Scaling Laws for the Principled Design, Initialization, and Preconditioning of ReLU Networks
Abstract In this work, we describe a set of rules for the design and initialization of well-conditioned neural networks, guided by the goal of naturally balancing the diagonal blocks of the Hessian at the start of training. We show how our measure of conditioning of a block relates to another natural measure of conditioning, the ratio of weight gradients to the weights. We prove that for a ReLU-based deep multilayer perceptron, a simple initialization scheme using the geometric mean of the fan-in and fan-out satisfies our scaling rule. For more sophisticated architectures, we show how our scaling principle can be used to guide design choices to produce well-conditioned neural networks, reducing guess-work.
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