Urdatorn/tereus-imputation

Tereus imputations

Machine restorations of the lacunae in P.Oxy. 3013, the papyrus of Sophocles' lost Tereus. The papyrus preserves the left-hand part of vv. 13-29; the rest of each of those seventeen verses is lost. Verses 1-12, also transmitted by Stobaeus, survive whole and are the fixed context for every restoration; they are stored once in context.json rather than repeated on every row.

These are imputations, not proposed readings. The point of the collection is coverage and the spread between completions, in the sense of Rubin's multiple imputation: an analysis should be run on many of them and the between-imputation variance reported, rather than a single reading being chosen. Nothing here has been endorsed by an editor.

Configurations

stoicheia — 410,000 complete restorations of vv. 13-29

One row is one whole imputation: all seventeen lacunae filled together, in the context of the surviving letters of the entire passage. Produced by Stoicheia, a character-level masked-diffusion encoder, by iterative confidence-based unmasking; gap widths are drawn from the Sophoclean trimeter length prior, truncated to the editors' estimate of each gap. Every verse is then scanned by Stoicheia-meter and tested against the iambic trimeter template.

run	rows	temperature	verse-end boundaries given	seed
t10	10,000	1.0	no	0
t065_seed0	10,000	0.65	yes	0
t065_seed1	90,000	0.65	yes	1
t065_seed2	100,000	0.65	yes	2
t065_seed3	100,000	0.65	yes	3
t065_seed4	100,000	0.65	yes	4

Columns: run, conjecture_id, temperature, seed, verse_boundaries; widths, fills, gap_logp, gap_mean_logp (17 each, the restored part only); verses, scansion, bracketed, is_trimeter (17 each, whole verses 13-29); logp_total, n_verses_trimeter, all_trimeter.

Scansion is one symbol per syllable, - heavy, u light, X verse-final. The trimeter test allows resolution of every long except the last and treats the anceps freely; it accepts 1,135 of the 1,139 distinct scansions of Aeschylus in the Hypotactic corpus. Verse 29 is scanned with ἧμιν, the short-iota prosody Sophocles uses, imposed before scansion.

candidates — 241,916 candidate fills, one verse at a time

One row is one distinct fill of one verse, from a separate pipeline with its own restorer, four search chains, a verse-tuned LLM proposer and a lexicon-constrained enumeration, already filtered for metre and ranked by five scores. Columns carry that pipeline's own judgements: lp_uni (restorer log-probability per letter), bits_trag/style_trag/style_soph/lex_trag/lex_gen (character 6-gram stylometry), llm_*, rank* including an LLM judge's verdict, translation and note, plus scansion, metre, caesura, porson_ok, word_status, found_by and chains.

accented is the verse with diacritics. accent_by records which pass supplied them: paper for the 117,250 the source pipeline accented, stoicheia_here for the 124,666 completed for this release with Stoicheia-doc_clean, predicting the fill's diacritics only and keeping the editors' accents on the visible prefix. The two passes agree on every letter but on only about a quarter of whole verses; scoring 20,000 verses both ways moves a classifier's argmax on 8.5 % of them, with a median posterior change of zero and a 95th percentile of 0.81. Treat accent_by as a covariate, or restrict to paper for an accent-uniform subset.

style_vectors — 5,826,792 verses as 768-d KainoBERT states

Every distinct verse in this dataset, plus the reference corpora, encoded once by Urdatorn/KainoBERT, the un-audited ModernBERT-base masked language model for Ancient Greek. The vector is the mean-pooled last hidden state, stored exactly as float16. There is no classification head and no author verdict here: the vector is an observable one can write a likelihood for.

Text is encoded on the model's own pretraining surface, lowercased and depunctuated with polytonic marks kept, and iota adscript normalised to subscript first (Diggle's Euripides, the papyrus and the restorers write adscript; the stylometric convention is subscript); surface is the string actually fed to the model and text the original.

sources	rows	what it is
corpus	27,506	real iambic trimeters: Aeschylus 1,779, Sophocles 7,545, Euripides 18,182
intact	12	vv. 1-12 of the papyrus, genuine Sophocles
henry	17	W. B. Henry's supplements to vv. 13-29
conjecture	5,557,357	distinct verses from the stoicheia configuration, all six runs
candidate	241,916	distinct verses from the candidates configuration

row is the position in the matrix and is stable within a release; authors is filled for corpus rows, verses for rows tied to a place in the papyrus. Thirteen surfaces occur in more than one source, so sources is a list. Rows are deduplicated on surface, so two verses that differ only in punctuation or capitalisation share a row and text is the first form seen.

