A Heterogeneous General Model for Neuromorphic-Inspired Computation

In recent years, both academia and industry have focused on the development of computational architectures inspired by the distributed, adaptive, and event-driven characteristics of biological neural systems, with the aim of reducing the computational cost associated with conventional training approaches [1]. However, a major challenge is the lack of general models and design guidelines for emerging computational systems and hardware. This work introduces a general model based on an input-dependent stochastic weight network, referred to as a substrate. The substrate weights evolve through input-triggered stochastic updates, with correlations between weight coefficients described by a matrix-valued covariance kernel. The proposed framework is implemented using quadratic polynomial weight functions, where the input amplitude controls the magnitude of the stochastic perturbation and a substrate-dependent distance determines the correlation structure. Numerical simulations show that correlations in the stochastic weight evolution significantly affect the system response, suggesting a potential mechanism for neuromorphic-inspired computation without conventional weight training. The aim of this work is to provide a general formulation of the model and identify its main properties and characteristics. 1 H. Jaeger, Towards a generalized theory comprising digital, neuromorphic and unconventional computing, Neuromorphic Comput. Eng., vol. 1, no. 1, p. 012002, Sep. 2021