论文标题
使用多项式系统嵌入的复发性神经ODE的实现理论
Realization Theory Of Recurrent Neural ODEs Using Polynomial System Embeddings
论文作者
论文摘要
在本文中，我们表明，可以将复发性（ODE-RNN）和长短期内存（ODE-LSTM）网络的神经颂歌类似物嵌入到多项式系统的类别中。这种嵌入了保留的投入输出行为，并且可以适当地扩展到其他神经架构。然后，我们使用多项式系统的实现理论为输入输出映射提供必要条件，以通过ODE-LSTM实现，并且有足够的条件使此类系统的最小化。这些结果代表了实现复发性神经胶体系结构的第一步，这对于复发性神经ODE的模型还原和学习算法分析有用。
In this paper we show that neural ODE analogs of recurrent (ODE-RNN) and Long Short-Term Memory (ODE-LSTM) networks can be algorithmically embeddeded into the class of polynomial systems. This embedding preserves input-output behavior and can suitably be extended to other neural DE architectures. We then use realization theory of polynomial systems to provide necessary conditions for an input-output map to be realizable by an ODE-LSTM and sufficient conditions for minimality of such systems. These results represent the first steps towards realization theory of recurrent neural ODE architectures, which is is expected be useful for model reduction and learning algorithm analysis of recurrent neural ODEs.