What this space is and is not good for, measured on held-out corpus lines:

• A weak author discriminator. The three author centroids have cosine similarity 0.993, and a linear discriminant over 200 principal components reaches macro-F1 0.517 against a 0.660 majority-accuracy baseline, with Aeschylus at F1 0.202. Do not use it to attribute a verse.
• A usable model of what a tragic trimeter looks like. Real Sophoclean lines sit at a mean Mahalanobis distance of 51.7 from the Sophoclean centroid, the twelve intact verses at 47.7 and Henry's seventeen at 52.1, all well inside the spread.
• Effectively high-dimensional. 344 components carry 90 % of the variance and the effective rank is about 335, so aggressive reduction destroys signal.
• Covariance should be shared, not per-author. An inverse-Wishart prior centred on the pooled within-author covariance beats per-author covariances for all three, by 312 nats per line for Aeschylus, and the chosen prior strength exceeds every author's line count.

Note that this encoder has read the whole Ancient Greek corpus, including the plays the reference rows come from and the Stobaeus transmission of vv. 1-12. It has not read the supplements to vv. 13-29, which are absent from its training material. Every corpus row is therefore familiar to the model and every conjectural row is novel, an asymmetry to keep in mind when fitting a likelihood on the former and applying it to the latter.

ll_verses and ll_imputations — the likelihood table for a Bayesian analysis

The per-verse evidence under each tragedian, ready to be summed into a Stan data block, and the index that maps every stoicheia imputation to its seventeen verse rows. Author order is Aeschylus, Sophocles, Euripides throughout.

ll_verses has one row per row of style_vectors, same row numbering:

• z1, z2: the vector's coordinates on the two discriminant directions of the three-class shared-covariance Gaussian fitted on the corpus rows (the third generalised eigenvalue is 1e-12: two directions are sufficient, not a reduction).
• ll_style2_<author>: log N(z | author) in that plane, shared 2×2 covariance refitted on the corpus; ll_style768_<author>: the same likelihood in the full 768-d space with the pooled covariance. Corpus rows are scored in-sample.
• is_trimeter, pattern, caesura, n_resolutions: Stoicheia-meter features derived identically for every row; the candidates verses, the intact verses and Henry's are re-scanned here so that one scanner underlies both sides.
• ll_pattern_<author>, ll_res_<author>, ll_caes_<author>: the multinomial-Dirichlet log posterior predictive (add-one) of the full 12-position pattern, the resolution count (0, 1, 2+) and the caesura under each author, from the 23,916 reference lines the scanner accepts as trimeters. NaN where the scanner rejects the verse.

ll_imputations has one row per stoicheia row: run, temperature, seed, conjecture_id, logp_total, all_trimeter, n_verses_trimeter; row_v13 … row_v29, the verse rows; log_w, the log ratio of the temperature-1 to the temperature-0.65 sampling probability of the whole conjecture, and log_w_v13 … log_w_v29 the same per gap, for the t065_seed2 run whose letter distributions were saved (NaN elsewhere). The whole-conjecture weights are degenerate (effective sample size 1 of 100,000); the per-gap ones keep an effective sample of 81 to 31,519 per verse.

library(arrow)
V <- read_parquet("data/ll/verses.parquet"); I <- read_parquet("data/ll/imputations.parquet")
idx <- as.matrix(I[I$all_trimeter, paste0("row_v", 13:29)]) + 1L
LL <- sapply(c("aeschylus", "sophocles", "euripides"),
             function(a) rowSums(matrix(V[[paste0("ll_style2_", a)]][idx], ncol = 17)))

corpus — the 27,523 reference trimeters

The iambic trimeters of the three tragedians that every prior and likelihood here is estimated from: Aeschylus 1,780 (the three plays scanned by hand in Hypotactic, hypotactic_scansion kept), Sophocles 7,545 and Euripides 18,198 (the TLG plays, dialogue trimeters found by a two-state HMM over line length, speaker and strophe labels, then audited by hand). work, line, edition and speaker give the provenance. Every line carries the same Stoicheia-meter scansion, bracketed text and metrical features as the restored verses (is_trimeter, pattern, caesura, n_resolutions, resolved, word_ends, porson_violation, n_elisions); the scanner accepts 93.9 %, 91.2 % and 84.4 % of the three authors' lines as trimeters.

classifier_stoicheia and classifier_candidates — the fine-tuned attribution classifier

For completeness, the outputs of the end-to-end fine-tuned KainoBERT tragedians classifier (three seeds, the leaderboard model that has not read the Tereus) on every distinct verse of the first two Stoicheia runs (1,452,914 rows, with the intact verses and Henry's as anchors) and on Eric's candidates (241,945 rows): logit_<seed>_<author> and prob_<seed>_<author>, label order Aeschylus, Euripides, Sophocles. These are the classifier's posteriors, not likelihoods, and the analysis above does not use them.

