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：本研究通过分析神经网络权重在训练过程中的奇异值分解，探索了其学习动态。我们的研究发现，多维权重SVD表示中的正交基在训练过程中趋于稳定。基于这一发现，我们提出了正交性感知自适应低秩训练方法——一种利用神经网络固有正交性的新型训练方法。OIALR能够以最小精度损失无缝集成到现有训练流程中，这一点通过在多个数据集和成熟网络架构上的基准测试得到了验证。通过适当的超参数调优，OIALR能够超越传统训练方案，包括当前最先进模型的训练配置。