论文标题
动态批处理适应
Dynamic Batch Adaptation
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Current deep learning adaptive optimizer methods adjust the step magnitude of parameter updates by altering the effective learning rate used by each parameter. Motivated by the known inverse relation between batch size and learning rate on update step magnitudes, we introduce a novel training procedure that dynamically decides the dimension and the composition of the current update step. Our procedure, Dynamic Batch Adaptation (DBA) analyzes the gradients of every sample and selects the subset that best improves certain metrics such as gradient variance for each layer of the network. We present results showing DBA significantly improves the speed of model convergence. Additionally, we find that DBA produces an increased improvement over standard optimizers when used in data scarce conditions where, in addition to convergence speed, it also significantly improves model generalization, managing to train a network with a single fully connected hidden layer using only 1% of the MNIST dataset to reach 97.79% test accuracy. In an even more extreme scenario, it manages to reach 97.44% test accuracy using only 10 samples per class. These results represent a relative error rate reduction of 81.78% and 88.07% respectively, compared to the standard optimizers, Stochastic Gradient Descent (SGD) and Adam.
