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With the increasing abundance of pretrained models in recent years, theproblem of selecting the best pretrained checkpoint for a particular downstreamclassification task has been gaining increased attention. Although severalmethods have recently been proposed to tackle the selection problem (e.g. LEEP,H-score), these methods resort to applying heuristics that are not wellmotivated by learning theory. In this paper we present PACTran, a theoreticallygrounded family of metrics for pretrained model selection and transferabilitymeasurement. We first show how to derive PACTran metrics from the optimalPAC-Bayesian bound under the transfer learning setting. We then empiricallyevaluate three metric instantiations of PACTran on a number of vision tasks(VTAB) as well as a language-and-vision (OKVQA) task. An analysis of theresults shows PACTran is a more consistent and effective transferabilitymeasure compared to existing selection methods.

PACTran: PAC-Bayesian Metrics for Estimating the Transferability of Pretrained Models to Classification Tasks