Favorability of Loss Landscape with Weight Decay Requires Both Large Overparametrization and Initialization
arXiv:2505.22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint. While weight decay is standard practice in modern training procedures, most theoretical analyses focus on unregularized settings. In this work, we investigate the loss landscape of the $\ell_2$-regularized training loss for two-layer ReLU networks. We show that the landscape becomes benign -- i.e., free of spurious local minima -- under large overparametrization, specifically when the network width $m$ satisfies $m \gtrsim \min(n^d,
This research emerges as the theoretical foundation for understanding neural network optimization, particularly with regularization techniques like weight decay, is still developing rapidly alongside practical advancements in AI.
A strategic reader should care as a deeper theoretical understanding of neural network training mechanisms, especially concerning overparametrization, can lead to more efficient, stable, and predictable AI model development and deployment.
This work clarifies conditions under which weight decay creates favorable loss landscapes, suggesting specific architectural considerations for neural networks to avoid suboptimal training outcomes.
- · AI researchers
- · Machine learning engineers
- · Deep learning framework developers
- · Trial-and-error AI development methodologies
Improved understanding of neural network training dynamics with regularization.
Development of more robust and theoretically-grounded AI architectures and training algorithms.
Potentially faster development cycles for complex AI models in various applications by reducing hyperparameter search space.
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Read at arXiv cs.LG