Fundamental Limit on Network Size Scaling of Oscillatory Neural Networks due to PrMnO3 based Oscillator Phase Noise

Abstract

Oscillatory Neural Networks (ONNs) have been reported to solve graphical constraint optimization and pattern recognition problems in a time efficient manner [1], [2]. In particular, the vertex coloring problem can be solved using a capacitively coupled network of relaxation oscillators of the same frequency $(f_{i})$ (Fig. 1) [1]. The critical information for the accuracy is governed by the permutation (ordering on phase circle) of the oscillator settling phases. Compact device level oscillators have been proposed to enable densely packed arrays for large network sizes [3]–[6]. These are based on physics like insulator to metal transitions (IMT), volatile conductive filament and Joule heating. Hence, they are prone to phase variability during operation. The impact of phase variability in relaxation oscillators on the network solutions for ONNs has not yet been demonstrated. Here, we study the cycle to cycle variability (C2CV) in transient Joule heating based PrMnO 3 (PMO) device [4]. Further, we demonstrate the effect of C2CV on the temporal distribution of the settling phases, i.e. the phase noise, in coupled oscillator networks. We show that the presence of phase noise in a finite output solution space (360°) puts a fundamental limit on the maximum size of the graphical problem for which the permutation of the output phases can be read-off reliably (Fig. 2).