Singularity-aware Optimization via Randomized Geometric Probing: Towards Stable Non-smooth Optimization

A new optimization technique called Singularity-aware Adam (S-Adam) has been introduced to enhance stability in non-smooth optimization scenarios, particularly in deep learning, where traditional optimizers like Adam face challenges due to non-smooth loss landscapes. S-Adam utilizes a Local Geometric Instability (LGI) metric to dynamically adjust step sizes, aiming to mitigate issues such as gradient chattering and poor convergence.

This development is significant as it addresses the limitations of existing adaptive optimizers, providing a more robust solution for training deep learning models that incorporate non-smooth components like ReLU activations. By improving convergence and generalization, S-Adam could lead to more effective training processes in various applications.

The introduction of S-Adam reflects a broader trend in the optimization field, where researchers are increasingly focused on enhancing the adaptability and stability of optimization methods. This shift is underscored by ongoing discussions about the trade-offs between different optimizers, such as Adam and SGD, and the need for frameworks that can better handle the complexities of modern deep learning architectures.