Access Sets Matter: Budgeting Expert Reads for Scalable Weight-Space Model Merging

LLM services need to offer a family of models spanning different capability--cost trade-offs to accommodate diverse user preferences. Model merging offers a practical way to construct such a model family by combining a reasoning-enhanced model with an instruction-tuned model. Compared with model-level merging, layer-wise merging offers finer control over the capability--cost trade-off by assigning different merge weights to individual layers. However, it introduces two practical challenges: the layer-wise search space is high-dimensional, and existing methods rarely exploit informative signals from the source models; moreover, the highly variable runtime of LLM evaluations makes synchronous batch optimization inefficient by leaving GPU resources idle while waiting for slow evaluations. To address these challenges, we propose Asynchronous Prior-Guided Bayesian Model Merging (AP-BMM), which formulates layer-wise merging as a multi-objective optimization problem to approximate a Pareto set of merged LLMs, yielding a family of Pareto-optimal merged models with diverse capability--cost trade-offs. AP-BMM leverages parameter and activation discrepancies between the source models to guide the early layer-wise search, employs asynchronous pending-aware Bayesian optimization to maximize GPU utilization through asynchronous evaluations and to select high-quality candidates via pending awareness, and applies lightweight ranking over an oversized candidate pool to improve Pareto-front coverage. Under fixed evaluation budgets, AP-BMM achieves higher hypervolume (HV) and broader Pareto-front coverage than synchronous layer-wise and representative model-level merging methods, while reducing wall-clock time through higher GPU utilization.

Model merging has emerged as a lightweight paradigm for enhancing Large Language Models (LLMs), yet its underlying mechanisms remain poorly understood. In this work, we analyze late-stage pre-training trajectories and uncover a \textbf{Rank-1 Subspace} phenomenon: while raw optimization steps oscillate violently, consecutive \emph{merged} checkpoints collapse onto a stable, approximately one-dimensional linear manifold. We theoretically ground this observation in a \emph{river-valley} landscape analysis: averaging acts as a geometric low-pass filter that dampens high-curvature noise to reveal the optimal descent direction. Capitalizing on this insight, we propose \textbf{Extra-Merge}, a training-free strategy that extrapolates along this subspace to minimize loss without additional gradient updates. Extensive experiments across GPT-2 and LLaMA families (124M to 2B) demonstrate that Extra-Merge consistently outperforms standard merging baselines. Notably, it yields consistent zero-shot accuracy gains on Pythia-12B downstream tasks and generalizes effectively to the Muon optimizer \citep{jordan2024muon}.

Dense expert merging combines domain-specialized language models into one single checkpoint, typically by admitting task-vector support in weight space. However, this admission is governed by three decisions that existing methods answer only partially: where to open layer capacity from cross-expert conflict, who should occupy that capacity based on domain demand, and how to admit the resulting support without relying on costly recipe search. To tackle these issues, we propose SigMerge (Signature-Guided Capacity Occupancy), a structured capacity assignment framework for dense expert merging. Starting from a dense base merge, conflict signatures set each layer's capacity from cross-expert conflict, positive base-merge deficits set each domain's share of that capacity, and a sequential occupancy rule admits each expert delta up to the resulting layer-domain budget. Across 21 paired settings spanning seven dense base merges and three model pools, SigMerge improves every one (by 15.0% on average) and achieves the best average rank (1.67) among six merging methods, outperforming three categories of merging baselines.