LyAm: Robust Non-Convex Optimization for Stable Learning in Noisy Environments

• URL: http://arxiv.org/abs/2507.11262v1
• Date: Tue, 15 Jul 2025 12:35:13 GMT
• Title: LyAm: Robust Non-Convex Optimization for Stable Learning in Noisy Environments
• Authors: Elmira Mirzabeigi, Sepehr Rezaee, Kourosh Parand,
• Abstract summary: Training deep neural networks, particularly in computer vision tasks, often suffers from noisy gradients.<n>We propose LyAm, a novel that integrates Adam's adaptive moment estimation with Lyapunov-based stability mechanisms.<n>LyAm consistently outperforms state-of-the-art settings in terms of accuracy, convergence, speed, and stability.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Training deep neural networks, particularly in computer vision tasks, often suffers from noisy gradients and unstable convergence, which hinder performance and generalization. In this paper, we propose LyAm, a novel optimizer that integrates Adam's adaptive moment estimation with Lyapunov-based stability mechanisms. LyAm dynamically adjusts the learning rate using Lyapunov stability theory to enhance convergence robustness and mitigate training noise. We provide a rigorous theoretical framework proving the convergence guarantees of LyAm in complex, non-convex settings. Extensive experiments on like as CIFAR-10 and CIFAR-100 show that LyAm consistently outperforms state-of-the-art optimizers in terms of accuracy, convergence speed, and stability, establishing it as a strong candidate for robust deep learning optimization.

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