# Space Alignment Matters: The Missing Piece for Inducing Neural Collapse in Long-Tailed Learning

arXiv: https://arxiv.org/abs/2512.07844 · HTML: https://mlsanity.com/paper/2512.07844/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 25 Nov 2025.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [BBN: Bilateral-Branch Network with Cumulative Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/1912.02413/) (2019)
- [Long-tailed Recognition by Routing Diverse Distribution-Aware Experts](https://mlsanity.com/paper/2010.01809/) (2020)
- [Cost Sensitive Learning of Deep Feature Representations from Imbalanced Data](https://mlsanity.com/paper/1508.03422/) (2015)
- [Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Training](https://mlsanity.com/paper/2101.12699/) (2021)
- [Balanced Contrastive Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2207.09052/) (2022)
- [Feature Space Augmentation for Long-Tailed Data](https://mlsanity.com/paper/2008.03673/) (2020)
- [Contrastive Learning based Hybrid Networks for Long-Tailed Image Classification](https://mlsanity.com/paper/2103.14267/) (2021)
- [Relay Backpropagation for Effective Learning of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1512.05830/) (2015)
- [Long-Tailed Recognition via Weight Balancing](https://mlsanity.com/paper/2203.14197/) (2022)
- [Neural Collapse Inspired Attraction-Repulsion-Balanced Loss for Imbalanced Learning](https://mlsanity.com/paper/2204.08735/) (2022)
- [Global and Local Mixture Consistency Cumulative Learning for Long-tailed Visual Recognitions](https://mlsanity.com/paper/2305.08661/) (2023)
- [Inducing Neural Collapse in Deep Long-tailed Learning](https://mlsanity.com/paper/2302.12453/) (2023)
- [Neural Collapse for Cross-entropy Class-Imbalanced Learning with Unconstrained ReLU Feature Model](https://mlsanity.com/paper/2401.02058/) (2024)

## Built on by (most cited first, 2 of 2)

- [Rethinking Loss Reweighting for Imbalance Learning as an Inverse Problem: A Neural Collapse Point of View](https://mlsanity.com/paper/2605.10047/) (2026)
- [CAENL: Collapse-Based Active Neural Learning with Objective-Aligned Representation Control](https://mlsanity.com/paper/2610.17509/) (2026)

## Abstract (arXiv)

Recent studies on Neural Collapse (NC) reveal that, under class-balanced conditions, the class feature means and classifier weights spontaneously align into a simplex equiangular tight frame (ETF). In long-tailed regimes, however, severe sample imbalance tends to prevent the emergence of the NC phenomenon, resulting in poor generalization performance. Current efforts predominantly seek to recover the ETF geometry by imposing constraints on features or classifier weights, yet overlook a critical problem: There is a pronounced misalignment between the feature and the classifier weight spaces. In this paper, we theoretically quantify the harm of such misalignment through an optimal error exponent analysis. Built on this insight, we propose three explicit alignment strategies that plug-and-play into existing long-tail methods without architectural change. Extensive experiments on the CIFAR-10-LT, CIFAR-100-LT, and ImageNet-LT datasets consistently boost examined baselines and achieve the state-of-the-art performances.