The Morelli test: art attribution, stylometry and the identity of a molecule, applied to isomer discrimination in MS/MS

TL;DR. Giovanni Morelli attributed paintings by the trivial details (earlobes, fingernails) that copyists never bother to imitate; the mass-spectrometry literature has quietly converged on the same instinct — every widely used similarity score flattens intensities (sqrt, I^0.25, or an entropy-adaptive power) so that minor fragments count more and the base peak counts less, and the one paper that says why (Li et al. 2021) states that "highly abundant MS/MS fragment ions are often shared between structurally similar molecules". But nobody has published the clean Morellian ablation (remove the base peak; keep only peaks < 10 %), so we design it here as a cheap MRR@25 experiment on isomer-rich held-out molecules. The second lesson, from the Rembrandt Research Project's collapse of binary A/B/C verdicts into graded argument, is that a ranker should output calibrated per-candidate confidence (COSMIC-style) rather than a hard top-1.

1. Morelli's method and the MS test

The method, precisely. Giovanni Morelli (1816–1891), a physician writing as "Ivan Lermolieff", published Die Werke italienischer Meister in den Galerien von München, Dresden und Berlin (1880; English 1893). Ginzburg's essay ("Morelli, Freud and Sherlock Holmes: Clues and Scientific Method", History Workshop 9, 1980, pp. 5–36; reprinted as "Clues: Roots of an Evidential Paradigm" in Clues, Myths and the Historical Method, JHU Press 1989; Italian original "Spie" 1978) summarises it: attention "should be diverted from the general impression and main features of a picture" to "minor details, of things like the drawing of the fingernails, of the lobe of an ear, of halos and such unconsidered trifles which the copyist neglects to imitate and yet which every artist executes in his own characteristic way" (quoted via Elden 2026; original in Ginzburg 1980). Zerner's three-level reading (quoted by Polasik 2011 from Ginzburg): (1) general character of the school, (2) the artist's "hand"/technical inimitability, (3) the artist's mannerisms "driven by reflex (senza intenzione)". Level 3 is the discriminator: it is produced unconsciously and so is neither copied by forgers nor varied by the master. Ginzburg's generalisation is the "evidential/conjectural paradigm": inference from marginal, involuntary traces (Freud's symptoms, Holmes's clues, Morelli's pictorial signs). Wikipedia's Morelli article records his own claim of ~80 % accuracy and the Dresden Sleeping Venus → Giorgione attribution as his most famous hit. Edgar Wind's Art and Anarchy (1963) discusses Morelli; I could not open Wind's text, so the often-quoted line about personality being found where effort is weakest is unverified here.

Mapping. Painting → spectrum; attribution → structure identification; the "famous features" copied by forgers → the base peak and the handful of dominant fragments that are dictated by the most labile bond and are shared by every molecule in the compound class; Morelli's earlobes → minor, low-intensity fragments produced by secondary pathways that depend on the exact connectivity. The question is whether MS literature supports that low-intensity peaks are more discriminative between look-alike isomers.

What is actually published (numbers).

Two negative findings matter most. (i) No paper I could open removes the base peak or keeps only peaks below X % and reports the identification-rate change; the field tested powers 0.25–0.6 and stopped. (ii) The only "frequency" weighting in use (Hart 2024) up-weights common m/z values, the opposite of IDF — and it helped. That is precisely Burrows (§3): discriminate with the most frequent tokens, judged against their norm, not with rare tokens.

Caveat on the ranking numbers: library-search differences between weightings in Hart 2024 are ~0.04 in P@1, far smaller than the challenge's candidate-coverage ceiling (~45 % of hidden molecules never reach top-25 at LB 0.417).

