Training deep learning neural networks often requires massive amounts of computational ressources. We propose to sequentially monitor network predictions to trigger retraining only if the predictions are no longer valid. This can reduce drastically computational costs and opens a door to green deep learning. Our approach is based on the relationship to projected second moments monitoring, a problem also arising in other areas such as computational finance. Various open-end as well as closed-end monitoring rules are studied under mild assumptions on the training sample and the observations of the monitoring period. The results allow for high-dimensional non-stationary time series data and thus, especially, non-i.i.d. training data. Asymptotics is based on Gaussian approximations of projected partial sums allowing for an estimated projection vector. Estimation of projection vectors is studied both for classical non-$\ell_0$-sparsity as well as under sparsity. For the case that the optimal projection depends on the unknown covariance matrix, hard- and soft-thresholded estimators are studied. The method is analyzed by simulations and supported by synthetic data experiments.

翻译：训练深度学习神经网络通常需要大量计算资源。我们提出通过顺序监测网络预测来仅在预测不再有效时触发重训练，从而显著降低计算成本，为绿色深度学习开辟新途径。该方法基于投影二阶矩监测的关联性，该问题同样出现在计算金融等其他领域。在训练样本与监测期观测值满足温和假设的条件下，我们研究了多种开放式与封闭式监测规则。所得结果适用于高维非平稳时间序列数据，特别是非独立同分布的训练数据。渐近理论基于投影部分和的高斯近似，允许使用估计的投影向量。我们分别针对经典非$\ell_0$稀疏性与稀疏性情形研究了投影向量的估计方法。当最优投影依赖于未知协方差矩阵时，分析了硬阈值与软阈值估计器的性能。通过仿真分析与合成数据实验对方法进行了验证。