论文标题
部分可观测时空混沌系统的无模型预测
Visualizing Deep Neural Networks with Topographic Activation Maps
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。
Machine Learning with Deep Neural Networks (DNNs) has become a successful tool in solving tasks across various fields of application. However, the complexity of DNNs makes it difficult to understand how they solve their learned task. To improve the explainability of DNNs, we adapt methods from neuroscience that analyze complex and opaque systems. Here, we draw inspiration from how neuroscience uses topographic maps to visualize brain activity. To also visualize activations of neurons in DNNs as topographic maps, we research techniques to layout the neurons in a two-dimensional space such that neurons of similar activity are in the vicinity of each other. In this work, we introduce and compare methods to obtain a topographic layout of neurons in a DNN layer. Moreover, we demonstrate how to use topographic activation maps to identify errors or encoded biases and to visualize training processes. Our novel visualization technique improves the transparency of DNN-based decision-making systems and is interpretable without expert knowledge in Machine Learning.
