\u3010Title\u3011\"Interpreting (some) neural networks with symbolic regression\"
\u3010Abstract\u3011 We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent representations when we train a GNN in a supervised setting, then we apply symbolic regression to components of the learned model to extract explicit physical relations. We find the correct known equations, including force laws and Hamiltonians, can be extracted from the neural network. We then apply our method to a non-trivial cosmology example\u2014a detailed dark matter simulation\u2014and discover a new analytic formula which can predict the concentration of dark matter from the mass distribution of nearby cosmic structures. Our approach offers alternative directions for interpreting neural networks and discovering novel physical principles from the representations they learn.<\/p>\n