Matrix multiplication by neuromorphic computing

Abstract

With increased requirements of processing power in many computing applications, and the consequent huge increases in resource costs including electrical power consumption, there is a push to find alternative computing architectures that achieve high speeds but require less resources. One direction that shows promise is brain-inspired neuromorphic computing; it has thus become an active area of research. Much of the current work in neuromorphic computing targets its applicability in solving machine learning and pattern recognition problems. We push this boundary to show the possibility of using neuromorphic architectures to solve matrix multiplication, a core mathematical task pertinent to a host of engineering problems. We use a neuromorphic simulator to present a solution to matrix multiplication that demonstrates a significant performance improvement, both in terms of processing time and intermediate storage over existing approaches. The basic principle of proposed method is operating on a single intermediate transformation matrix that is flattened into an ensemble array represented as a neural node that is operated on. This is an optimisation over memory and time over the existing approach which uses two sparse intermediate matrices. Theoretical and experimental analysis indicates the importance of the proper choice of neuromorphic parameters, specifically the number of neurons and radius of the ensemble along with the dimensions and elements in input matrices has on accuracy, time and memory. We indicate an approach to compute the proper choice of neuromorphic resources given relevant benchmark constraints.