  Model merging has emerged as an effective approach to combine multiple
single-task models, fine-tuned from the same pre-trained model, into a
multitask model. This process typically involves computing a weighted average
of the model parameters without any additional training. Existing model-merging
methods focus on enhancing average task accuracy. However, interference and
conflicts between the objectives of different tasks can lead to trade-offs
during model merging. In real-world applications, a set of solutions with
various trade-offs can be more informative, helping practitioners make
decisions based on diverse preferences. In this paper, we introduce a novel
low-compute algorithm, Model Merging with Amortized Pareto Front (MAP). MAP
identifies a Pareto set of scaling coefficients for merging multiple models to
reflect the trade-offs. The core component of MAP is approximating the
evaluation metrics of the various tasks using a quadratic approximation
surrogate model derived from a pre-selected set of scaling coefficients,
enabling amortized inference. Experimental results on vision and natural
language processing tasks show that MAP can accurately identify the Pareto
front. To further reduce the required computation of MAP, we propose (1) a
Bayesian adaptive sampling algorithm and (2) a nested merging scheme with
multiple stages.
