Catastrophic forgetting as a dynamical phenomenon: Understanding parameter evolution under sequential task exposure

Catastrophic forgetting occurs when performance on previously learned tasks deteriorates during sequential training. We examine whether the temporal organization of task exposure influences forgetting and whether properties of the schedule generator predict learning outcomes. Sequential learning is formulated as a forced optimization process, and periodic, balanced-random, and three logistic-map schedules are compared across Split MNIST, Permuted MNIST, and Split CIFAR-10. Using five paired seeds, we analyze terminal accuracy and forgetting alongside exposure-gap associations, autocorrelation, spectral entropy, and recurrence measures. Descriptive outcome differences are largest in Split MNIST, negligible at the end of the near-ceiling Permuted-MNIST experiment, and modest for terminal accuracy but larger for terminal forgetting in Split CIFAR-10. However, none of the comparisons remained significant after Holm correction. Holm-adjusted temporal tests identify differences in inactive-task gap–forgetting associations and recurrence measures in Split MNIST and in autocorrelation, spectral entropy, and recurrence measures in Split CIFAR-10, but no adjusted temporal differences in Permuted MNIST. Increasing positive Lyapunov exponents of the logistic-map generators do not correspond monotonically to forgetting. Learning-rate, mitigation-method, and architecture analyses further reveal condition-dependent accuracy–retention trade-offs. Overall, temporal exposure structure influences sequential-learning behavior, but its effects depend on the task setting, optimization, and model configuration rather than following a universal periodic–random–chaotic ordering.