ISAAC Newton: Input-based Approximate Curvature for Newton's Method

Felix Petersen, Tobias Sutter, Christian Borgelt, Dongsung Huh, Hilde Kuehne, Yuekai Sun, Oliver Deussen

Abstract: We present ISAAC (Input-baSed ApproximAte Curvature), a novel method that conditions the gradient using selected second-order information and has an asymptotically vanishing computational overhead, assuming a batch size smaller than the number of neurons. We show that it is possible to compute a good conditioner based on only the input to a respective layer without a substantial computational overhead. The proposed method allows effective training even in small-batch stochastic regimes, which makes it competitive to first-order as well as quasi-Newton methods.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2305.00604/code)