Frank and Frank (Leonardo 54(6), 2021) trained convolutional neural networks (CNNs) on about a dozen securely attributed Leonardo da Vinci paintings and applied them to Salvator Mundi, the painting sold at Christie's in 2017 for a record price: the face received high Leonardo probability (overall image probabilities 0.74 and 0.62 for the best models) while the blessing hand and parts of the background were classified as not Leonardo. The authors treated their results as provisional, and the study leaves unresolved the scientific question of whether such tile-level attributions carry valid evidential weight, given a tiny heterogeneous training corpus, the painting's extensive restoration and overpainting, unquantified sensitivity to curatorial and architectural choices, and the absence of any calibration between model probabilities and art-historical decisions. The problem is whether controlled validation can establish a calibrated account of whether CNN-based attribution can adjudicate the whole/partial/none Leonardo authorship of Salvator Mundi, or whether its outputs are dominated by restoration, corpus-construction, and pipeline artifacts.

Background

Attribution in art history — deciding who painted a given work — has traditionally been settled by connoisseurship (expert judgment of style and technique), provenance research (documented ownership history), and technical analysis of materials. For Leonardo da Vinci (1452–1519) this is exceptionally hard: experts accept fewer than twenty paintings as attributable in whole or large part, spanning portraits and several distinct religious genres, and excluding all questioned attributions would leave fewer than half a dozen images. Leonardo also ran a busy workshop whose assistants' contributions are poorly understood, so 'authorship' may be partial rather than binary. Salvator Mundi, rediscovered in 2005 and heavily restored by conservator Dianne Modestini, was accepted as an original by some scholars (Kemp, Simon, and Dalivalle 2019), rejected by others (Hope 2020), and given a third reading — the paper quotes a curator's hypothesis that much of the surface may be by Leonardo's pupil Boltraffio with specific passages (the blessing hand, sleeve, and orb) by Leonardo himself, against the opposite view that the blessing hand's pallid flesh tones are workshop-like. The painting's whereabouts have been unknown since its 2017 sale.

Frank and Frank's study (published in Leonardo 54(6), 2021; arXiv:2005.10600) introduced a computational angle. A convolutional neural network (CNN) is a deep learning architecture that learns visual features directly from image pixels; their 'Salient Slices' method (Neural Computation 32, 2020) splits a high-resolution painting into small tiles, keeps only tiles whose image entropy (roughly, visual diversity) matches the source image, and trains a CNN to classify tiles as by the studied artist or by others. Because one painting yields hundreds of overlapping tiles, the method can train on very few source images — at the price of heavy redundancy. Trained on 12 Leonardo paintings against dozens of comparative works by Leonardo's teacher, pupils, contemporaries, and imitators, their best models reached high in-sample accuracy, consistently classified known workshop and formerly misattributed works (Seated Bacchus, Isleworth Mona Lisa) as not Leonardo, and produced spatial probability maps for Salvator Mundi: the face strongly Leonardo, the blessing hand and part of the background not. The overall probabilities the models assigned to Salvator Mundi correlated almost linearly (R2=0.81R^2 = 0.81) with each model's false-positive rate — the more lenient the model, the more of the painting it attributed to Leonardo.

The authors explicitly treated these results as provisional. Only two Leonardo paintings were available for testing; results varied across curated versus randomly split training sets and across 5- versus 8-layer architectures; the blue (not-Leonardo) regions coincide with the most heavily restored parts of the painting, so restoration and workshop authorship are confounded; and the Isleworth Mona Lisa analysis was distorted by poor image quality. Because the paper's Salvator Mundi discussion centers on the disputed partial-attribution hypothesis, a further question arises that the probability maps do not by themselves answer: what combination of subregion assignments would count as 'partial by Leonardo'. The same open questions recur field-wide: adjacent studies of machine-learning authentication (Vision Transformers — transformer-based neural networks that classify an image from a sequence of patches — for van Gogh; one-class methods — classifiers trained only on the target artist's works — for Goya with X-ray radiographs; and forger-specific forgery detection) still report accuracy figures without calibration to art-historical thresholds or controls for restoration and image-acquisition artifacts. The only other scientific study of Salvator Mundi, an inverse rendering analysis — reconstructing the lighting of a depicted scene from the image itself — of the orb's illumination effects (Liang, Zhao, and Goodrich, Leonardo 53(4), 2020), addresses the painting's optics rather than its authorship. What is missing is precisely what Frank and Frank's study could not supply: a validated, calibrated account of whether this kind of computational attribution can, in principle and for this painting, decide between wholly Leonardo, partly Leonardo with workshop, and not Leonardo.

Problem Statement

Determine whether tile-level CNN attribution of the type applied to Salvator Mundi can provide valid, calibrated evidence on the painting's authorship modality — wholly by Leonardo, partly by Leonardo with workshop participation, or not by Leonardo — and, if it can, what that evidence supports for this painting. Resolving this question involves three linked aspects: (1) Restoration bias: quantitatively measure how restoration, overpainting, damage, and image-acquisition quality affect CNN subregion probability maps and whole-image probabilities, and in particular determine whether the low Leonardo probabilities assigned to the blessing hand and background of Salvator Mundi survive once conservation state is controlled for, or whether they are artifacts of the extensive repainting of exactly those areas. (2) Validation and calibration under extreme data scarcity: design a validation methodology for attribution models trained on the tiny, heterogeneous corpus of securely attributed Leonardo paintings (about 12 training images in the Frank and Frank study) whose out-of-sample performance and uncertainty estimates are demonstrably not artifacts of curatorial set construction, tile-overlap augmentation, or architecture choice, and map model outputs onto calibrated error rates with respect to art-historical decision thresholds; the study's reported R2=0.81R^2 = 0.81 relationship between a model's false-positive rate and the probability it assigns to Salvator Mundi illustrates why such calibration is needed. (3) Mixed-authorship semantics: specify, and test on controlled cases, what calibrated subregion probability pattern would discriminate partial authorship by Leonardo plus workshop from whole or none, in terms defensible to both computer-vision and art-historical standards. The question is resolved either by a validated, calibrated methodology applied to the publicly available Salvator Mundi imagery that addresses all three aspects (1)–(3), or by a controlled demonstration that such attributions are dominated by restoration, corpus-construction, and pipeline confounds and therefore cannot adjudicate the authorship question.

References

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