Asymptotic Edge of Chaos as Guiding Principle for Neural Network Training

Lin Zhang, Ling Feng, Kan Chen, Choy Heng Lai
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引用次数: 0

Abstract

It has been recently demonstrated that optimal neural networks operate near the asymptotic edge of chaos for state-of-the-art feed-forward neural networks, where its generalization power is maximal due to the highest number of asymptotic metastable states. However, how to leverage this principle to improve the model training process remains open. Here, by mapping the model evolution during training to the phase diagram in the classic analytic result of Sherrington–Kirkpatrick model in spin glasses, we illustrate on a simple neural network model that one can provide principled training of the network without manually tuning the training hyper-parameters. In particular, we provide a semi-analytical method to set the optimal weight decay strength, such that the model will converge toward the edge of chaos during training. Consequently, such hyper-parameter setting leads the model to achieve the highest test accuracy. Another benefit for restricting the model at the edge of chaos is its robustness against the common practical problem of label noise, as we find that it automatically avoids fitting the shuffled labels in the training samples while maintaining good fitting to the correct labels, providing simple means of achieving good performance on noisy labels without any additional treatment.
混沌的渐近边作为神经网络训练的指导原则
最近的研究表明,最优神经网络运行在最先进的前馈神经网络的混沌渐近边缘附近,由于其渐近亚稳态的数量最多,其泛化能力最大。然而,如何利用这一原则来改进模型训练过程仍然是开放的。在这里,通过将模型在训练过程中的演化映射到经典的自旋玻璃中的Sherrington-Kirkpatrick模型分析结果中的相图,我们在一个简单的神经网络模型上说明,人们可以在不手动调整训练超参数的情况下对网络进行原则性训练。特别地,我们提供了一种半解析的方法来设置最优权值衰减强度,使模型在训练过程中向混沌边缘收敛。因此,这种超参数设置使模型达到最高的测试精度。将模型限制在混沌边缘的另一个好处是它对标签噪声这一常见实际问题的鲁棒性,因为我们发现它会自动避免拟合训练样本中被混淆的标签,同时保持对正确标签的良好拟合,提供了在有噪声标签上获得良好性能的简单方法,而无需任何额外的处理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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