# Hyperspherical Prototype Networks

arXiv: https://arxiv.org/abs/1901.10514 · HTML: https://mlsanity.com/paper/1901.10514/

## Key facts

- Cited by 86 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2019.

## Built on by (most cited first, 30 of 86)

- [Rethinking Semantic Segmentation: A Prototype View](https://mlsanity.com/paper/2203.15102/) (2022)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [nGPT: Normalized Transformer with Representation Learning on the Hypersphere](https://mlsanity.com/paper/2410.01131/) (2024)
- [Dissecting Supervised Contrastive Learning](https://mlsanity.com/paper/2102.08817/) (2021)
- [A Neuro-vector-symbolic Architecture for Solving Raven's Progressive Matrices](https://mlsanity.com/paper/2203.04571/) (2022)
- [Visual Recognition with Deep Nearest Centroids](https://mlsanity.com/paper/2209.07383/) (2022)
- [von Mises-Fisher Loss: An Exploration of Embedding Geometries for Supervised Learning](https://mlsanity.com/paper/2103.15718/) (2021)
- [Hyperbolic Busemann Learning with Ideal Prototypes](https://mlsanity.com/paper/2106.14472/) (2021)
- [Rotating Features for Object Discovery](https://mlsanity.com/paper/2306.00600/) (2023)
- [SphereFace Revived: Unifying Hyperspherical Face Recognition](https://mlsanity.com/paper/2109.05565/) (2021)
- [Maximum Class Separation as Inductive Bias in One Matrix](https://mlsanity.com/paper/2206.08704/) (2022)
- [SphereFed: Hyperspherical Federated Learning](https://mlsanity.com/paper/2207.09413/) (2022)
- [ID3: Identity-Preserving-yet-Diversified Diffusion Models for Synthetic Face Recognition](https://mlsanity.com/paper/2409.17576/) (2024)
- [VNE: An Effective Method for Improving Deep Representation by Manipulating Eigenvalue Distribution](https://mlsanity.com/paper/2304.01434/) (2023)
- [Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projections](https://mlsanity.com/paper/2211.10066/) (2022)
- [Latent SDEs on Homogeneous Spaces](https://mlsanity.com/paper/2306.16248/) (2023)
- [COARSE3D: Class-Prototypes for Contrastive Learning in Weakly-Supervised 3D Point Cloud Segmentation](https://mlsanity.com/paper/2210.01784/) (2022)
- [A step towards understanding why classification helps regression](https://mlsanity.com/paper/2308.10603/) (2023)
- [Detecting Anomalies in Semantic Segmentation with Prototypes](https://mlsanity.com/paper/2106.00472/) (2021)
- [HYPO: Hyperspherical Out-of-Distribution Generalization](https://mlsanity.com/paper/2402.07785/) (2024)
- [Distance-based Hyperspherical Classification for Multi-source Open-Set Domain Adaptation](https://mlsanity.com/paper/2107.02067/) (2021)
- [Prototype-based Dataset Comparison](https://mlsanity.com/paper/2309.02401/) (2023)
- [Raising the Bar in Graph OOD Generalization: Invariant Learning Beyond Explicit Environment Modeling](https://mlsanity.com/paper/2502.10706/) (2025)
- [HyperFed: Hyperbolic Prototypes Exploration with Consistent Aggregation for Non-IID Data in Federated Learning](https://mlsanity.com/paper/2307.14384/) (2023)
- [FedFN: Feature Normalization for Alleviating Data Heterogeneity Problem in Federated Learning](https://mlsanity.com/paper/2311.13267/) (2023)
- [Equiangular Basis Vectors](https://mlsanity.com/paper/2303.11637/) (2023)
- [Temporal Test-Time Adaptation with State-Space Models](https://mlsanity.com/paper/2407.12492/) (2024)
- [Low-distortion and GPU-compatible Tree Embeddings in Hyperbolic Space](https://mlsanity.com/paper/2502.17130/) (2025)
- [Learning Towards the Largest Margins](https://mlsanity.com/paper/2206.11589/) (2022)

## Abstract (arXiv)

This paper introduces hyperspherical prototype networks, which unify classification and regression with prototypes on hyperspherical output spaces. For classification, a common approach is to define prototypes as the mean output vector over training examples per class. Here, we propose to use hyperspheres as output spaces, with class prototypes defined a priori with large margin separation. We position prototypes through data-independent optimization, with an extension to incorporate priors from class semantics. By doing so, we do not require any prototype updating, we can handle any training size, and the output dimensionality is no longer constrained to the number of classes. Furthermore, we generalize to regression, by optimizing outputs as an interpolation between two prototypes on the hypersphere. Since both tasks are now defined by the same loss function, they can be jointly trained for multi-task problems. Experimentally, we show the benefit of hyperspherical prototype networks for classification, regression, and their combination over other prototype methods, softmax cross-entropy, and mean squared error approaches.