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".

Problems in dimension three with rotations around combinations of axes in multiples of 90 degrees are of particular interest in many natural applications. Let us fix the order of six such allowable rotations in dimension three arbitrarily and define: The Container Loading Problem (CLP): Given dimensions of a large box ("container") x, y, z 0 and dimensions of n small boxes D

We prove that the so called "loading problem" for (recurrent) neural networks is unsolvable. This extends several results which already demonstrated that training and related design problems for neural networks are (at least) NPcomplete. Our result also implies that it is impossible to find or to formulate a universal training algorithm, which for any neural 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.

We prove that the so called "loading problem" for (recurrent) neural networks isunsolvable. This extends several results which already demonstrated thattraining and related design problems for neural networks are (at least) NPcomplete. Our result also implies that it is impossible to find or to formulate a universal training algorithm, which for any neural networkarchitecture 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.