A property of a recurrent neural network (RNN) is called \emph{extensional} if, loosely speaking, it is a property of the function computed by the RNN rather than a property of the RNN algorithm. Many properties of interest in RNNs are extensional, for example, robustness against small changes of input or good clustering of inputs. Given an RNN, it is natural to ask whether it has such a property. We give a negative answer to the general question about testing extensional properties of RNNs. Namely, we prove a version of Rice's theorem for RNNs: any nontrivial extensional property of RNNs is undecidable.

翻译：递归神经网络（RNN）的一个性质被称为\emph{扩展性质}，粗略地说，如果它是RNN所计算函数的性质，而非RNN算法本身的性质。RNN中许多重要性质都是扩展性的，例如对输入微小变化的鲁棒性或输入的良好聚类性。给定一个RNN，很自然地会询问其是否具有此类性质。我们对测试RNN扩展性质的一般性问题给出了否定答案。具体而言，我们证明了RNN的莱斯定理版本：任何非平凡的RNN扩展性质都是不可判定的。