2. The Rembrandt Research Project and confidence tiers

The RRP ran 1968–2014 (NWO-funded from 1968; original team resigned 1993; van de Wetering chaired from 1993 and finished the Corpus alone). Volume I (1982, Leiden period to 1631) sorted pictures into A (by Rembrandt), B ("Paintings Rembrandt's authorship of which cannot be positively either accepted or rejected") and C (not by Rembrandt): 42 A, 8 B, 44 C; "eleven previously unchallenged works, approximately twenty per cent of the artist's accepted œuvre, are here rejected" (Brown, Burlington editorial, Nov 1983). The editorial already named the failure mode: the catalogue's own preface admits "A closely knit group tends to feel less doubts or hesitations than an individual. The dilemmas of a team member were occasionally washed away by the cogency of the others" — committee consensus manufactured certainty. The de-attribution wave peaked with Man with the Golden Helmet (Berlin; Jan Kelch, November 1985, "probably painted in 1650 by one of Rembrandt's students"; withdrawn for good 1986, now "circle of Rembrandt") and The Polish Rider (Frick; Bruyn 1984 suggested Willem Drost; a 1998 RRP study argued several hands; Schama 1999 and van de Wetering later defended Rembrandt; the Frick never changed its label). Under van de Wetering, Volume IV (2005, Self-Portraits) abandoned the A/B/C sort for argument-based entries, and the Wallace Collection, which "went into the 20th century with 11 Rembrandts", has one (CSM 1991).

Lesson → MS. A binary A/C verdict on a stylistic (MS2-only) basis is brittle; what survived was graded evidence with explicit arguments. The MS analogue is COSMIC (Hoffmann et al. 2022 Nat Biotechnol 40:411, PMC8926923): raw CSI:FingerID hit scores "do not allow for a satisfactory separation" of correct from incorrect top hits — on CASMI 2016, raw-score ROC AUC for CSI:FingerID, CFM-ID, MAGMa+ and MetFrag lay around 0.40–0.55, i.e. chance, because wrong candidates vastly outnumber right ones. COSMIC's confidence (kernel-density E-value on the candidate score distribution + linear SVM with enforced feature directionality on features such as the top-1/top-2 score gap, Tanimoto among top candidates, log number of candidates, explained intensity; Platt-scaled) reached AUC 0.82 and annotated ~1,400 structures at 10 % FDR where library search gave 52. SIRIUS docs add the calibration caveat: a COSMIC score of 0.64 "approximately corresponded to a 10 % FDR", and the scores "are not probabilities". MassSpecGym (Bushuiev et al. 2024, arXiv 2410.23326) evaluates retrieval with Hit rate@1/5/20 and MCES@1 on ≤256 mass-matched candidates, 231 k spectra / 29 k molecules, MCES-threshold-10 split: MIST 14.64 % / 34.87 % / 59.15 %, fingerprint FFN 2.54 / 7.59 / 20.00, random 0.37 / 2.01 / 8.22 — no calibration metric at all. For MRR@25 the RRP lesson is operational: the quantity to learn is "P(candidate i is correct | the whole ranked list)", because that is what orders the 25 and what chooses between engines per query.

3. Stylometry → a "Delta" for spectra

Mosteller & Wallace (1964, Inference and Disputed Authorship: The Federalist) settled the 12 disputed papers (Nos. 49–58, 62–63) with ~30 non-contextual function words under a Bayesian (Poisson/negative-binomial) model trained on 50 Madison and 49 Hamilton essays: Hamilton used upon 3.24 per 1,000 words, Madison almost never; Madison preferred whilst, Hamilton while; by roughly twice as frequent in Madison; 22 known essays classified perfectly, all 12 disputed → Madison, odds up to 12.6 million to 1 (Priceonomics summary; the book itself not opened). Burrows (2002, Lit Linguist Comput 17:267) made it a distance: take the N (~150) most frequent words of the corpus, z-score each word's relative frequency against the corpus mean/SD, Delta = mean |z_test − z_candidate|; works for texts >1,500 words and narrows candidates at 100 words; fails across genre and across decades of a career.

