Harnessing Orthogonality to Train Low-Rank Neural Networks

arXiv:2401.08505v2 Announce Type: replace
Abstract: This study explores the learning dynamics of neural networks by analyzing the singular value decomposition (SVD) of their weights throughout training. Our investigation reveals that an orthogonal basis within each multidimensional weight's SVD representation stabilizes during training. Building upon this, we introduce Orthogonality-Informed Adaptive Low-Rank (OIALR) training, a novel training method exploiting the intrinsic orthogonality of neural networks. OIALR seamlessly integrates into existing training workflows with minimal accuracy loss, as demonstrated by benchmarking on various …

abstract arxiv building cs.ai cs.lg dynamics investigation low multidimensional networks neural networks representation singular study svd train training type value