Transient learning dynamics drive escape from sharp valleys in Stochastic Gradient Descent

2026-01-16

AI Summary

This work addresses the unresolved dynamical mechanism underlying stochastic gradient descent’s (SGD) preference for flat minima that exhibit better generalization. By integrating analytically tractable physical models with numerical experiments, we demonstrate that SGD undergoes a brief exploratory phase early in training, during which its intrinsic noise effectively reshapes the loss landscape into an “effective potential,” steering trajectories away from sharp minima toward flatter regions. In later stages, rising energy barriers cause the dynamics to freeze within a single basin. We propose a nonequilibrium perspective to explain SGD’s solution selection behavior, clarifying the role of transient freezing and the critical influence of noise magnitude in converging to flat, generalizable solutions. This framework unifies learning dynamics, loss landscape geometry, and generalization performance, offering theoretical foundations for designing optimization algorithms with enhanced generalization capabilities.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Stochastic gradient descent (SGD) is central to deep learning, yet the dynamical origin of its preference for flatter, more generalizable solutions remains unclear. Here, by analyzing SGD learning dynamics, we identify a nonequilibrium mechanism governing solution selection. Numerical experiments reveal a transient exploratory phase in which SGD trajectories repeatedly escape sharp valleys and transition toward flatter regions of the loss landscape. By using a tractable physical model, we show that the SGD noise reshapes the landscape into an effective potential that favors flat solutions. Crucially, we uncover a transient freezing mechanism: as training proceeds, growing energy barriers suppress inter-valley transitions and ultimately trap the dynamics within a single basin. Increasing the SGD noise strength delays this freezing, which enhances convergence to flatter minima. Together, these results provide a unified physical framework linking learning dynamics, loss-landscape geometry, and generalization, and suggest principles for the design of more effective optimization algorithms.

Problem

• stochastic gradient descent
• loss landscape
• flat minima
• learning dynamics
• generalization

Innovation

• transient dynamics
• SGD noise
• loss landscape
• flat minima
• nonequilibrium mechanism