  This paper investigates the dynamics of a deep neural network (DNN) learning
interactions. Previous studies have discovered and mathematically proven that
given each input sample, a well-trained DNN usually only encodes a small number
of interactions (non-linear relationships) between input variables in the
sample. A series of theorems have been derived to prove that we can consider
the DNN's inference equivalent to using these interactions as primitive
patterns for inference. In this paper, we discover the DNN learns interactions
in two phases. The first phase mainly penalizes interactions of medium and high
orders, and the second phase mainly learns interactions of gradually increasing
orders. We can consider the two-phase phenomenon as the starting point of a DNN
learning over-fitted features. Such a phenomenon has been widely shared by DNNs
with various architectures trained for different tasks. Therefore, the
discovery of the two-phase dynamics provides a detailed mechanism for how a DNN
gradually learns different inference patterns (interactions). In particular, we
have also verified the claim that high-order interactions have weaker
generalization power than low-order interactions. Thus, the discovered
two-phase dynamics also explains how the generalization power of a DNN changes
during the training process.
