Neural Controlled Differential Equations with Quantum Hidden Evolutions
This work proposes a novel method for classification tasks, but it is incremental as it builds on existing neural controlled differential equations with a quantum twist.
The authors tackled the problem of modeling dynamics using a neural controlled differential equation inspired by quantum mechanics, specifically by analogizing the Schrödinger equation to interpret classification probabilities, and they implemented and compared four variants on a toy spiral classification problem.
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 Schrödinger 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.