论文标题
部分可观测时空混沌系统的无模型预测
Implicit Feature Decoupling with Depthwise Quantization
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。
Quantization has been applied to multiple domains in Deep Neural Networks (DNNs). We propose Depthwise Quantization (DQ) where $\textit{quantization}$ is applied to a decomposed sub-tensor along the $\textit{feature axis}$ of weak statistical dependence. The feature decomposition leads to an exponential increase in $\textit{representation capacity}$ with a linear increase in memory and parameter cost. In addition, DQ can be directly applied to existing encoder-decoder frameworks without modification of the DNN architecture. We use DQ in the context of Hierarchical Auto-Encoder and train end-to-end on an image feature representation. We provide an analysis on cross-correlation between spatial and channel features and we propose a decomposition of the image feature representation along the channel axis. The improved performance of the depthwise operator is due to the increased representation capacity from implicit feature decoupling. We evaluate DQ on the likelihood estimation task, where it outperforms the previous state-of-the-art on CIFAR-10, ImageNet-32 and ImageNet-64. We progressively train with increasing image size a single hierarchical model that uses 69% less parameters and has a faster convergence than the previous works.
