Turning Back Without Forgetting: Selective Backward Refinement for Parameter-Efficient Continual Learning

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 in Large Language Models (LLMs) is hindered by the plasticity-stability dilemma, where acquiring new capabilities often leads to catastrophic forgetting of previous knowledge. Existing methods typically treat parameters uniformly, failing to distinguish between specific task knowledge and shared capabilities. We introduce Mixture of Sparse Experts for Task Agnostic Continual Learning (SETA), a framework that resolves the plasticity-stability conflict through adaptive sparse subspace decomposition into task-specific expert modules. Unlike standard updates, where tasks compete for the same parameters, SETA separates knowledge into unique experts, designed to isolate task-specific patterns, and shared experts, responsible for capturing common features. This structure is maintained through adaptive elastic anchoring and a routing-aware regularization that jointly protect shared knowledge at both the weight and routing levels and enable a unified gating network to automatically retrieve the correct expert combination during inference. Extensive experiments across diverse domain-specific benchmarks demonstrate that SETA achieves competitive or superior overall performance relative to state-of-the-art continual learning baselines, with particularly strong retention of early-task knowledge and improved backward transfer on LLaMA-2 7B and Qwen3-4B.

Achieving continual learning (CL) with deep neural networks requires balancing stability and plasticity while enabling knowledge transfer. In this work, we focus on offline learning algorithms under the constraints: (I) no access to training data from prior tasks (II) no access to task-id at inference time. We introduce a novel measure, the relative parameter-importance, which measures the relative importance of each parameter with respect to both the current and past tasks. Parameters with high relative importance are interpreted as more important for maintaining past-task stability and thus heavily regularised, whereas parameters with low relative-importance are allowed to be more freely updated. Unlike existing methods, our approach allows the update of parameters with high past-task importance when they have low relative-importance, thus enabling backward knowledge transfer in addition to tackling the stability-plasticity trade-off. We demonstrate improvements against state-of-the-art CL methods on both class-incremental and domain-incremental learning text classification problems and provide insights for extending our method to text generation problems. Code available at: https://github.com/itsmemala/LACL