Solving Constraint-Satisfaction Problems with Distributed Neocortical-Like Neuronal Networks
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Author(s)
Rutishauser, Ueli
Douglas, Rodney J.
Slotine, Jean-Jacques E
Date Issued
April 2018
Journal
Neural Computation
Publisher
MIT Press - Journals
Citation
Rutishauser, Ueli, Jean-Jacques Slotine, and Rodney J. Douglas. “Solving Constraint-Satisfaction Problems with Distributed Neocortical-Like Neuronal Networks.” Neural Computation 30, no. 5 (May 2018): 1359–1393. © 2018 Massachusetts Institute of Technology
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Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1162/NECO_A_01074