Function words are frequent, content-free and unconsciously used — the written earlobe. Their MS analogue is the set of fragment m/z (or sub-formula) tokens that appear in a large fraction of spectra of a given adduct/instrument class: common losses (H2O, CO, C2H2O, CH3), low-mass ions (m/z 91.054, 105.070, 147.044, 163.039…). Their presence says nothing (everyone has them); their intensity relative to the population norm might.

Spectral Delta (design). Reference set R = enveda-180 timsTOF spectra, one adduct, CE-merged like the test. Tokenise peaks at 0.01 Da (or SIRIUS/MIST-style sub-formula where assignable). For the N = 150–500 most frequent tokens compute per token the mean μ_t and SD σ_t of sqrt-intensity over spectra in which it is present (and a presence rate p_t). Represent a spectrum by z_t = (sqrt(I_t) − μ_t)/σ_t with a learned fill for absent tokens. Score candidates via (i) a Delta distance to predicted z-profiles (from a fingerprint→z regressor), or simply (ii) feed z-features instead of raw intensities to the spectrum→fingerprint MLP. Contrast with IDF weighting (rare tokens up-weighted) and with Hart's freq^0.25 (common tokens up-weighted, no z-scoring). Nothing like per-token z-scoring against a reference population appears in the sources I opened; Spec2Vec's Word2Vec implicitly learns token co-occurrence but weights each occurrence by I^0.5 only (its min_count vocabulary pruning drops rare tokens — again anti-IDF). MS2Query/Dührkop IDF-style search: not found; marked as open.

4. Technical art history = the MS1/IMS channels

Dendrochronology, pigment anachronism (Prussian blue cannot predate 1704, titanium white 1920) and X-radiography carry no stylistic information and so cannot be fooled by a good imitation of style. The MS equivalents, all independent of the MS2 peak list: precursor exact mass (→ formula; the "panel date"), isotope pattern (elemental composition; the "pigment chemistry"), CCS from TIMS (the X-radiograph: shape under the surface), retention time (provenance). In this challenge only precursor_mz and adduct survive into the test rows; no MS1 isotope cluster, no 1/K0, no RT — the X-ray room is locked, and the forensics worker covers what remains.

5. Timbre: same note, different instrument

Same precursor m/z, different fragment-intensity envelope = same pitch, different overtone envelope. MFCCs compress a spectrum via log-frequency (mel) filterbank + log power + DCT. MS analogues exist but are partial: constant-ppm mass accuracy makes log-m/z bins the natural "mel" scale; DreaMS (Bushuiev et al. 2025 Nat Biotechnol, PMC13090125; 116 M parameters, pretrained on GeMS-A10 of a 42 M-spectrum GeMS-A) encodes each peak as a 2-D continuous token with Fourier (sine/cosine) features of the m/z that "capture both the integer and the floating-point part" — the fractional mass (mass defect) is a chroma/pitch-class feature — and intensity through a shallow feed-forward net; MIST (Goldman 2023 Nat Mach Intell) uses "sinusoidal embeddings of formula count integers". No cepstral (DCT-of-log-binned) descriptor was found in MS ML; PRISM's binning: not verified. One DreaMS detail is a Morelli hazard: masking is "sampled proportionally to corresponding intensities" — pretraining is tuned on the loud peaks.

6. Philosophy: what the metric calls "the same molecule"

Identity in this challenge = InChIKey14 after RDKit 2026.03.3 tautomer canonicalisation: stereo erased, tautomers merged — a Ship of Theseus where every plank-swap below the connectivity level is declared not to matter. COCONUT 2.0 (Chandrasekhar et al. 2025 NAR, 10.1093/nar/gkae1063) holds 695,133 unique structures defined by canonical isomeric SMILES: 539,350 with preserved stereo, 73,563 with undefined absolute stereo, 82,220 without stereocentres, from 63 collections (1.02 M raw entries). LOTUS (Rutz et al. 2022 eLife, PMC9135406) holds 290,000+ unique structures, stereo-aware. No published count of how many collapse under InChIKey14 was found in either paper; the collapse must be computed (RDKit, minutes). The number matters twice: it sizes the true candidate pool, and duplicate InChIKey14 entries in a candidate list silently waste slots in the 25.

