Bayesian Model Merging

Modern deep learning usually treats models as separate artifacts: trained independently, specialized for particular purposes, and replaced when improved versions appear. This thesis studies model merging as an alternative paradigm: combining independently trained neural networks directly in weight space, with little or no optimization and without requiring access to the original training data. The thesis considers two main regimes. In the single-task setting, where models share an objective but differ in initialization, we introduce C$^2$M$^3$, a cycle-consistent merging algorithm based on Frank-Wolfe optimization. C$^2$M$^3$ aligns multiple networks into a shared, reference-free parameter space, making weight averaging meaningful without privileging any individual model. In the multi-task setting, where models are fine-tuned for different downstream tasks from a common pretrained initialization, we first develop a theoretical account of task vectors as approximate gradients. This explains both the effectiveness and the limitations of task arithmetic. Building on this view, we show that task vectors inherit the low-rank structure of gradients and introduce Task Singular Vectors (TSV), a decomposition that enables compression and interference reduction through TSV-Merge. We then present MASS, an input-adaptive routing method that uses TSV geometry to select task-relevant subspaces at inference time. Finally, we introduce MERGE$^3$, an evolutionary merging framework that uses Item Response Theory to reduce evaluation costs by up to 50$\times$ while preserving solution quality. Together, these contributions provide theoretical and algorithmic foundations for model merging, supporting a paradigm in which learned capabilities can be composed, reused, and extended across models.

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 has emerged as a promising paradigm for enabling multi-task capabilities without additional training. However, traditional basic merging methods often experience performance degradation due to parameter conflicts, even when applied to similar tasks. While recent personalized merging frameworks successfully preserve task-specific information to maintain performance, they typically incur storage overhead. In this paper, we propose Decomposition, Thresholding, and Scaling (DTS), an approximation-based personalized merging framework that pushes task-specific storage efficiency. DTS first applies singular value decomposition to the task-specific information and retains only a small subset of singular values and vectors. It then introduces a novel thresholding strategy that partitions singular vector elements into groups and assigns a scaling factor to each group. To enable generalization to unseen tasks, we further extend DTS with a variant that fuses task-specific information in a data-free manner based on the semantic similarity of task characteristics. Extensive experiments demonstrate that DTS consistently outperforms state-of-the-art baselines while requiring only 1% extra storage per task. Furthermore, experiments on unseen tasks show that the DTS variant achieves significantly better generalization performance. Our code is available at https://github.com/krumpguo/DTS.