Simplified state update calculation for fast and accurate digital emulation of CNN dynamics

Abstract

Compared to other one-step integration methods, the 4th-order Runge-Kutta is much more accurate while still consisting in a rather reduced algorithmic structure. However, in terms of the computing power, it is more expensive than others. While the Forward Euler's method updates the state variable with a single evaluation of the derivative, 4th-order Runge-Kutta's method requires four. This is the reason why, when simulation speed is a central matter, e. g. in the digital emulation of CNN dynamics, the speed-accuracy trade-off is resolved in favour of the simpler, though less accurate, methods. A workaround for the computationally intensive calculation of the state variable update can be found for certain CNN models. If a FSR CNN model is employed, where the state variable is not allowed to go beyond the limits of the linear region of the cell output characteristic, the output can be identified with the state. In these conditions, and having linear templates, the update of the state variable can be computed, for a 4th-order Runge-Kutta's method, with a single function evaluation. It means that a digital emulation of the CNN dynamics following this method is as light-weighted as a Forward Euler's integrator, but much more accurate.