Forced analogy: the Morelli test (MRR@25 protocol)

Analogy. Minor fragments (<10 % relative intensity) are the earlobes: the base peak is the famous feature that isomers share; the identity signal lives in the small peaks.

Set. From train, take molecules (InChIKey14) that have at least one other train molecule with the same molecular formula but a different InChIKey14, and that have ≥1 spectrum with instrument_type matching timsTOF/Bruker qTOF, [M+H]+ or [M−H]−; hold out 2,000 such InChIKey14 (novel-molecule split: no spectrum of the held-out InChIKey14 in training), merge multi-CE spectra per molecule as the test does. Candidate pool per query: all COCONUT 2.0 + train structures with the same formula, deduplicated by InChIKey14 (formula-exact, the hard setting; ±10 ppm mass window as a second setting).

Ranker. One architecture throughout: spectrum→fingerprint MLP (Morgan r2 2048 + MACCS), candidates scored by cosine between predicted and true fingerprint, ties broken by predicted probability. Input bins: 0.01 Da over 20–1,000 m/z. Seven inputs: (a) raw normalised intensity; (b) sqrt; (c) log1p(1,000·I)/log1p(1,000); (d) entropy-adaptive power w = 0.25 + 0.25·S for S < 3 (Li 2021), else raw; (e) base peak removed (set to 0), raw otherwise; (f) only peaks < 10 % relative intensity, raw; (g) IDF-weighted I·log(N/df_t) from the training corpus, plus (g′) Hart-style I^0.25·f_t^0.25 and (g″) the Delta z-scores of §3. Five seeds each. Report MRR@25, hit@1, and the isomer-swap rate: fraction of queries whose top-ranked candidate is a same-formula train isomer of the truth.

Expected. If the analogy holds: (b)(c)(d) > (a) by ≥0.01 MRR (the field's consensus), (e) ≈ (a) within seed noise (losing the famous feature costs nothing), (f) retains > 60 % of (a)'s MRR and reduces the swap rate, (g″) > (g′) > (a) ≥ (g). Falsified if (f) falls near the random baseline (≈ mean 1/rank over the pool) and (e) loses ≥ 30 % of MRR while (a)–(d) differ by < 0.005: then intensity flattening is a noise-robustness trick, not a Morellian signal. Partial outcomes are informative too: (e) ≈ (a) but (f) collapses means minor peaks help only together with the mid-intensity backbone.

Where it breaks. Noise peaks are also low-intensity, and their rate differs by ingest_lib (GNPS raw vs curated MassBank vs enveda-180), so (f) and (g) can learn library-of-origin instead of structure; low-intensity centroids have worse mass accuracy (few ions), so earlobes are blurrier than faces — use 20–50 mDa tolerance for peaks < 5 %. There are no forgers in MS: nobody optimises an isomer to mimic another's base peak; the "copying" is physics (shared labile bonds), which is weaker than intent but also uniform, so it may be more exploitable. And Morelli attributed to a hand with hundreds of works; here each hidden molecule has one to sixteen spectra and no training spectrum at all for ~90 % of them — the comparison is to predicted, not observed, earlobes.

