arXiv:2602.16340v3 Announce Type: replace Abstract: We study the implicit bias of momentum-based optimizers on smooth homogeneous models. We show that \textit{momentum steepest descent} algorithms like Muon (spectral norm), MomentumGD ($\ell_2$ norm), and Signum ($\ell_\infty$ norm) are \textit{approximate} steepest descent trajectories under a decaying learning rate schedule, proving that these algorithms have a bias towards KKT points of the corresponding margin maximization problem. We extend the analysis to Adam (without the stability constant), which maximizes the $\ell_\infty$ margin, an
This research provides deeper theoretical understanding of momentum-based optimizers in neural networks, a crucial area of contemporary AI development.
A more profound grasp of optimizer behavior can lead to more efficient, robust, and predictable AI models, significantly impacting the performance and deployment of advanced AI systems.
This paper offers theoretical insights into the implicit biases of widely used optimizers like Adam, potentially guiding future algorithm design and application rather than immediately altering current practices.
- · AI researchers
- · Machine learning engineers
- · Cloud AI providers
Improved understanding of existing AI optimization algorithms.
Development of next-generation optimizers that leverage these theoretical insights for better performance.
Acceleration of AI model development and deployment across various industries due to more efficient learning systems.
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