# Geometric Analysis of Unconstrained Feature Models with d=K

arXiv: https://arxiv.org/abs/2407.10702 · HTML: https://mlsanity.com/paper/2407.10702/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 13 references that are in the map.
- First posted on arXiv 15 Jul 2024.

## Builds on (most cited first, 7 of 7)

- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path](https://mlsanity.com/paper/2106.02073/) (2021)
- [Neural collapse with unconstrained features](https://mlsanity.com/paper/2011.11619/) (2020)
- [On the Optimization Landscape of Neural Collapse under MSE Loss: Global Optimality with Unconstrained Features](https://mlsanity.com/paper/2203.01238/) (2022)
- [Neural Collapse: A Review on Modelling Principles and Generalization](https://mlsanity.com/paper/2206.04041/) (2022)
- [An Unconstrained Layer-Peeled Perspective on Neural Collapse](https://mlsanity.com/paper/2110.02796/) (2021)

## Abstract (arXiv)

Recently, interesting empirical phenomena known as Neural Collapse have been observed during the final phase of training deep neural networks for classification tasks. We examine this issue when the feature dimension d is equal to the number of classes K. We demonstrate that two popular unconstrained feature models are strict saddle functions, with every critical point being either a global minimum or a strict saddle point that can be exited using negative curvatures. The primary findings conclusively confirm the conjecture on the unconstrained feature models in previous articles.