# A Coding-Theoretic Analysis of Hyperspherical Prototypical Learning Geometry

arXiv: https://arxiv.org/abs/2407.07664 · HTML: https://mlsanity.com/paper/2407.07664/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 10 Jul 2024.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Hyperspherical Prototype Networks](https://mlsanity.com/paper/1901.10514/) (2019)
- [Spherical Latent Spaces for Stable Variational Autoencoders](https://mlsanity.com/paper/1808.10805/) (2018)
- [von Mises-Fisher Mixture Model-based Deep learning: Application to Face Verification](https://mlsanity.com/paper/1706.04264/) (2017)
- [Maximum Class Separation as Inductive Bias in One Matrix](https://mlsanity.com/paper/2206.08704/) (2022)
- [The Role of Entropy and Reconstruction in Multi-View Self-Supervised Learning](https://mlsanity.com/paper/2307.10907/) (2023)

## Built on by (most cited first, 1 of 1)

- [What Do Scan-Derived Class Prototypes Add? Disentangling Supervision, Prototype Content and Query Protocol in Recognition over Frozen Foundation Features](https://mlsanity.com/paper/2609.04381/) (2026)

## Abstract (arXiv)

Hyperspherical Prototypical Learning (HPL) is a supervised approach to representation learning that designs class prototypes on the unit hypersphere. The prototypes bias the representations to class separation in a scale invariant and known geometry. Previous approaches to HPL have either of the following shortcomings: (i) they follow an unprincipled optimisation procedure; or (ii) they are theoretically sound, but are constrained to only one possible latent dimension. In this paper, we address both shortcomings. To address (i), we present a principled optimisation procedure whose solution we show is optimal. To address (ii), we construct well-separated prototypes in a wide range of dimensions using linear block codes. Additionally, we give a full characterisation of the optimal prototype placement in terms of achievable and converse bounds, showing that our proposed methods are near-optimal.