Gotchas / what could fool us

1. ms2_normalized_intensities makes the base peak information-free: it is always 1.0, so the "famous feature" carries only its m/z. Any model that upweights intensity is already downweighting the base peak relative to raw counts.
2. Noise floor ≠ earlobe. Library-specific noise thresholds (Li 2021 drops <1 %; MS2DeepScore <0.1 %; GNPS raw none) are a leakage path: small peaks encode ingest_lib. Validate on enveda-180 timsTOF only.
3. Multi-CE merged test spectra change intensity statistics (high-CE fragments appear as small peaks in the merged list). Train transforms on merged spectra of the same CE lists, not single-CE rows.
4. Entropy weighting is per-spectrum adaptive: a 3-peak spectrum gets flattened (w ≈ 0.25–0.5), a 60-peak one does not. Reproducing the paper's gain in an ML input requires the same conditional rule, not a fixed power.
5. Same-formula ≠ isomer under the metric: stereoisomers share InChIKey14. Isomer sets must be built on InChIKey14, not InChIKey.
6. Hart 2024 library-search numbers are read off a figure (~0.48–0.52 P@1); the networking numbers (2,773→3,568 edges) are exact.
7. Hard ablation absent in the literature — any claim that "the literature shows minor peaks discriminate isomers" overstates; it shows that flattening helps and gives a rationale.
8. Committee confidence (RRP preface) = ensemble confidence: engines trained on the same GNPS/MassBank pool agree for shared reasons (sibling project: Chai errors correlated with Boltz). Agreement is not calibration.
9. Raw ranker scores are not probabilities (COSMIC: AUC ≈ 0.4–0.55 for raw scores; SIRIUS: 0.64 ≈ 10 % FDR, "not probabilities"). Per-query calibration features (gap, candidate count) are needed before mixing engines.
10. DreaMS-style pretraining masks proportionally to intensity; fine-tuned embeddings may carry little minor-peak information — test (f) on embeddings too.
11. MassSpecGym's MCES-10 split is stricter than the challenge's novel-molecule split, so its hit rates are pessimistic; conversely an InChIKey14 split with near-identical analogues in train is optimistic.
12. Candidate duplicates: without InChIKey14 deduplication of the pool, stereo variants of one connectivity can fill several of the 25 slots.

Implications for the challenge

1. Run the Morelli ablation first (one MLP, 7–9 inputs, 5 seeds, < 1 GPU-day): it fixes the input transform for every later model and tells us whether minor-peak features deserve engineering.
2. Default input transform: sqrt (Stein & Scott, Horai, Sokolow, Spec2Vec, MS2DeepScore all converge there); test the Li 2021 entropy-adaptive power as a second channel.
3. Build the spectral Delta features (z-scored intensities of the 150–500 most frequent tokens from enveda-180 timsTOF) as an extra ranker; it is cheap and orthogonal to fingerprint prediction.
4. For the ~10 % of hidden molecules with a training spectrum, use weighted modified cosine (Hart freq^0.25 or Sokolow) and Flash-entropy similarity, not plain cosine.
5. Learn a COSMIC-style per-query confidence (top-1/top-2 gap, log candidate count, Tanimoto among top-5, explained intensity) and use it to pick which engine orders the 25 for that query.
6. Compute the InChIKey14 collapse of COCONUT 2.0 and deduplicate the pool before ranking.
7. Add mass-defect (fractional m/z) features — the chroma of a spectrum — to any binned representation; they are what DreaMS's Fourier features capture.
8. Do not plan on orthogonal channels (isotopes, CCS, RT): the test rows do not carry them.

Open questions

• Does any 2024–2026 paper ablate the base peak or minor-peak-only inputs? (Search budget exhausted before this could be checked beyond the sources above.)
• Exact Stein & Scott exponents in the full text (abstract says sqrt and m/z^2–3; Hart cites 0.6/3).
• Bittremieux 2022 intensity preprocessing (bioRxiv rate-limited).
• The Wind 1963 wording on Morelli; Ginzburg's full text.
• Fraction of COCONUT/LOTUS collapsing under InChIKey14; fraction of test-like formulas with > 25 COCONUT isomers.
• Whether Spec2Vec's min_count and Hart's frequency weighting are the whole story, or a z-scored Delta adds signal.

