用分布式类新皮层神经元网络求解约束满足问题
Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks
摘要：
找到满足外部输入和内部表示所施加的约束的行动是决策的核心。我们证明了一些重要的约束满足问题（CSP）的类可以解决由同质的合作竞争模块，具有类似的新皮层的表层中观察到的图案连接组成的网络。赢者通吃模块通过编程神经元稀疏耦合，编程神经元将约束嵌入到同质模块化计算基底上。我们展示了嵌入CSP平面四色图着色，最大独立集和数独的任何实例的规则，并提供数学证明，保证这些图着色问题将收敛到一个解决方案。该网络由非饱和线性阈值神经元组成。它们缺乏正确的饱和度，使得整个网络能够通过经常性激励产生的不稳定动态来探索问题空间。探索的方向是由约束神经元。虽然许多问题可以仅使用线性抑制约束来解决，但当这些负约束通过非线性乘法抑制来实现时，硬问题的网络性能将显着受益。总的来说，我们的研究结果表明，在网络计算的不稳定性，而不是稳定性的重要性，也提供了深入了解神经回路中的双重抑制机制的计算作用。
英文摘要：
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.
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