When the Merge Coefficient Stops Mattering: Proximity Regularized Merging for Continual LoRA Adaptation

Abstract:Rehearsal-free continual learning with parameter-efficient adapters can be cast as a sequence of task-vector write-in operations: for each new task, a low-rank adapter is learned and merged into a running model. We propose Proximity Regularized Merging (PRM), a minimal modification to sequential LoRA merging that adds a proximal penalty during task-vector training without changing the subsequent write-in rule. PRM acts as a robust task-vector regularizer: in the reported Base->+Prox diagnostics, it improves AAA across multiple write-in rules, backbones, and class-incremental settings, while its fixed-coefficient variant remains competitive with strong coefficient-based baselines. Mechanistically, matched-prefix norm controls and proximal-strength sweeps show that proximal training shrinks the task-vector radius, lowers Fisher-weighted interference, broadens the coefficient plateau, and exposes a stability-plasticity trade-off. Together, these results suggest that the effectiveness of sequential LoRA merging depends not only on how much of a task vector is written in, but also on whether the task vector itself has been trained to be mergeable.

Machine Learning (cs.LG)

arXiv:2609.32332 [cs.LG]

(or arXiv:2609.32332v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.32332 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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