Solving Optimal Neural Layout by Gibbs Sampling

Neural systems of organisms derive their functionality largely from the numerous and intricate connections between individual components. These connections are costly and have been refined via evolutionary pressure that acts to maximize their functionality while minimizing the associated cost. This tradeoff can be formulated as a constrained optimization problem. In this paper, we use simulated annealing, implemented through Gibbs sampling, to investigate the minimal cost placement of individual components in neural systems. We show that given the constraints and the presumed cost function associated with the neural interconnections, we can find the configuration corresponding to the minimal cost. We restrict the mechanisms considered to those involving incremental improvement through local interactions since real neural systems are likely to be subject to such constraints. By adjusting the cost function and comparing with the actual configuration in neural systems, we can infer the actual cost function associated with the connections used by nature. This provides a powerful tool to biologists for investigating the configurations of neural systems.