Towards the Dynamics of a DNN Learning Symbolic Interactions
It addresses the problem of understanding DNN generalization dynamics for researchers, providing a theoretical mechanism for how interactions evolve during training, but it is incremental as it builds on prior observations and theorems.
This study mathematically proves the two-phase dynamics of deep neural networks (DNNs) learning interactions between input variables, showing how DNNs transition from under-fitting to over-fitting during training, with experiments confirming the theory predicts real dynamics across different DNNs and tasks.
This study proves the two-phase dynamics of a deep neural network (DNN) learning interactions. Despite the long disappointing view of the faithfulness of post-hoc explanation of a DNN, a series of theorems have been proven in recent years to show that for a given input sample, a small set of interactions between input variables can be considered as primitive inference patterns that faithfully represent a DNN's detailed inference logic on that sample. Particularly, Zhang et al. have observed that various DNNs all learn interactions of different complexities in two distinct phases, and this two-phase dynamics well explains how a DNN changes from under-fitting to over-fitting. Therefore, in this study, we mathematically prove the two-phase dynamics of interactions, providing a theoretical mechanism for how the generalization power of a DNN changes during the training process. Experiments show that our theory well predicts the real dynamics of interactions on different DNNs trained for various tasks.