On the Initialisation of Wide Low-Rank Feedforward Neural Networks

Thiziri Nait Saada; Jared Tanner

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arXiv · 2301.13710

On the Initialisation of Wide Low-Rank Feedforward Neural Networks

Thiziri Nait Saada·Jared Tanner

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Abstract

The edge-of-chaos dynamics of wide randomly initialized low-rank feedforward networks are analyzed. Formulae for the optimal weight and bias variances are extended from the full-rank to low-rank setting and are shown to follow from multiplicative scaling. The principle second order effect, the variance of the input-output Jacobian, is derived and shown to increase as the rank to width ratio decreases. These results inform practitioners how to randomly initialize feedforward networks with a reduced number of learnable parameters while in the same ambient dimension, allowing reductions in the computational cost and memory constraints of the associated network.

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Thiziri Nait Saada, Jared Tanner. 2023-01-31. On the Initialisation of Wide Low-Rank Feedforward Neural Networks. https://arxiv.org/abs/2301.13710

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