The Infinite-Dimensional Nature of Spectroscopy and Why Models Succeed, Fail, and Mislead
Machine learning (ML) models have achieved strikingly high accuracies in spectroscopic classification tasks, often without a clear proof that those models used chemically meaningful features. Existing studies have linked these results to data preprocessing choices, noise sensitivity, and model complexity, but no unifying explanation is available so far. In this work, we show that these phenomena arise naturally from the intrinsic high dimensionality of spectral data. Using a theoretical analysis grounded in the Feldman-Hajek theorem and the concentration of measure, we show that even infinitesimal distributional differences, caused by noise, normalisation, or instrumental artefacts, may b...
| Authors | Umberto Michelucci, Francesca Venturini |
|---|---|
| Primary category | cs.LG |
| Published | 6 April 2026 |
| Last updated at source | 6 April 2026 |
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