# Neural collapse in the orthoplex regime

arXiv: https://arxiv.org/abs/2603.20587 · HTML: https://mlsanity.com/paper/2603.20587/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 11 references that are in the map.
- First posted on arXiv 21 Mar 2026.

## Builds on (most cited first, 3 of 3)

- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Neural collapse with unconstrained features](https://mlsanity.com/paper/2011.11619/) (2020)
- [Generalized Neural Collapse for a Large Number of Classes](https://mlsanity.com/paper/2310.05351/) (2023)

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

- [CAENL: Collapse-Based Active Neural Learning with Objective-Aligned Representation Control](https://mlsanity.com/paper/2610.17509/) (2026)

## Abstract (arXiv)

When training a neural network for classification, the feature vectors of the training set are known to collapse to the vertices of a regular simplex, provided the dimension d of the feature space and the number n of classes satisfies n≤ d+1. This phenomenon is known as neural collapse. For other applications like language models, one instead takes ngg d. Here, the neural collapse phenomenon still occurs, but with different emergent geometric figures. We characterize these geometric figures in the orthoplex regime where d+2≤ n≤ 2d. The techniques in our analysis primarily involve Radon's theorem and convexity.