lexicon_bare and lexicon_forms — the word lexicon of the AncientGreek corpus

Token counts of every word form in Ericu950/AncientGreek (361.6 M tokens): lexicon_forms keeps the accented form (6.56 M types, iota adscript normalised to subscript, lowercased) and lexicon_bare the form with every diacritic stripped and final sigma folded (5.21 M types), which is the surface the restorers' fills are judged on since their accents are guesses. n_sources is the number of source works a form occurs in.

fills — a shortlist of one hundred restorations per verse

For each of vv. 13-29, the hundred distinct restored verses (either restorer) that scan as trimeters, contain no non-word and no immediate word repetition, ranked by the log odds Sophocles : (Aeschylus or Euripides) from the style and metre streams at equal priors and tau = 1. "No non-word" means every word's Bayes factor real : not-Greek is above one under the word mixture of scripts/real_greek.py (Dirichlet process over the lexicon against a letter 4-gram model of Greek phonotactics), and every one-letter token is a Greek word or an elision remnant. n_imputations is how many Stoicheia imputations contain the verse (0: from the candidates pipeline only). Under the same mixture the reference corpora and the intact verses score as entirely real, Henry's supplements 0.993, the Stoicheia imputations 0.873 and the candidates 0.856 real words; 37 % and 35 % of their metrically clean verses contain no non-word (data/real_greek/summary.json).

walk — 4,800 complete restorations from a constrained Metropolis walk

scripts/babel_walk.py: starting from Henry's text, one word (or two) of one damaged verse is masked at a time, Stoicheia proposes replacements in the context of the whole passage, and a proposal is kept only if every word is real Greek, the verse still scans, and a Metropolis rule accepts it. 24 chains of 3,000 steps each with the state recorded every 25 steps after a burn-in of 500, at two settings of the style tilt: style_tilt = 0 samples Stoicheia's own distribution restricted to formally correct texts (the imputation source; 2,344 of 2,400 states metrical throughout), style_tilt = 1 tilts it by the Sophocles log odds (an exploration, not an imputation: analysing it with the same style likelihood is circular). Per state: verses, scansion, is_trimeter, caesura, n_resolutions and the three style log densities per verse, the chain, seed, iteration and passage score.

parser — parser-confidence scores

scripts/parser_confidence.py: the mean log-probability per token that Ericu950/Stoicheia-tagger-parser assigns to its own UPOS, head and label choices, for the three corpora, the intact verses, Henry's, the shortlist and 30,000-verse samples of restored text. Real text of all three authors scores −0.04 nats per token, the intact verses −0.03, Stoicheia's metrical restorations −0.07 and the candidates −0.10; 11 % and 20 % of them fall below the 5th percentile of real Sophocles, against 5 % by construction. A posterior predictive check on syntax, complementary to the word mixture.

Usage

from datasets import load_dataset

passages = load_dataset("Urdatorn/tereus-imputation", "stoicheia", split="train")
fills = load_dataset("Urdatorn/tereus-imputation", "candidates", split="train")

# the style vectors, as a matrix
import numpy as np, pyarrow.parquet as pq, glob
from huggingface_hub import snapshot_download
d = snapshot_download("Urdatorn/tereus-imputation", repo_type="dataset",
                      allow_patterns="data/style_vectors/*")
t = pq.read_table(sorted(glob.glob(f"{d}/data/style_vectors/*.parquet")))
X = np.stack(t.column("embedding").to_numpy(zero_copy_only=False)).astype(np.float16)  # (5826792, 768)

# the 1,186-in-100,000 of one run whose every verse scans
clean = passages.filter(lambda r: r["all_trimeter"] and r["run"] == "t065_seed2")

Caveats

• Coverage is far from complete. Good-Turing over the 200,000 imputations at temperature 0.65 puts the unseen probability mass near 75 % per verse on average, from 39.5 % at v. 14 to 98.5 % at v. 25, and the accumulation curves are still close to linear. The true reading may be absent.
• The imputations are improper in Rubin's sense. They come from fixed checkpoints at a temperature below one, so model uncertainty is absent and the distribution is tempered. Frequency of a fill across rows is not its posterior probability. Entropy or missing mass is the safer summary.
• Metrically acceptable is not metrically correct. The filter is a scansion model plus the trimeter template. Caesura, Porson's law and restrictions on resolution are recorded where available but not enforced.
• The two configurations are not commensurable. One is passage-level and jointly sampled, the other verse-level and independently searched.

Provenance and credit

The candidates configuration derives from work by Eric Cullhed (Uppsala University) on the Tereus papyrus, including the Stoicheia model family used by both configurations. The stoicheia configuration and this packaging are by Albin Thörn Cleland, Lund University (ORCID 0009-0003-3731-4038).

The underlying papyrus text is that of the editio princeps; the restorations are machine-generated and carry no editorial authority.