Co-Adaptive Multi-Task LoRA: Transfer-Aware, Label-Free Control of Domain Participation
Authors: Wei Zhang, Lin Tang, Ming Zhao, Yuxuan Wang
Organizations: 1Sichuan University, Chengdu, China · University of Electronic Science and Technology of China, Chengdu, China
Abstract
Fine-tuning a single low-rank adapter on many domains at once is multi-task learning: the domains must be co-learned, and how they share the adapter decides whether they help or hurt one another. Most efficient fine-tuning pipelines ignore this and train on a fixed, uniform mixture, leaving two coupled questions unanswered: how much should each domain participate, and which domains should be co-trained given that some transfer positively and others interfere? We show that both answers can be read off cheaply and without labels. A forward pass of the current shared adapter over a small unlabeled probe yields, per domain, a competence signal whose level tracks remaining headroom and whose trajectory tracks learning speed; the drift of these probe representations yields a signed cross-domain affinity that predicts pairwise transfer. We fold both into CoDA, a co-adaptive controller that solves a small entropy-regularized quadratic program on the simplex to set each domain's participation -- jointly its loss weight and its share of the sampled data -- rewarding high-headroom, still-learning, mutually synergistic domains and damping interfering ones. The controller is forward-only, adds no trainable parameters, and wraps any multi-task LoRA pipeline. Across five heterogeneous domains and two backbones, CoDA improves the average over uniform mixing, learned mixtures, gradient-surgery multi-task optimizers, and online data selection while using half the data, and lowers cross-domain gradient conflict. We prove that the competence signal tracks domain risk, that the participation program has a unique fixed point reached by a contraction, and that its solution performs transfer-aware water-filling; analysis, ablations, and controls corroborate each claim.
Multi-domain fine-tuning of large language models requires improving performance on target domains while preserving performance on constrained domains, such as general knowledge, instruction following, or safety evaluations. Existing data mixing strategies rely on fixed heuristics or adaptive rules that cannot explicitly enforce preservation of such capabilities. We propose DynaMiCS, a dynamic mixture optimizer that casts multi-domain fine-tuning as a constrained optimization problem. At each update, DynaMiCS performs short domain-specific probing runs to estimate a slope matrix of local cross-domain effects, capturing how training on each fine-tuning dataset affects each evaluation domain. These estimates are then used to compute mixture weights through optimization over the probability simplex, with the objective of improving target-domain performance while keeping constrained-domain losses below reference levels. Across multi-domain fine-tuning scenarios with varying numbers of target and constrained domains, DynaMiCS achieves stronger target-domain improvements and higher constraint satisfaction than fixed-mixture baselines, at lower computational cost and without reference models, per-example scoring, or manually tuned mixture weights.
Combining a task LoRA adapter with a domain LoRA adapter into a single unified model is a practical yet largely unexplored challenge. Existing methods treat both adapters as symmetric peers, applying uniform weights across all layers. We argue that task and domain adapters exhibit a consistent depth-dependent asymmetry across transformer architectures. Domain dominance increases with layer depth, while shallower layers retain stronger task-relevant signals. Motivated by this observation, we propose TaDA (Task-Domain LoRA Merging), a training-free algorithm that exploits this structure through calibrated probe-guided per-layer gating and per-component subspace-aware merging. The gating assigns individual weights per layer and projection type using a probe signal proved invariant to adapter weight magnitude. The merging discards conflicting singular directions before combining the remaining components. TaDA produces a standard rank-r LoRA adapter with zero inference overhead. On six scientific QA benchmarks with Llama-2-7B, TaDA achieves an average accuracy of 0.452, outperforming DARE-TIES by +3.6 percentage points and obtaining the best result on all six benchmarks. On six image classification benchmarks with ViT-L/16, TaDA reaches 85.9% average accuracy, improving over the strongest merging baseline while leading in three of the six individual benchmarks.
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.