Audit Before You Merge: Provenance, Probing, and Continual LoRA Composition

Low-rank adaptation (LoRA) makes it cheap to train many domain- and task-specific language model adapters, but whether two adapters can be merged is usually discovered only after both have been fully trained and evaluated. This late feedback is costly: adapters that are strong in isolation can interfere destructively once their updates are combined. We ask whether this outcome can be anticipated. We formalize adapter mergeability as the degree to which an adapter preserves its single-task utility after merging, and show that it can be forecast from signals measured in the first few percent of training -- chiefly how the low-rank updates and their gradients align across tasks and how much they disturb shared representations. We package these signals into MergeProbe, a lightweight predictor that estimates pairwise and set-level retention and turns the estimate into a concrete decision: merge directly, reweight, prune, or route. On MERGE-PEFT, a five-domain benchmark spanning math, code, science, instruction following, and safety, MergeProbe attains the best average and worst-case retention among strong interference-aware merge baselines while adding far less deployment overhead than full task routing. This turns LoRA merging from a post-hoc engineering step into an anticipatory measurement problem.

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.

Low-rank adaptation (LoRA) is the de facto method for parameter-efficient fine-tuning of large neural networks, achieving strong task adaptation with minimal trainable parameters and low optimization cost. Beyond this efficiency, practitioners have observed two striking properties: robustness to catastrophic forgetting and the ability to merge independently trained adapters into a single model that performs competitively across multiple tasks. These properties are central to continual and multi-task learning, yet remain poorly understood. In this work, we provide a theoretical explanation through a unified margin-based perspective. We analyze LoRA in multiclass linear classification under a near-orthogonal task regime with $\ell_2$-regularization, and characterize the optimal LoRA adapter across regularization regimes. Our analysis shows that, in an intermediate regime of regularization parameters, the optimal adapter aligns with the max-margin solution on the fine-tuning data. Building on this characterization, we derive two key consequences. First, we obtain closed-form expressions for the margins on pre-training and fine-tuning data, revealing a precise margin trade-off: the regularization parameter controls the balance between retention and adaptation. Second, we analyze adapter merging, proving that merged models achieve positive margin on each task and deriving optimal mixing coefficients that balance margins across tasks and maximize the margin over their union. These results lead to a simple, training-free merging rule, which we term margin-based LoRA merging (MaLoRA). Experiments on modern architectures and real datasets validate our theoretical predictions, showing that MaLoRA matches or outperforms several adapter-merging baselines across a range of vision and language classification tasks.