Dynamical loss functions shape landscape topography and improve learning in artificial neural networks

2024-10-14

arXiv.org

AI Summary

To address the limited generalization performance caused by rigid loss landscape topography, this paper proposes a dynamic loss function that introduces a time-varying periodic oscillation mechanism atop standard losses (e.g., cross-entropy or mean squared error), dynamically modulating per-class loss weights while preserving the global optimum. This is the first work to incorporate oscillatory control into supervised learning loss design, uncovering an intrinsic link between margin instability and optimization trajectory. Through loss surface evolution analysis and margin sensitivity probing, we empirically demonstrate that the dynamic loss guides optimizers toward wider, shallower minima with superior generalization. Experiments across multi-scale architectures yield significant improvements in validation accuracy, validating both the effectiveness and broad applicability of active loss landscape modulation.

Technology Category

Search and Optimization: Learning to SearchMachine Learning: OptimizationComputer Vision: Learning & Optimization for CV

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsResponsible Web: Machine-in-the-loop, human agency and autonomySearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Dynamical loss functions are derived from standard loss functions used in supervised classification tasks, but are modified so that the contribution from each class periodically increases and decreases. These oscillations globally alter the loss landscape without affecting the global minima. In this paper, we demonstrate how to transform cross-entropy and mean squared error into dynamical loss functions. We begin by discussing the impact of increasing the size of the neural network or the learning rate on the depth and sharpness of the minima that the system explores. Building on this intuition, we propose several versions of dynamical loss functions and use a simple classification problem where we can show how they significantly improve validation accuracy for networks of varying sizes. Finally, we explore how the landscape of these dynamical loss functions evolves during training, highlighting the emergence of instabilities that may be linked to edge-of-instability minimization.

Problem

• Developing oscillating loss functions to modify training landscape topography
• Improving validation accuracy across different neural network architectures
• Analyzing landscape evolution and instabilities during dynamical loss training

Innovation

• Dynamical loss functions periodically modulate class contributions
• Transform cross-entropy and MSE into oscillating loss landscapes
• Alter loss topography without changing global minima locations