# Hyperspherical Classification with Dynamic Label-to-Prototype Assignment

arXiv: https://arxiv.org/abs/2403.16937 · HTML: https://mlsanity.com/paper/2403.16937/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 56 references that are in the map.
- First posted on arXiv 25 Mar 2024.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [Distributed Representations of Sentences and Documents](https://mlsanity.com/paper/1405.4053/) (2014)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Exploring Cross-Image Pixel Contrast for Semantic Segmentation](https://mlsanity.com/paper/2101.11939/) (2021)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [No Fuss Distance Metric Learning using Proxies](https://mlsanity.com/paper/1703.07464/) (2017)
- [Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Training](https://mlsanity.com/paper/2101.12699/) (2021)
- [Partial FC: Training 10 Million Identities on a Single Machine](https://mlsanity.com/paper/2010.05222/) (2020)
- [Neural Collapse Inspired Feature-Classifier Alignment for Few-Shot Class Incremental Learning](https://mlsanity.com/paper/2302.03004/) (2023)
- [End-to-end Lane Shape Prediction with Transformers](https://mlsanity.com/paper/2011.04233/) (2020)
- [Inducing Neural Collapse in Imbalanced Learning: Do We Really Need a Learnable Classifier at the End of Deep Neural Network?](https://mlsanity.com/paper/2203.09081/) (2022)
- [Unsupervised Learning by Predicting Noise](https://mlsanity.com/paper/1704.05310/) (2017)
- [Striking the Right Balance with Uncertainty](https://mlsanity.com/paper/1901.07590/) (2019)
- [Learning towards Minimum Hyperspherical Energy](https://mlsanity.com/paper/1805.09298/) (2018)
- [Killing Two Birds with One Stone:Efficient and Robust Training of Face Recognition CNNs by Partial FC](https://mlsanity.com/paper/2203.15565/) (2022)
- [Visual Recognition with Deep Nearest Centroids](https://mlsanity.com/paper/2209.07383/) (2022)
- [Neural Collapse with Cross-Entropy Loss](https://mlsanity.com/paper/2012.08465/) (2020)
- [Decoupled Networks](https://mlsanity.com/paper/1804.08071/) (2018)
- [Fix your classifier: the marginal value of training the last weight layer](https://mlsanity.com/paper/1801.04540/) (2018)
- [Hyperbolic Busemann Learning with Ideal Prototypes](https://mlsanity.com/paper/2106.14472/) (2021)

## Built on by (most cited first, 3 of 3)

- [All-around Neural Collapse for Imbalanced Classification](https://mlsanity.com/paper/2408.07253/) (2024)
- [Hyperspherical Forward-Forward with Prototypical Representations](https://mlsanity.com/paper/2605.00082/) (2026)
- [Computation and Communication Efficient Federated Unlearning via On-server Gradient Conflict Mitigation and Expression](https://mlsanity.com/paper/2603.13795/) (2026)

## Abstract (arXiv)

Aiming to enhance the utilization of metric space by the parametric softmax classifier, recent studies suggest replacing it with a non-parametric alternative. Although a non-parametric classifier may provide better metric space utilization, it introduces the challenge of capturing inter-class relationships. A shared characteristic among prior non-parametric classifiers is the static assignment of labels to prototypes during the training, ie, each prototype consistently represents a class throughout the training course. Orthogonal to previous works, we present a simple yet effective method to optimize the category assigned to each prototype (label-to-prototype assignment) during the training. To this aim, we formalize the problem as a two-step optimization objective over network parameters and label-to-prototype assignment mapping. We solve this optimization using a sequential combination of gradient descent and Bipartide matching. We demonstrate the benefits of the proposed approach by conducting experiments on balanced and long-tail classification problems using different backbone network architectures. In particular, our method outperforms its competitors by 1.22% accuracy on CIFAR-100, and 2.15% on ImageNet-200 using a metric space dimension half of the size of its competitors. Code: https://github.com/msed-Ebrahimi/DL2PACVPR24