Some results on the computational complexity of symmetric connectionist networks

Connectionists models are currently being investigated actively by many researchers in artificial intelligence, information theory and computational neuroscience. These networks have been shown to be applicable to a wide range of domains such as content addressable memories, semantic nets, computer vision, natural language parsing, speech recognition, and approximation schemes for difficult optimization problems. In this paper, we address several basic problems related to the computational complexity of discrete Hopfield nets (connectionist networks with symmetric connections).

[1]  Daniel J. Amit.  Modeling brain function: Introduction , 1989 .

[2]  Mihalis Yannakakis,et al.  On the complexity of local search , 1990, STOC '90.

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4]  Jerome A. Feldman.  Energy and the Behavior of Connectionist Models. , 1985 .

[5]  Noga Alon.  Asynchronous threshold networks , 1985, Graphs Comb..

[6]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[7]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[8]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[9]  Geoffrey E. Hinton,et al.  Massively Parallel Architectures for AI: NETL, Thistle, and Boltzmann Machines , 1983, AAAI.

[10]  Mihalis Yannakakis,et al.  How easy is local search? , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[11]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[12]  Philipp Slusallek,et al.  Introduction to real-time ray tracing , 2005, SIGGRAPH Courses.

[13]  Michael Luby,et al.  Steepest Descent Can Take Exponential Time for Symmetric Connection Networks , 1988, Complex Syst..

[14]  Richard M. Karp,et al.  Reducibility among combinatorial problems" in complexity of computer computations , 1972 .