Neural Controlled Differential Equations with Quantum Hidden Evolutions

TL;DR

This paper introduces Neural Quantum Controlled Differential Equations (NQDEs), a novel model inspired by quantum mechanics, where the hidden state models the wave function and classification is linked to wave function collapse.

Contribution

The paper proposes a new quantum-inspired neural differential equation framework, extending controlled differential equations with quantum mechanics concepts.

Findings

NQDE variants successfully modeled the toy spiral classification problem.

Quantum-inspired dynamics offer a new perspective for neural differential equations.

Comparison of four NQDE variants demonstrates their effectiveness on a synthetic task.

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.