Neural Controlled Differential Equations with Quantum Hidden Evolutions

arXiv:2404.19673v1 Announce Type: new
Abstract: We introduce a class of neural controlled differential equation inspired by quantum mechanics. Neural quantum controlled differential equations (NQDEs) model the dynamics by analogue of the Schr\"{o}dinger equation. Specifically, the hidden state represents the wave function, and its collapse leads to an interpretation of the classification probability. We implement and compare the results of four variants of NQDEs on a toy spiral classification problem.

abstract arxiv class classification cs.lg differential differential equation dynamics equation function hidden interpretation leads probability quantum quantum mechanics state type