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This paper relates parameter distance to gradient breakdown for a broad classof nonlinear compositional functions. The analysis leads to a new distancefunction called deep relative trust and a descent lemma for neural networks.Since the resulting learning rule seems to require little to no learning ratetuning, it may unlock a simpler workflow for training deeper and more complexneural networks. The Python code used in this paper is here:https://github.com/jxbz/fromage.

On the distance between two neural networks and the stability of learning