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Efficient model selection for identifying a suitable pre-trained neuralnetwork to a downstream task is a fundamental yet challenging task in deeplearning. Current practice requires expensive computational costs in modeltraining for performance prediction. In this paper, we propose a novelframework for neural network selection by analyzing the governing dynamics oversynaptic connections (edges) during training. Our framework is built on thefact that back-propagation during neural network training is equivalent to thedynamical evolution of synaptic connections. Therefore, a converged neuralnetwork is associated with an equilibrium state of a networked system composedof those edges. To this end, we construct a network mapping $\phi$, convertinga neural network $G_A$ to a directed line graph $G_B$ that is defined on thoseedges in $G_A$. Next, we derive a neural capacitance metric $\beta_{\rm eff}$as a predictive measure universally capturing the generalization capability of$G_A$ on the downstream task using only a handful of early training results. Wecarried out extensive experiments using 17 popular pre-trained ImageNet modelsand five benchmark datasets, including CIFAR10, CIFAR100, SVHN, Fashion MNISTand Birds, to evaluate the fine-tuning performance of our framework. Our neuralcapacitance metric is shown to be a powerful indicator for model selectionbased only on early training results and is more efficient thanstate-of-the-art methods.

Neural Capacitance: A New Perspective of Neural Network Selection via Edge Dynamics