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This paper introduces a layer-wise information-theoretic framework to analyze the generalization behavior of replay-based continual learning, addressing the dual effects of empirical proxy replacement and optimization coupling. By decomposing the expected generalization gap into distinct components鈥攔epresentation drift and optimization dependence鈥攊t reveals how these factors interact at different network depths. The findings include a depth-dependent drift-sensitivity trade-off and a novel diagnostic for task-wise forgetting, validated through controlled experiments that confirm the theoretical predictions.
Layer-wise analysis reveals that replay-induced representation drift and optimization dependence are key to understanding catastrophic forgetting in continual learning.
Continual learning must absorb new tasks without erasing old ones, and replay---mixing a small buffer of past examples into current training---is among the most effective remedies for catastrophic forgetting. Yet its generalization behavior is shaped by two coupled effects that existing analyses fold into a single hypothesis-level quantity: finite memory replaces each past distribution with an empirical proxy, and repeated reuse couples the buffer, the current data, and the final hypothesis through a shared optimization trajectory. We develop a layer-wise information-theoretic framework that separates these effects at every depth. Our main result decomposes the expected generalization gap into a replay-induced representation drift and an optimization-dependence term, the latter further resolved into stability, plasticity, interaction, and residual-coupling components. Two refinements make the framework operational. A Wasserstein relaxation of the drift term, valid under support mismatch, yields a depth-dependent drift--sensitivity trade-off whose minimizer identifies which interior layer to stabilize. An SGLD instantiation of the optimization term reduces it to a trajectory-level log-determinant budget, exposing a curvature-aware gradient-alignment statistic that serves as an online diagnostic of task-wise forgetting. Controlled and benchmark experiments confirm the predicted memory scaling, the interior funnel, and the alignment signal's link to forgetting.
