Variational Model Merging for Pareto Front Estimation in Multitask Finetuning

Model merging aims to combine existing single-task solutions into a multi-task solution without additional data-driven fine-tuning.~Most existing approaches achieve this using geometric properties of local solution spaces. However, such geometric views provide limited guidance for scoring how statistically useful each task-specific update direction is across tasks during merging. To address this, we formulate model merging from a new perspective of probabilistic inference under a product-of-experts (PoE) scenario where each single-task solution defines an energy-based expert model (EBM) over the merged parameters. We show that several existing model merging methods arise as special cases of our framework under energy designs that impose implicit Gaussian assumptions on directional residuals between merged and task-specific models. Empirically, we find that these residuals are often heavy-tailed which exposes a mismatch with the imposed light-tailed Gaussian structures. We address this with a heavy-tailed PoE design based on Cauchy experts, which better captures the observed residual behavior while admitting a provably convergent inference procedure. Experiments across multiple tasks and architectures show significant improvements over state-of-the-arts baselines. Our code is available at https://github.com/MinhLong210/PoE-EBM-Merging.git.

Model merging aims to combine multiple task-specific expert models into a single model without joint retraining, offering a practical alternative to multi-task learning when data access or computational budget is limited. Existing methods, however, face two key limitations: (1) they overlook the valuable inductive bias of strong anchor models and estimate the merged weights from scratch, and (2) they rely on a shared hyperparameter setting across different modules of the network, lacking a global optimization strategy. This paper introduces Bayesian Model Merging (BMM), a plug-and-play bi-level optimization framework, where the inner level formulates the model merging as an activation-based Bayesian regression under a strong prior induced by an anchor model, yielding an efficient closed-form solution; and the outer level leverages a Bayesian optimization procedure to search module-specific hyperparameters globally based on a small validation set. Furthermore, we reveal a key alignment between activation statistics and task vectors, enabling us to derive a data-free variant of BMM that estimates the Gram matrix for regression without any auxiliary data. Across extensive benchmarks, including up to 20-task merging in vision and 5-task merging in language, BMM consistently outperforms all plug-and-play anchor baselines (e.g., TA, WUDI-Merging, and TSV). In particular, on the ViT-L/14 benchmark for 8-task merging, a single merged model reaches 95.1, closely matching the average performance of eight task-specific experts (95.8).

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.