Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks

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 CSPs 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 non-saturating 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 non-linear multiplicative inhibition. Overall, our results demonstrate the importance of instability rather than stability in network computation, and also offer insight into the computational role of dual inhibitory mechanisms in neural circuits.Comment: Accepted manuscript, in press, Neural Computation (2018

Solving Sudoku with Ant Colony Optimization

In this paper we present a new algorithm for the well-known and computationally-challenging Sudoku puzzle game. Our Ant Colony Optimization-based method significantly out-performs the state-of-the-art algorithm on the hardest, large instances of Sudoku. We provide evidence that – compared to traditional backtracking methods – our algorithm offers a much more efficient search of the solution space, and demonstrate the utility of a novel anti-stagnation operator. This work lays the foundation for future work on a general-purpose puzzle solver, and establishes Japanese pencil puzzles as a suitable platform for benchmarking a wide range of algorithms