FINDING APPROXIMATE SOLUTIONS TO NP-HARD PROBLEMS BY NEURAL NETWORKS IS HARD

Finding approximate solutions to hard combinatorial optimization problems by neural networks is a very attractive prospect. Many empirical studies have been done in the area. However, recent research about a neural network model indicates that for any NP-hard problem the existence of a polynomial size network that solves it implies that NP = co-NP, which is contrary to the well-known conjecture that NP not-equal co-NP. This paper shows that even finding approximate solutions with guaranteed performance to some NP-hard problems by a polynomial size network is also impossible unless NP = co-NP.