  Efficient model selection for identifying a suitable pre-trained neural
network to a downstream task is a fundamental yet challenging task in deep
learning. Current practice requires expensive computational costs in model
training for performance prediction. In this paper, we propose a novel
framework for neural network selection by analyzing the governing dynamics over
synaptic connections (edges) during training. Our framework is built on the
fact that back-propagation during neural network training is equivalent to the
dynamical evolution of synaptic connections. Therefore, a converged neural
network is associated with an equilibrium state of a networked system composed
of those edges. To this end, we construct a network mapping $\phi$, converting
a neural network $G_A$ to a directed line graph $G_B$ that is defined on those
edges 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. We
carried out extensive experiments using 17 popular pre-trained ImageNet models
and five benchmark datasets, including CIFAR10, CIFAR100, SVHN, Fashion MNIST
and Birds, to evaluate the fine-tuning performance of our framework. Our neural
capacitance metric is shown to be a powerful indicator for model selection
based only on early training results and is more efficient than
state-of-the-art methods.
