On the Non-Existence of a Universal Learning Algorithm for Recurrent Neural Networks

We prove that the so called "loading problem" for (recurrent) neural net(cid:173) works is unsolvable. This extends several results which already demon(cid:173) strated that training and related design problems for neural networks are (at least) NP-complete. Our result also implies that it is impossible to find or to formulate a universal training algorithm, which for any neu(cid:173) ral network architecture could determine a correct set of weights. For the simple proof of this, we will just show that the loading problem is equivalent to "Hilbert's tenth problem" which is known to be unsolvable. It seems that there are relatively few commonly accepted general formal definitions of the notion of a "neural network".