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 datasets and well-established network architectures. With appropriate hyperparameter tuning, OIALR can surpass conventional training setups, including those of state-of-the-art models.

翻译：本研究通过分析训练过程中神经网络权重的奇异值分解（SVD），深入探讨了网络的学习动态。我们的研究发现，在神经网络多维权重的SVD表示中，正交基会在训练过程中趋于稳定。基于此，我们提出了一种名为“正交性感知自适应低秩训练”（OIALR）的新型训练方法，该方法利用神经网络的内在正交性。OIALR能够无缝集成到现有训练流程中，且精度损失极小，这一优势在多个数据集和经典网络架构上的基准测试中得到了验证。通过适当调整超参数，OIALR甚至能够超越包括最先进模型在内的传统训练方案。