arXiv:2602.11557v2 Announce Type: replace Abstract: A variety of widely used optimization methods like SignSGD and Muon can be interpreted as instances of steepest descent under different norm-induced geometries. In this work, we study the implicit bias of mini-batch stochastic steepest descent in multi-class classification, characterizing how batch size, momentum, and variance reduction shape the limiting max-margin behavior and convergence rates under general entry-wise and Schatten-$p$ norms. We show that, without momentum, worst-case convergence and successful classification can only be gu
This paper represents continued academic progress in understanding the fundamental mechanisms and theoretical underpinnings of widely used machine learning optimization methods, building on a rich body of existing research.
For a strategic reader, this research deepens the understanding of how optimization techniques work in AI, which can inform the development of more efficient and robust AI models and hardware.
The characterization of implicit bias under different norms and the impact of batch size, momentum, and variance reduction provides more granular insights into AI model training dynamics.
- · AI researchers
- · AI developers
- · Machine learning startups
- · Cloud AI providers
- · AI models without optimized training
- · Inefficient compute resource allocation
Improved theoretical understanding of AI optimization algorithms.
Development of more efficient and accurate AI models, potentially reducing training costs and time.
Accelerated progress in specific AI applications by optimizing underlying learning processes, though this remains indirect.
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