Sources

• Ginzburg C. "Morelli, Freud and Sherlock Holmes: Clues and Scientific Method." History Workshop 9 (1980) 5–36; reprinted in Clues, Myths and the Historical Method, JHU Press 1989. Quoted via Elden S., "The Historian as Detective", progressivegeographies.com, 2 Aug 2026 (https://progressivegeographies.com/2026/08/02/the-historian-as-detective-carlo-ginzburg-and-the-search-for-clues/) and Polasik K., Sensus Historiae II (2011/1) 43–50 (https://sensushistoriae.epigram.eu/english/index.php/sensus/article/viewFile/63/62).
• Giovanni Morelli — Wikipedia (https://en.wikipedia.org/wiki/Giovanni_Morelli).
• Brown C., Editorial "The Rembrandt research project", Burlington Magazine CXXV/968, Nov 1983 (https://www.burlington.org.uk/media/_file/generic/the-rembrandt-research-project-november-1983.pdf).
• Rembrandt Research Project — Wikipedia (https://en.wikipedia.org/wiki/Rembrandt_Research_Project); The Man with the Golden Helmet — Wikipedia (https://en.wikipedia.org/wiki/The_Man_with_the_Golden_Helmet); The Polish Rider — Wikipedia (https://en.wikipedia.org/wiki/The_Polish_Rider); Christian Science Monitor, "Rethinking Rembrandt", 25 Nov 1991 (https://www.csmonitor.com/1991/1125/25101.html); Freedberg D., NYRB 19 Jan 1989 (https://www.nybooks.com/articles/1989/01/19/how-rembrandt-made-it/).
• Stein S.E., Scott D.R. J Am Soc Mass Spectrom 5 (1994) 859–866, doi:10.1016/1044-0305(94)87009-8 (abstract via https://zenodo.org/record/1258660).
• Li Y., Kind T., Folz J. et al. Nat Methods 18 (2021) 1524–1531, doi:10.1038/s41592-021-01331-z (PMC11492813).
• Hart P. et al. "Weighting Low-Intensity MS/MS Ions and m/z Frequency for Spectral Library Annotation", 2024 (https://pmc.ncbi.nlm.nih.gov/articles/PMC10854760).
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• de Jonge N.F. et al. J Cheminform 2024, doi:10.1186/s13321-024-00878-1 (PMC11285329).
• matchms filtering docs (https://matchms.readthedocs.io/en/latest/api/matchms.filtering.html).
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• Hoffmann M.A. et al. COSMIC, Nat Biotechnol 40 (2022) 411–421, doi:10.1038/s41587-021-01045-9 (PMC8926923); SIRIUS 6 docs, methods background (https://v6.docs.sirius-ms.io/methods-background/).
• Bushuiev R. et al. MassSpecGym, arXiv:2410.23326 (https://arxiv.org/html/2410.23326v1).
• Bushuiev R. et al. DreaMS, Nat Biotechnol 2025, doi:10.1038/s41587-025-02663-3 (PMC13090125); README https://github.com/pluskal-lab/DreaMS.
• Goldman S. et al. MIST, Nat Mach Intell 2023, doi:10.1038/s42256-023-00708-3 (README https://github.com/samgoldman97/mist).
• Burrows J. Lit Linguist Comput 17 (2002) 267–287 (https://academic.oup.com/dsh/article/17/3/267/929277).
• Mosteller F., Wallace D.L. 1964 — via Frederick Mosteller, Wikipedia (https://en.wikipedia.org/wiki/Frederick_Mosteller) and Priceonomics, "How Statistics Solved a 175-Year-Old Mystery" (https://priceonomics.com/how-statistics-solved-a-175-year-old-mystery-about/); The Federalist Papers — Wikipedia (disputed Nos. 49–58, 62–63).
• COCONUT 2.0, Nucleic Acids Res 2025, doi:10.1093/nar/gkae1063 (PMC11701633, via Europe PMC full-text XML).
• Rutz A. et al. LOTUS, eLife 2022, doi:10.7554/eLife.70780 (PMC9135406, via Europe PMC full-text XML).
• Not opened (hence unverified): Wind E. Art and Anarchy 1963; Kim et al. optimal-weight-factor paper (exponents taken from Hart 2024's comparison table); PRISM (Enveda) representation.