Image Classification with Differentiable Prototypes Assignment](https://mlsanity.com/paper/2112.02902/) (2021)
- [ProtoPFormer: Concentrating on Prototypical Parts in Vision Transformers for Interpretable Image Recognition](https://mlsanity.com/paper/2208.10431/) (2022)
- [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)
- [Interpretability Benchmark for Evaluating Spatial Misalignment of Prototypical Parts Explanations](https://mlsanity.com/paper/2308.08162/) (2023)
- [Parameter Efficient Fine-tuning of Self-supervised ViTs without Catastrophic Forgetting](https://mlsanity.com/paper/2404.17245/) (2024)
- [LucidPPN: Unambiguous Prototypical Parts Network for User-centric Interpretable Computer Vision](https://mlsanity.com/paper/2405.14331/) (2024)
- [Mixture of Gaussian-distributed Prototypes with Generative Modelling for Interpretable and Trustworthy Image Recognition](https://mlsanity.com/paper/2312.00092/) (2023)
- [Interpretable Image Classification via Non-parametric Part Prototype Learning](https://mlsanity.com/paper/2503.10247/) (2025)

## Abstract (arXiv)

Prototype-based neural networks aim to provide intrinsic interpretability by grounding predictions in a small set of part prototypes. However, modern vision backbones typically operate in normalized, directional embedding spaces where each semantic part exhibits substantial intra-class variability. As a result, point prototypes often become redundant or unstable, hurting both explanation quality and robustness. We propose vMFProto, a distributional part-prototype framework that models each class as a mixture of von Mises-Fisher components on the hypersphere. Each prototype learns its own concentration, capturing part-specific variability, and we use entropic optimal transport (OT) to obtain structured patch-to-prototype assignments. A two-stage training schedule performs OT-driven prototype discovery followed by end-to-end refinement with patch-level distillation and distribution-aware diversity regularization. Experiments with frozen DINO backbones show that vMFProto achieves leading consistency and distinctiveness on CUB-200-2011 and competitive classification accuracy across CUB, Stanford Dogs, and Stanford Cars. Qualitative results confirm that vMFProto yields localized, non-redundant part evidence.