On the distance between two neural networks and the stability of learning
This paper relates parameter distance to gradient breakdown for a broad class of nonlinear compositional functions. The analysis leads to a new distance function called deep relative trust and a descent lemma for neural networks. Since the resulting learning rule seems to require little to no learning rate tuning, it may unlock a simpler workflow for training deeper and more complex neural networks. The Python code used in this paper is here: https://github.com/jxbz/fromage
The authors would like to thank Dillon Huff, Jeffrey Pennington and Florian Schaefer for useful conversations. They made heavy use of a codebase built by Jiahui Yu. They are much obliged to Sivakumar Arayandi Thottakara, Jan Kautz, Sabu Nadarajan and Nithya Natesan for infrastructure support. JB is supported by an NVIDIA fellowship.
Accepted Version - 2002.03432.pdf