Neural units with time-dependent functionality

TL;DR

This paper demonstrates that underdamped harmonic oscillators can perform multiple nonlinear computations at different times within a single dynamical trajectory, enabling multifunctional temporal processing.

Contribution

It introduces a novel approach where a single oscillator or a set of oscillators can execute various logic and classification tasks through time-dependent dynamics.

Findings

Oscillators can solve XOR and other nonlinear problems.

Single oscillators can emulate all elementary logic gates and perform binary addition.

Sets of oscillators can carry out multiple analog-to-digital conversions.

Abstract

We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude of an oscillator whose inputs influence its frequency. The activity of the oscillator at fixed time is a nonmonotonic function of its inputs, and so it can solve problems such as XOR that are not linearly separable. The activity of the oscillator at fixed input is a nonmonotonic function of time, and so it is multifunctional in a temporal sense, able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. We show that a single oscillator, observed at different times, can act as all of the elementary logic gates and can perform binary addition, the latter usually implemented in hardware using 5 logic gates. We show that a set of $n$ oscillators, observed at different times, can perform an arbitrary number of analog-to-$n$-bit digital conversions. We also show that oscillators can be trained by gradient descent to perform distinct classification tasks at distinct times. Computing with time-dependent functionality can be done in or out of equilibrium, and suggests a way of reducing the number of parameters or devices required to do nonlinear computations.