ATM: Improving Model Merging by Alternating Tuning and Merging

Model merging has recently emerged as a cost-efficient paradigm for multi-task learning. Among current approaches, task arithmetic stands out for its simplicity and effectiveness. In this paper, we motivate the effectiveness of task vectors by linking them to multi-task gradients. We show that in a single-epoch scenario, if the optimization is performed via gradient descent, task vectors are after one step mathematically equivalent to the gradients obtained via gradient descent in a multi-task setting, and still approximate these gradients in subsequent epochs. Furthermore, we show that the effectiveness of task vectors is largely driven by the first epoch's gradient. Given this parallel between task vectors and gradients, we propose viewing model merging as a single step in an iterative process that alternates between tuning and merging (ATM). We then propose two ways to utilize ATM. The first is to replace multi-task learning with ATM in scenarios where data sharing is prohibited, such as federated learning. The second is to improve the outcome of any model merging algorithm by applying a few post-hoc iterations of ATM on a small validation dataset, which is commonly available for hyperparameter tuning. Finally, we provide both empirical and theoretical support for the effectiveness of ATM, demonstrating that it minimizes an upper bound on the loss obtained by jointly finetuning all tasks.