# Quantum Harmonic Analysis and the Structure in Data: Augmentation

arXiv: https://arxiv.org/abs/2509.19474 · HTML: https://mlsanity.com/paper/2509.19474/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 0 of its 7 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Abstract (arXiv)

In this short note, we study the impact of data augmentation on the smoothness of principal components of high-dimensional datasets. Using tools from quantum harmonic analysis, we show that eigenfunctions of operators corresponding to augmented data sets lie in the modulation space M1(ℝd), guaranteeing smoothness and continuity. Numerical examples on synthetic and audio data confirm the theoretical findings. While interesting in itself, the results suggest that manifold learning and feature extraction algorithms can benefit from systematic and informed augmentation principles.