We investigate how neural networks (NNs) understand physics using 1D quantum mechanics. After training an NN to accurately predict energy eigenvalues from potentials, we used it to confirm the NN's understanding of physics from four different aspects. The trained NN could predict energy eigenvalues of different kinds of potentials than the ones learned, predict the probability distribution of the existence of particles not used during training, reproduce untrained physical phenomena, and predict the energy eigenvalues of potentials with an unknown matter effect. These results show that NNs can learn physical laws from experimental data, predict the results of experiments under conditions different from those used for training, and predict physical quantities of types not provided during training. Because NNs understand physics in a different way than humans, they will be a powerful tool for advancing physics by complementing the human way of understanding.

Quantifying which neurons are important with respect to the classification decision of a trained neural network is essential for understanding their inner workings. Previous work primarily attributed importance to individual neurons. In this work, we study which groups of neurons contain synergistic or redundant information using a multivariate mutual information method called the O-information. We observe the first layer is dominated by redundancy suggesting general shared features (i.e. detecting edges) while the last layer is dominated by synergy indicating local class-specific features (i.e. concepts). Finally, we show the O-information can be used for multi-neuron importance. This can be demonstrated by re-training a synergistic sub-network, which results in a minimal change in performance. These results suggest our method can be used for pruning and unsupervised representation learning.