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Neural Comput. 2018 May;30(5):1359-1393. doi: 10.1162/NECO_a_01074. Epub 2018 Mar 22.

Solving Constraint-Satisfaction Problems with Distributed Neocortical-Like Neuronal Networks.

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Computation and Neural Systems, Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125, U.S.A., and Cedars-Sinai Medical Center, Departments of Neurosurgery, Neurology and Biomedical Sciences, Los Angeles, CA 90048, U.S.A.
Nonlinear Systems Laboratory, Department of Mechanical Engineering and Department of Brain and Cognitive Sciences, MIT, Cambridge, MA 02139, U.S.A.
Institute of Neuroinformatics, University and ETH Zurich, Zurich 8057, Switzerland


Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by networks composed of homogeneous cooperative-competitive modules that have connectivity similar to motifs observed in the superficial layers of neocortex. The winner-take-all modules are sparsely coupled by programming neurons that embed the constraints onto the otherwise homogeneous modular computational substrate. We show rules that embed any instance of the CSP's planar four-color graph coloring, maximum independent set, and sudoku on this substrate and provide mathematical proofs that guarantee these graph coloring problems will convergence to a solution. The network is composed of nonsaturating linear threshold neurons. Their lack of right saturation allows the overall network to explore the problem space driven through the unstable dynamics generated by recurrent excitation. The direction of exploration is steered by the constraint neurons. While many problems can be solved using only linear inhibitory constraints, network performance on hard problems benefits significantly when these negative constraints are implemented by nonlinear multiplicative inhibition. Overall, our results demonstrate the importance of instability rather than stability in network computation and offer insight into the computational role of dual inhibitory mechanisms in neural circuits.

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