Regularizing Scale-Adaptive Central Moment Sharpness for Neural Networks | JoVE Visualize

Area of Science:

Deep Learning
Machine Learning Optimization

Background:

Improving generalization in deep learning is crucial and often achieved by finding flat minima of the loss function.
Existing sharpness minimization algorithms lack flexibility due to their disregard for loss values, hindering optimization and generalization.
This study addresses the limitations of current methods by exploring novel approaches to sharpness minimization.

Purpose of the Study:

To propose a novel scale-invariant sharpness measure, scale-adaptive central moment sharpness (SA-CMS), for clearer loss surface characterization.
To introduce a new regularization term integrating different orders of sharpness, encompassing existing functions like local entropy.
To develop a computationally efficient two-stage algorithm (TSLSM) for minimizing a new objective function, offering flexible optimization.

Main Methods:

Introduction of scale-adaptive central moment sharpness (SA-CMS) for scale-invariant loss surface analysis.
Derivation of a new regularization term by combining various orders of sharpness.
Development of a central moment sharpness generating function as a new objective function.
Implementation of a computationally efficient two-stage loss-sharpness minimization (TSLSM) algorithm.

Main Results:

The proposed SA-CMS measure effectively characterizes loss surfaces and is scale-invariant.
The new regularization term provides a unified framework for various sharpness minimization functions.
Theoretical analysis confirms the new objective function's smoother landscape, favoring convergence to flat local minima.
The TSLSM algorithm demonstrates superior flexibility and effectiveness across diverse learning tasks and batch sizes.

Conclusions:

The novel SA-CMS and TSLSM algorithm offer a more flexible and effective approach to sharpness minimization in deep learning.
These advancements lead to improved generalization performance, matching or exceeding state-of-the-art methods.
The proposed methods provide a robust framework for optimizing deep learning models by considering both loss value and surface sharpness.