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-a detailed dark matter
simulation-and discover a new analytic formula which can predict the
concentration of dark matter from the mass distribution of nearby cosmic
structures. The symbolic expressions extracted from the GNN using our technique
also generalized to out-of-distribution data better than the GNN itself. Our
approach offers alternative directions for interpreting neural networks and
discovering novel physical principles from the representations they learn.

该研究采用强归纳偏置的通用方法，将符号化表示从学习的深层模型中提取出来，应用于图神经网络。该技术可以从神经网络中提取物理方程，如力学定律和哈密顿量，并在耗费较小的计算资源上快速发现新的物理原则。