On the computational efficiency of symmetric neural networks

AbstractAn open problem concerning the computational power of neural networks with symmetric weights is solved. It is shown that these networks possess the same computational power as general networks with asymmetric weights; i.e., these networks can compute any recursive function. The computations of these networks can be described as a minimmization process of a certain energy function; it is shown that for uninitialized symmetric neural networks this process presents a Σ2-complete problem