How early can we average Neural Networks?

Abstract

There is a recurring observation in deep learning that neural networks can be combined simply with arithmetic averages over their parameters. This observation has led to many new research directions in model ensembling, meta-learning, federated learning, and optimization. We investigate the evolution of this phenomenon during the training trajectory of neural network models initialized from a common set of parameters (parent). Surprisingly, the benefit of averaging the parameters persists over long child trajectories from parent parameters with minimal training. Furthermore, we find that the parent can be merged with a single child with significant improvement in both training and test loss. Through analysis of the loss landscape, we find that the loss becomes sufficiently convex early on in training, and, as a consequence, models obtained by averaging multiple children often outperform any individual child.