TSR consistently improves forward transfer while maintaining stability, outperforming existing replay baselines across heterogeneous and homogeneous task streams and argues for treating transfer as a first-class objective of continual learning, to be understood before it is engineered.
Abstract
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.
Reinforcement learning with verifiable rewards (RLVR) commonly post-trains reasoning models on multiple tasks, while rerunning multitask RLVR (MTRL) as new tasks are added makes capability expansion costly. We therefore study continual RLVR, which updates the existing model as each task arrives. The central question is whether a model updated this way can perform as well as a jointly trained model. To answer this question, we introduce Continual Reasoning Gym, a continual-RLVR environment that organizes text and visual reasoning tasks into five task sequences. In this setting, we identify two key observations: Sequential RLVR exhibits modest forgetting, yet its final performance remains below that of MTRL. To understand the latter, we decompose final performance and show that forgetting accounts for only part of the gap. To explain the former, we identify shared reasoning: transferable reasoning structure allows training on one task to support others on average. We therefore introduce Continual Prompt Replay (CPR), which harnesses shared reasoning to improve learning on the arriving and future tasks by replaying previous-task prompts and regenerating their responses with the current policy. On average, only CPR reaches MTRL-level performance.
Lirui Luo, Guo-Xi Zhang, Hong-Ming Xu et al.· 0 citations
Spaced Repetition Training (SRT) is introduced, a continual learning framework inspired by cognitive science, which schedules sample-rehearsal using the SuperMemo-2 (SM-2) algorithm, and preserves broad benchmark performance that naive continual pre-training and uniform replay substantially degrade.
Experiments on challenging reasoning benchmarks show that H$^2$SD achieves the strongest overall performance among representative RLVR and self-distillation baselines, with stable optimization and a favorable accuracy-efficiency trade-off.
Qi Cai, Yi-Chuan Ma, Linyang Li et al.· arXiv.org· 2 citations
This work proposes TTCD, a TTT framework that introduces a self-supervised objective for allocating limited memory capacity for future use, and focuses on an in-place variant: In-Place TTCD, which uses the existing MLP parameters as the fast weights.
Zixuan Wang, Xingyu Dang, Ruiming Zhu et al.· 0 citations
RL-based post-training for reasoning models is increasingly bottlenecked by repeated fresh rollout generation, particularly in agentic settings where environment interaction dominates wall-clock cost. Replay can reduce this burden by reusing past trajectories, but existing methods typically embed it within larger training pipelines involving exploration, experience restructuring, or mixed-policy optimization. This makes replay's own contribution difficult to isolate. We ask a focused question: how far can principled replay selection alone go? We introduce Headroom-Drift Replay, a group-level replay control primitive for GRPO that separates reuse into two decisions. Headroom ranks stored groups by remaining learning value, while Drift gates them by compatibility with the current policy. The fresh on-policy stream remains unchanged, and the method adds no auxiliary generation or training machinery. Across mathematical reasoning, multimodal reasoning, and Agentic Search benchmarks, this single intervention outperforms naive replay and matches or exceeds broader replay methods on Avg Mean@32. In Agentic Search, where environment interaction dominates cost, it delivers comparable quality at materially lower wall-clock time.
The results suggest that the combination of sparse representations, local learning, and persistent memory is a promising direction for continual learning, while motivating further investigation into the respective roles of learning rules, representations, and architectural design in mitigating catastrophic forgetting.
