# Quantum Dynamics of Machine Learning

arXiv: https://arxiv.org/abs/2407.19890 · HTML: https://mlsanity.com/paper/2407.19890/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 7 Jul 2024.

## Builds on (most cited first, 3 of 3)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Multi-scale Diffusion Denoised Smoothing](https://mlsanity.com/paper/2310.16779/) (2023)

## Abstract (arXiv)

The quantum dynamic equation (QDE) of machine learning is obtained based on Schr"odinger equation and potential energy equivalence relationship. Through Wick rotation, the relationship between quantum dynamics and thermodynamics is also established in this paper. This equation reformulates the iterative process of machine learning into a time-dependent partial differential equation with a clear mathematical structure, offering a theoretical framework for investigating machine learning iterations through quantum and mathematical theories. Within this framework, the fundamental iterative process, the diffusion model, and the Softmax and Sigmoid functions are examined, validating the proposed quantum dynamics equations. This approach not only presents a rigorous theoretical foundation for machine learning but also holds promise for supporting the implementation of machine learning algorithms on quantum computers.