Neural Succession: A Mesoscopic Theory of Invasion, Coexistence, and Stabilization in Continual Learning

2026-09-28

AI Summary

This study addresses catastrophic forgetting and task interference in continual learning by proposing Succession Learning Theory (SLT), which pioneers a mesoscopic perspective that treats representations as ecological communities governed by invasion, coexistence, and stabilization mechanisms. Methodologically, the work introduces pre-invasion compatibility as a core predictive metric. By integrating mesoscopic dynamics modeling with specialized Lotka-Volterra equation analysis, it reveals fundamental principles governing niche modification and displacement lower bounds. Experiments on benchmarks such as Split-CIFAR demonstrate that this metric significantly predicts forgetting (r≈-0.79), accurately discriminates between coexistence and exclusion states (AUC>0.93), and effectively optimizes replay efficiency. Ultimately, SLT provides a novel theoretical framework for enhancing model stability in continual learning scenarios.

Abstract

Continual learning is usually studied through mechanisms that preserve old knowledge. We develop Successional Learning Theory (SLT), a mesoscopic account in which the current representation is a resident community, the incoming task is an invader, forgetting is resident displacement, joint retention is coexistence, replay is resident reinforcement, and training moves from establishment toward stabilization. Its empirical coordinate is directional pre-invasion compatibility, measured on the resident model before the incoming task is learned. Across eight experiments, compatibility orders later forgetting on the 20 directed Split-CIFAR-10 transitions (three-repeat r=-0.789, incoming-task cluster 95% CI [-0.90,-0.72], every repeat alone r<=-0.67), forecasts held-out forgetting with 24% lower error than a no-information baseline, and reproduces under controlled MNIST permutations and CIFAR-10 rotations (r=-0.804, -0.718). On an 84-transition suite, compatibility separates coexistence from exclusion at every retention threshold (AUC 0.93-0.97). Replay repairs every transition with at most 325 stored examples and is most efficient where displacement is largest. Compatibility reaches |r|=0.720, while activation, representation, Jacobian, and fixed-coefficient Lotka-Volterra specializations do not. Plasticity and feature turnover fall reliably from early to late training (15/15 and 14/15 runs). We formalize a minimum habitat-modification bound, a displacement floor, a sufficient coexistence condition, an identifiability law with a range-restriction corollary, successional stabilization, and local reinforcement. The identifiability law also predicts where the coordinate loses leverage, and the prediction matches three CIFAR-100 partitions and five optimizer regimes. SLT is a pre-adaptation diagnostic that complements replay, regularization, and projection methods.

Problem

• continual learning
• catastrophic forgetting
• coexistence
• mesoscopic theory
• task interference

Innovation

• Continual Learning
• Successional Learning Theory
• Pre-invasion Compatibility
• Mesoscopic Theory
• Ecological Dynamics