Access control in large language models (LLMs) requires modular mechanisms to enable domain-specific behavior without retraining or cross-domain interference. A common hypothesis is that interference during adapter composition arises from overlap in linear parameter updates, suggesting that enforcing orthogonality or directional independence should improve multi-domain performance. We test this hypothesis using DoRA-RBAC, a hierarchical adapter composition framework based on weight-decomposed low-rank adaptation. We compare conventional Euclidean merging with a geometry-aware Riemannian-inspired merging strategy that approximates the Frechet mean via normalized directional averaging across multiple QA benchmarks (GPQA, PubMedQA, SimpleQA, WMDP) on LLaMA-3.1-8B and Mistral-7B. Our results show that while single-domain performance matches LoRA, geometry-aware merging provides no consistent advantage over standard averaging in multi-domain settings.Diagnostic analysis further reveals that angular alignment and orthogonality of adapter updates are weak predictors of composition performance. These findings suggest that adapter interference is not governed primarily by parameter-space geometry, but is instead consistent with interactions in shared nonlinear representations.
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.
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) is a widely used parameter-efficient fine-tuning method that places trainable low-rank adapters into frozen pre-trained models. Recent studies show that using fewer LoRA adapters may still maintain or even improve performance, but existing methods still distribute adapters broadly, leaving where to place a limited number of adapters to maximize performance largely open. To investigate this, we introduce PAGE (Projected Adapter Gradient Energy), a gradient-based sensitivity probe that estimates the initial trainable gradient energy available to each candidate LoRA adapter. Surprisingly, we find that PAGE is highly concentrated on a single shallow FFN down-projection across two model families and four downstream tasks. We term this module the dominant adaptation module and show that its layer index is architecture-dependent but task-stable. Motivated by this finding, we propose DomLoRA, a placement method that places a single adapter at the dominant adaptation module. With only ~0.7% of vanilla LoRA's trainable parameters, DomLoRA outperforms it on average across various downstream tasks, including instruction following, mathematical reasoning, code generation, and multi-turn conversation. This method also improves other LoRA variants, supporting the dominant adaptation module perspective as a practical placement guideline.