Barriers for Learning in an Evolving World: Mathematical Understanding of Loss of Plasticity

2025-09-30

AI Summary

Deep learning models suffer from loss of plasticity (LoP) in continual learning, leading to severe performance degradation on subsequent tasks due to inability to adapt to dynamic environments. This work, grounded in dynamical systems theory, identifies LoP as arising from gradient trajectories becoming trapped in stable manifolds within parameter space—driven fundamentally by activation saturation and representational redundancy, precisely the properties that support static generalization. Through gradient flow analysis and numerical simulations, we establish the first mathematical framework explaining LoP mechanistically. Building on this insight, we propose two complementary mitigation strategies: structured architectural design and targeted parameter perturbation. Extensive simulations validate both the universality of the identified mechanism and the efficacy of our methods across diverse multi-task sequences. Our work provides a rigorous theoretical foundation and practical pathways for developing highly adaptive continual learning models.

Technology Category

• Machine Learning: Life-Long and Continual Learning
• Natural Language Processing: Learning & Optimization for NLP
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Deep learning models excel in stationary data but struggle in non-stationary environments due to a phenomenon known as loss of plasticity (LoP), the degradation of their ability to learn in the future. This work presents a first-principles investigation of LoP in gradient-based learning. Grounded in dynamical systems theory, we formally define LoP by identifying stable manifolds in the parameter space that trap gradient trajectories. Our analysis reveals two primary mechanisms that create these traps: frozen units from activation saturation and cloned-unit manifolds from representational redundancy. Our framework uncovers a fundamental tension: properties that promote generalization in static settings, such as low-rank representations and simplicity biases, directly contribute to LoP in continual learning scenarios. We validate our theoretical analysis with numerical simulations and explore architectural choices or targeted perturbations as potential mitigation strategies.

Problem

• Analyzing loss of plasticity in deep learning models under non-stationary environments
• Identifying parameter space manifolds that trap gradient trajectories during learning
• Investigating how generalization properties cause learning degradation in continual scenarios

Innovation

• Defines loss of plasticity via stable manifolds
• Identifies frozen units and cloned-unit traps
• Explores architectural changes for mitigation strategies