Complete virtual unwrapping and reading of a rolled Herculaneum papyrus

The carbonized papyri from Herculaneum preserve the only large-scale library to survive from classical antiquity, but many unopened rolls remain unread because physical opening risks irreversible damage. X-ray computed microtomography ($μ$CT) and virtual unwrapping offer a non-invasive route to their texts, yet previous work on sealed Herculaneum scrolls has recovered only localized readings or limited surface regions. Here, using high-resolution phase-contrast $μ$CT acquired on the BM18 beamline at the European Synchrotron Radiation Facility (ESRF), together with improved computational unrolling and machine learning, we achieve the complete virtual unwrapping and reading of PHerc. 1667 under explicit coverage and papyrological-review criteria. This makes PHerc. 1667 the first Herculaneum papyrus to be fully digitally unrolled and read for extended scholarly study without physical opening. In PHerc. Paris 4, the optimized scan protocol makes ink directly visible in the tomographic volume, allowing three-dimensional ink segmentation and independent validation of surface-conditioned ink recovery. In PHerc. 139, we recover title and author-attribution evidence identifying the scroll as Philodemus, On Gods, Book 8. These results move virtual unwrapping of the Herculaneum scrolls beyond isolated demonstrations towards a scalable framework for systematic recovery of the still-unopened library.

DNNR: Differential Nearest Neighbors Regression

K-nearest neighbors (KNN) is one of the earliest and most established algorithms in machine learning. For regression tasks, KNN averages the targets within a neighborhood which poses a number of challenges: the neighborhood definition is crucial for the predictive performance as neighbors might be selected based on uninformative features, and averaging does not account for how the function changes locally. We propose a novel method called Differential Nearest Neighbors Regression (DNNR) that addresses both issues simultaneously: during training, DNNR estimates local gradients to scale the features; during inference, it performs an n-th order Taylor approximation using estimated gradients. In a large-scale evaluation on over 250 datasets, we find that DNNR performs comparably to state-of-the-art gradient boosting methods and MLPs while maintaining the simplicity and transparency of KNN. This allows us to derive theoretical error bounds and inspect failures. In times that call for transparency of ML models, DNNR provides a good balance between performance and interpretability.