# Neural collapse with unconstrained features

arXiv: https://arxiv.org/abs/2011.11619 · HTML: https://mlsanity.com/paper/2011.11619/

## Key facts

- Cited by 142 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2020.

## Built on by (most cited first, 30 of 142)

- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Training](https://mlsanity.com/paper/2101.12699/) (2021)
- [Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path](https://mlsanity.com/paper/2106.02073/) (2021)
- [Investigating the Catastrophic Forgetting in Multimodal Large Language Models](https://mlsanity.com/paper/2309.10313/) (2023)
- [Neural Collapse Inspired Feature-Classifier Alignment for Few-Shot Class Incremental Learning](https://mlsanity.com/paper/2302.03004/) (2023)
- [Extended Unconstrained Features Model for Exploring Deep Neural Collapse](https://mlsanity.com/paper/2202.08087/) (2022)
- [On the Role of Neural Collapse in Transfer Learning](https://mlsanity.com/paper/2112.15121/) (2021)
- [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)
- [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)
- [Imbalance Trouble: Revisiting Neural-Collapse Geometry](https://mlsanity.com/paper/2208.05512/) (2022)
- [Are All Losses Created Equal: A Neural Collapse Perspective](https://mlsanity.com/paper/2210.02192/) (2022)
- [Label-Imbalanced and Group-Sensitive Classification under Overparameterization](https://mlsanity.com/paper/2103.01550/) (2021)
- [Unintentional Unalignment: Likelihood Displacement in Direct Preference Optimization](https://mlsanity.com/paper/2410.08847/) (2024)
- [Limitations of Neural Collapse for Understanding Generalization in Deep Learning](https://mlsanity.com/paper/2202.08384/) (2022)
- [Neural Collapse with Normalized Features: A Geometric Analysis over the Riemannian Manifold](https://mlsanity.com/paper/2209.09211/) (2022)
- [Understanding Imbalanced Semantic Segmentation Through Neural Collapse](https://mlsanity.com/paper/2301.01100/) (2023)
- [Neural Collapse Inspired Attraction-Repulsion-Balanced Loss for Imbalanced Learning](https://mlsanity.com/paper/2204.08735/) (2022)
- [Deep Neural Collapse Is Provably Optimal for the Deep Unconstrained Features Model](https://mlsanity.com/paper/2305.13165/) (2023)
- [Benign Overfitting in Multiclass Classification: All Roads Lead to Interpolation](https://mlsanity.com/paper/2106.10865/) (2021)
- [NECO: NEural Collapse Based Out-of-distribution detection](https://mlsanity.com/paper/2310.06823/) (2023)
- [Generalized Neural Collapse for a Large Number of Classes](https://mlsanity.com/paper/2310.05351/) (2023)
- [Neural Collapse for Unconstrained Feature Model under Cross-entropy Loss with Imbalanced Data](https://mlsanity.com/paper/2309.09725/) (2023)
- [Linguistic Collapse: Neural Collapse in (Large) Language Models](https://mlsanity.com/paper/2405.17767/) (2024)
- [Perturbation Analysis of Neural Collapse](https://mlsanity.com/paper/2210.16658/) (2022)
- [Improving Self-Supervised Learning by Characterizing Idealized Representations](https://mlsanity.com/paper/2209.06235/) (2022)
- [Detecting Out-of-Distribution Through the Lens of Neural Collapse](https://mlsanity.com/paper/2311.01479/) (2023)
- [Towards a Unified Theoretical Understanding of Non-contrastive Learning via Rank Differential Mechanism](https://mlsanity.com/paper/2303.02387/) (2023)
- [On the Effect of Negative Gradient in Group Relative Deep Reinforcement Optimization](https://mlsanity.com/paper/2505.18830/) (2025)

## Abstract (arXiv)

Neural collapse is an emergent phenomenon in deep learning that was recently discovered by Papyan, Han and Donoho. We propose a simple "unconstrained features model" in which neural collapse also emerges empirically. By studying this model, we provide some explanation for the emergence of neural collapse in terms of the landscape of empirical risk.