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

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.

20 pages, 10 figures, 7 tables. Code available at this https URL

Machine Learning (cs.LG)

arXiv:2609.36375 [cs.LG]

(or arXiv:2609.36375v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.36375 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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