Beta调度：来自临界阻尼的动量作为神经网络训练的诊断和修正工具

Standard neural network training employs a constant momentum (typically 0.9), a convention that dates back to 1964 with limited theoretical justification for its optimality. A time-varying momentum schedule is derived from the critically damped harmonic oscillator: mu(t) = 1 - 2*sqrt(alpha(t)), where alpha(t) is the current learning rate. This beta-schedule requires no additional free parameters beyond the existing learning rate schedule. On ResNet-18/CIFAR-10, beta-scheduling achieves 1.9 times faster convergence to 90% accuracy compared to constant momentum. More importantly, the per-layer gradient attribution under this schedule produces a cross-optimizer invariant diagnostic: the same three problem layers are identified regardless of the optimizer used for training.