论文标题
学习非线性系统的复发神经网模型
Learning Recurrent Neural Net Models of Nonlinear Systems
论文作者
论文摘要
我们考虑以下学习问题：给定未知非线性系统产生的输入和输出信号的样本对（假定为因果或时间不变），我们希望找到具有近似于高度的I/O行为具有高度宽容的I/O行为的连续时间复发性神经网。利用与给定有限顺序相匹配的匹配衍生产品有关的早期工作，我们以熟悉的系统理论语言重新制定了学习问题，并根据学识渊博的模型的SUP-NORM风险获得定量保证，以神经元的数量，样本大小，衍生物的数量，匹配的衍生物数量以及匹配的衍生物数量以及输入属性的定期性能，以及输入属性，输出属性，以及输出的定期属性。
We consider the following learning problem: Given sample pairs of input and output signals generated by an unknown nonlinear system (which is not assumed to be causal or time-invariant), we wish to find a continuous-time recurrent neural net with hyperbolic tangent activation function that approximately reproduces the underlying i/o behavior with high confidence. Leveraging earlier work concerned with matching output derivatives up to a given finite order, we reformulate the learning problem in familiar system-theoretic language and derive quantitative guarantees on the sup-norm risk of the learned model in terms of the number of neurons, the sample size, the number of derivatives being matched, and the regularity properties of the inputs, the outputs, and the unknown i/o map.
