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On the Initialisation of Wide Low-Rank Feedforward Neural Networks
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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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LOST: Low-rank and Sparse Pre-training for Large Language Models
LOST pre-trains LLaMA models from 60M to 7B using an SVD-initialized low-rank plus channel-wise sparse decomposition and reports C4 perplexity at or below full-rank models with substantially smaller memory.
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