New theory pinpoints which layer to stabilize in replay-based continual learning

Replay—mixing a small buffer of past examples into current training—remains one of the most effective defenses against catastrophic forgetting in continual learning. Yet its generalization behavior has been poorly understood, with existing analyses lumping two coupled effects into a single hypothesis-level quantity: finite memory replacing past distributions with an empirical proxy, and repeated reuse coupling the buffer, current data, and final hypothesis through a shared optimization trajectory. In arXiv:2608.11690, Tieliang Gong, Zhongbo Zhang, Wen Wen, and Yong-Jin Liu develop a layer-wise information-theoretic framework that separates these effects at every depth, decomposing the expected generalization gap into a replay-induced representation drift term and an optimization-dependence term. The latter further splits into stability, plasticity, interaction, and residual-coupling components.

To make the framework operational, the authors introduce two refinements. First, 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—the so-called "interior funnel." Second, an SGLD (stochastic gradient Langevin dynamics) 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 structure, and the alignment signal's link to forgetting. This provides practitioners with a principled way to decide where to intervene in a network to prevent catastrophic forgetting, rather than relying on heuristic layer freezing.