On the Initialisation of Wide Low-Rank Feedforward Neural Networks

Thiziri Nait Saada, Jared Tanner
1/31/2023
stat.MLcs.LG

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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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Cite this paper

@article{saada2023initialisation,
  title  = {On the Initialisation of Wide Low-Rank Feedforward Neural Networks},
  author = {Thiziri Nait Saada and Jared Tanner},
  year   = {2023},
  eprint = {2301.13710},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2301.13710v1}
}

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