Run · Voynich Manuscript

Generation 4: deterministic annealing and population annealing of the lattice EM; both fall into a degenerate basin

Population-annealed EM for the lattice key, compared with independent restarts: Training log-likelihood, key accuracy by use, held-out dictionary coverage (bar 0.7 x true plaintext's), on the planted control.

Annealing does worse than independent restarts on likelihood and on key recovery: at low beta every member is pulled into one symmetric solution that reads half the words as copied nulls and maps signs to common Latin fragments. That solution raises dictionary coverage without reading anything (key 0 %, character similarity 0.06), so the one-sign-per-letter population-annealing control clears the coverage bar on paper. By the fixed rule the manuscript is decoded under that system in generation 5 and must then beat the structure-preserving null with permutation p < 0.01; the pseudo-Latin null's 0.432 coverage under the same scheme shows how little the coverage figure means here. The full-setting runs were stopped after their controls failed (their nulls were not finished).One sign per letter, no nulls: deterministic annealing ll -42,066, key 0.000, coverage 0.477 (bar 0.483); population annealing ll -42,067, key 0.000, coverage 0.496 (above the bar), 55 % of words read as nulls. Full T39 setting: deterministic annealing ll -55,506, key 0.000, coverage 0.457; population annealing ll -55,598, key 0.000, coverage 0.414 (bar 0.488). Pseudo-Latin null under deterministic annealing: coverage 0.4320

Result

Run	Measured	Result	Against	Decision	Date
Run	Training log-likelihood, key accuracy by use, held-out dictionary coverage (bar 0.7 x true plaintext's), on the planted control	One sign per letter, no nulls: deterministic annealing ll -42,066, key 0.000, coverage 0.477 (bar 0.483); population annealing ll -42,067, key 0.000, coverage 0.496 (above the bar), 55 % of words read as nulls. Full T39 setting: deterministic annealing ll -55,506, key 0.000, coverage 0.457; population annealing ll -55,598, key 0.000, coverage 0.414 (bar 0.488). Pseudo-Latin null under deterministic annealing: coverage 0.432	Independent restarts on the same controls: ll -41,322 (key 0.376) and -53,904 (key 0.364) · EM from the true key -40,505 and -53,462	Annealing does worse than independent restarts on likelihood and on key recovery: at low beta every member is pulled into one symmetric solution that reads half the words as copied nulls and maps signs to common Latin fragments. That solution raises dictionary coverage without reading anything (key 0 %, character similarity 0.06), so the one-sign-per-letter population-annealing control clears the coverage bar on paper. By the fixed rule the manuscript is decoded under that system in generation 5 and must then beat the structure-preserving null with permutation p < 0.01; the pseudo-Latin null's 0.432 coverage under the same scheme shows how little the coverage figure means here. The full-setting runs were stopped after their controls failed (their nulls were not finished).

What it used and found

Population-annealed EM for the lattice key, compared with independent restarts

Method

MTH

Herbal A and Herbal B paragraph text: training and held-out pages

Dataset

DAT

Latin genre texts

Dataset

DAT

Naibbe cipher tables and example plaintexts (greshko/naibbe-cipher, commit 719f2f4c)

Dataset

DAT

Latin as a re-spaced homophonic stream (period practices)

Answer it tests

ANS

Parameters

DA = 20 annealing iterations, beta 0.2 to 1 geometric, then 60 at beta 1; 20 restarts (one sign per letter), 30 (full), PA = population 32, 8-step beta ladder from 0.2, 3 EM iterations per step, resampling by exp(dbeta x log-likelihood), then EM to convergence for each distinct survivor, pw = 0.25, alpha = 0.05, permutations = 10-20

Cite it

Mysteries Department. (2026). Generation 4: deterministic annealing and population annealing of the lattice EM; both fall into a degenerate basin [Run RUN0DCGEKE5D3QC]. https://mysteriesdept.com/r/RUN0DCGEKE5D3QC

@misc{mysteriesdept_run0dcgeke5d3qc,
  title     = {Generation 4: deterministic annealing and population annealing of the lattice EM; both fall into a degenerate basin},
  author    = {{Mysteries Department}},
  year      = {2026},
  note      = {Run, catalog key RUN0DCGEKE5D3QC},
  url       = {https://mysteriesdept.com/r/RUN0DCGEKE5D3QC}
}