A Neural Architecture Based on Hadamard Designs

Abstract

We describe a simple Hadamard design for neural architecture with an equal number of input and output ele- ments that is both error-tolerant and robust to missing information. The design provides a basis for calculation using a classification scheme based on the Chinese remainder theorem, producing an abstract representation of the physical world. The underlying co-prime arrays can be generated in a simple manner biologically and can evolve into more complex de- signs. The approach differs from previously described neural network constructions in that all connectivity is specified by design, with each correctly wired array producing a single output for each subset of inputs. The wiring is consistent with the "On-Off" schema observed for different senses because only about half the inputs can be active at any one time. The arrays can be tuned through by varying the number of simultaneous inputs required for activation within a range specified by the array size. The architecture is scalable.