# Space Alignment Matters: The Missing Piece for Inducing Neural Collapse in Long-Tailed Learning Source: [Space Alignment Matters: The Missing Piece for Inducing Neural Collapse in Long-Tailed Learning]() Collection index: [llms.txt]() Data updated: 2025-12-11T05:03:10.792Z Authors: Jinping Wang, Zhiqiang Gao, Zhiwu Xie Published: 2025-11-25T07:38:40.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()