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.

翻译：在本文中,我们展示了经常性网络(ODE-RNN)和长期短期内存网络(ODE-LSTM)的神经代号模拟可按逻辑嵌入多边系统类别。这种嵌入保存了输入输出行为,并可以适当扩展到其他神经设计。然后,我们利用多元系统实现理论为输入-输出图提供必要的条件,以通过ODE-LNNM实现输入-输出图,并为这类系统的最低化提供足够条件。这些结果代表了实现经常性神经代号结构理论的第一步,预计这对经常性神经代号的模型减少和学习算法分析有用。