A Coding-Theoretic Analysis of Hyperspherical Prototypical Learning Geometry

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.

@article{lindström2025_2407.07664,
  title={ A Coding-Theoretic Analysis of Hyperspherical Prototypical Learning Geometry },
  author={ Martin Lindström and Borja Rodríguez-Gálvez and Ragnar Thobaben and Mikael Skoglund },
  journal={arXiv preprint arXiv:2407.07664},
  year={ 2025 }
}