Reliable Replay through Spatial Coherence in Online Continual Learning

Continued pretraining enables language models to adapt to new domains and knowledge, but often at the cost of forgetting previously acquired capabilities. Replay can mitigate this trade-off, but fixed replay mixtures allocate training independently of the model's actual retention needs. We introduce Replay on Demand (RoD), which instead derives the replay allocation from the model's learning dynamics. RoD jointly prioritizes adaptation samples by their remaining learning potential and replay samples by their observed forgetting. Their competition for a shared training budget yields an online curriculum that determines what to train on at each step. Across models, scales, and adaptation domains, RoD reaches or improves upon the adaptation-forgetting frontier of tuned fixed-replay baselines and model merging without prescribing a replay allocation in advance. Replay concentrates on sources that are more vulnerable to forgetting and dynamically increases and redistributes as forgetting emerges during training. Together, our results show that replay can be allocated online from the model's evolving state, targeting what is needed, when it is needed.

Continual learning studies how deployed language models can continually acquire new tasks without expensive retraining from scratch. Existing methods, whether rehearsal-based (replaying stored past data) or rehearsal-free (regularising or isolating parameters), overwhelmingly target one objective: preventing catastrophic forgetting. Forward transfer, the past helping the future, has meanwhile been pursued almost exclusively through parameter reuse, with no explicit account of when transfer should be expected at all. We begin one step earlier: before designing a transfer mechanism, we ask when transfer should exist at all. We answer with a framework of three measurable conditions: the target task must leave room for improvement beyond its own limited supervision, transferable information must survive continued optimisation, and replay must come from compatible previous tasks. We instantiate this view as Transfer-Selective Replay (TSR), which selects replay data predicted to benefit the incoming task rather than replaying past examples indiscriminately. Selection is guided by a zero-training task signature, while distillation preserves stability on previous tasks. Under the standard continual learning protocol in the low-budget regime, TSR consistently improves forward transfer while maintaining stability, outperforming existing replay baselines across heterogeneous and homogeneous task streams. More broadly, the results argue for treating transfer as a first-class objective of continual learning, to be understood before it is engineered.

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.