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arXiv · 2603.22824

Towards The Implicit Bias on Multiclass Separable Data Under Norm Constraints

Shengping Xie·Zekun Wu·Quan Chen·Kaixu Tang
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Abstract

Implicit bias induced by gradient-based algorithms is essential to the generalization of overparameterized models, yet its mechanisms can be subtle. This work leverages the Normalized Steepest Descent} (NSD) framework to investigate how optimization geometry shapes solutions on multiclass separable data. We introduce NucGD, a geometry-aware optimizer designed to enforce low rank structures through nuclear norm constraints. Beyond the algorithm itself, we connect NucGD with emerging low-rank projection methods, providing a unified perspective. To enable scalable training, we derive an efficient SVD-free update rule via asynchronous power iteration. Furthermore, we empirically dissect the impact of stochastic optimization dynamics, characterizing how varying levels of gradient noise induced by mini-batch sampling and momentum modulate the convergence toward the expected maximum margin solutions.Our code is accessible at: https://github.com/Tsokarsic/observing-the-implicit-bias-on-multiclass-seperable-data.

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Shengping Xie, Zekun Wu, Quan Chen, Kaixu Tang. 2026-03-24. Towards The Implicit Bias on Multiclass Separable Data Under Norm Constraints. https://arxiv.org/abs/2603.22824

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