Model Merging as Probabilistic Inference in Fine-Tuning Parameter Space

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).

Model merging integrates the capabilities of multiple expert models to create strong models for multiple tasks without additional training, thereby reducing computational resource requirements. However, existing methods operate within the convex combination space of expert models, failing to explore high-performance regions outside this space. This paper proposes the MERGEvolve framework, which unifies model merging and evolution within an evolution strategy by treating the merged model as the initialization for evolutionary exploration of the parameter space. During the merging phase, expert models act as deterministic sources to build a strong initial point. The evolution phase then explores the parameter space using random noise. Theoretical analysis shows that MERGEvolve explores regions outside the convex combination space. Extensive experiments on single-task and multi-task benchmarks demonstrate that MERGEvolve consistently achieves performance competitive with advanced model merging baselines. Ablation studies confirm that a high-quality initial point is critical for efficient exploration of the parameter space.

Model merging combines fine-tuned checkpoints into a single multi-task model without retraining. Existing methods - such as task arithmetic, model soups, TIES, and DARE - are computationally efficient and empirically successful, but rely on heuristic design choices and lack formal optimality guarantees. We show that merging can be formulated as a convex quadratic programme over residual updates, yielding weights that minimise a squared-output calibration objective using calibration inputs and fine-tuned model outputs, and subsuming existing methods as special cases. Our framework yields a closed-form diagnostic - the fraction of residual energy captured by a chosen basis - that predicts downstream merge quality using only the calibration set. Empirically, the QP matches or outperforms existing methods in the single-layer setting, and we characterise when the optimal basis provides significant gains over the cheaper diagonal QP. We extend to multi-layer merging via a sequential layer-wise algorithm and demonstrate consistent gains across language and vision benchmarks.