  As neural networks grow in scale, their training becomes both computationally
demanding and rich in dynamics. Amidst the flourishing interest in these
training dynamics, we present a novel observation: Parameters during training
exhibit intrinsic correlations over time. Capitalizing on this, we introduce
Correlation Mode Decomposition (CMD). This algorithm clusters the parameter
space into groups, termed modes, that display synchronized behavior across
epochs. This enables CMD to efficiently represent the training dynamics of
complex networks, like ResNets and Transformers, using only a few modes.
Moreover, test set generalization is enhanced. We introduce an efficient CMD
variant, designed to run concurrently with training. Our experiments indicate
that CMD surpasses the state-of-the-art method for compactly modeled dynamics
on image classification. Our modeling can improve training efficiency and lower
communication overhead, as shown by our preliminary experiments in the context
of federated learning.
