Towards a Compiler for a Polychronous Wavefront Computer: Programming by Optimization

The incorporation of delay based computing, or polychronicity, into models of neural networks has helped to increase the memory and representational capacity of spiking neural networks. However, the computational advantages of spiking neural networks are largely obviated if they are instantiated on a conventional computer architecture. An alternative architecture that has been advanced is the paradigm of polychronous wavefront computation (PWC). PWC is a framework in which transponders embedded in some kind of wave-conductive medium are used as a simplified representation of computational processes similar to those exhibited by spiking neural networks. Programming such a network amounts to determining the proper geometrical arrangement of transponders within the conductive medium. With this in mind we therefore conjecture that transforming a mathematical function into the corresponding PWC geometry (i.e., compiling the representational code for that function) could best be done by some form of swarm-based optimization within the physical space of potential geometries. We herein test the ability of a swarm algorithms (particle swarm optimization) to select arrangements capable of encoding simple mathematical functions and compare the convergence times against one another as well as against optimization algorithms with less obvious geometrical interpretations (genetic algorithms).