Barriers for Learning in an Evolving World: Mathematical Understanding of Loss of Plasticity
This addresses a key problem for continual learning in AI by providing a mathematical understanding of why models fail to adapt over time, though it is incremental as it builds on existing theories of plasticity.
The paper investigates loss of plasticity (LoP), where deep learning models degrade in non-stationary environments, by formally defining it through stable manifolds in parameter space and identifying mechanisms like frozen units and cloned-unit manifolds that trap gradient trajectories.
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.