Quadratic models for understanding catapult dynamics of neural networks

arXiv:2205.11787v3 Announce Type: replace
Abstract: While neural networks can be approximated by linear models as their width increases, certain properties of wide neural networks cannot be captured by linear models. In this work we show that recently proposed Neural Quadratic Models can exhibit the "catapult phase" [Lewkowycz et al. 2020] that arises when training such models with large learning rates. We then empirically show that the behaviour of neural quadratic models parallels that of neural networks in generalization, especially in …

abstract arxiv cs.lg dynamics linear math.oc networks neural networks show stat.ml type understanding while work