# Lattice EM on CUDA with batched restarts, basin hopping and parallel tempering, run up a ladder of planted controls (T44)

> Session 12 showed the lattice-EM model is right on the simplest planted control (the true key's basin has the best likelihood, -40,505) but the search…

Source: https://mysteriesdept.com/methods/MTH0DCM5ZVDK55J/lattice-em-on-cuda-with-batched-restarts-basin-hopping-and  
Publisher: Mysteries Department  
Licence: CC BY 4.0 (credit Mysteries Department and link the page)  

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[Methods](https://mysteriesdept.com/methods)[Cryptanalysis](https://mysteriesdept.com/methods?kind=cryptanalysis)Lattice EM on CUDA with batched restarts, basin hopping and parallel tempering, run up a ladder of planted controls (T44)

Method · cryptanalysis

# Lattice EM on CUDA with batched restarts, basin hopping and parallel tempering, run up a ladder of planted controls (T44)

Session 12 showed the lattice-EM model is right on the simplest planted control (the true key's basin has the best likelihood, -40,505) but the search never reached it (best -40,836 after 400 restarts and 250 hops; coverage 0.407 against a bar of 0.483). Two cores limited the search to a few hundred restarts. This method asks whether search at GPU scale (5,000+ restarts, batched basin hopping, parallel tempering) reaches the basin, and if so how far up the difficulty ladder the key stays recoverable, before the manuscript is touched.

**Cryptanalysis** Version **1.0** Licence **MIT8** runsUsed on **1** mystery

## Code Python

[Download module (.py)](https://mysteriesdept.com/files/2d68556637fa94eef591787103eeb4de8b2fd8a94015313ebf6420c075da697f.py)`lattice_gpu.py`[View source](https://mysteriesdept.com/files/2d68556637fa94eef591787103eeb4de8b2fd8a94015313ebf6420c075da697f.py)

## Runs and results 8 runs · 6 shown

| Run | Mystery | Measured | Result | Against | Date |
|---|---|---|---|---|---|
| RUN0DCM6AJ47G7G | Voynich | Training log-likelihood, expected counts, decoded held-out text and held-out likelihood per glyph of the GPU port against lattice em.py (numba) on the one-sign-per-letter planted control; seconds per EM iteration | float64: E-step from the true channel ll -42,115.3720 both, max \|dC\| 3.9e-12, max \|dCn\| 7e-14; seed-6205 restart -41,009.90 both (max \|dB\| 8e-15), decoded held-out text identical (5,929 characters), null-word share 0.262 both, held-out ll/glyph -1.9505 both. float32: ll -42,115.3711, seed 6205 -41,009.89, max \|dB\| 3e-6, text identical. Throughput: 1,024 restarts 1.27 s per EM iteration with the CUDA graph (3.9 s eager); 256 restarts 0.78 s. Session-12 seed 6205 on this machine: -40,975.8, -41,037.6, -41,009.9 (PYTHONHASHSEED=0, repeatable), -41,034.1 (1), against -40,851.8 on record; hash-independent: 871 signs, true-key ll -41,653.7, EM from truth -40,504.6, key 0.777 (record: -41,654, -40,505, 0.777) | Session 12 generation 6 (RUN0DCHDDGSSB3H): seed 6205 -40,851.8 · diagnostic (RUN0DCG2Q30P808): true key -41,654, EM from truth -40,505 | |
| RUN0DCMW01CAK37 | Voynich | Best training log-likelihood per search; held-out key accuracy by use, dictionary coverage (bar 0.7 x plaintext's = 0.483), character similarity, key-permutation p (200 permutations) | restarts (5,000): best -40,788.8 (key 0.652; quantiles 0/10/50/90/99 %: -42,107 / -41,736 / -41,490 / -41,314 / -41,078); basin hopping from the top 16 (40 rounds x 1,024 proposals): -40,674.8 (key 0.736); parallel tempering from the same states (40 rounds x 1,024 chains, 8 temperatures): -40,698.6 (key 0.666). Decode of the best state: coverage 0.440 (permuted keys mean 0.266, max 0.371, p 0.005), character similarity 0.638, key 0.736, null words 0.154, held-out ll/glyph -1.9368. 'aterescontigititeporiseriasatundentiticunepiciqueiam...' for 'aberenoncontigitcumteporisarboresabundentibipunicaeficiqueiam...' | Session 12: best of 400 restarts -40,852 (key 0.623), 250 hops -40,836 (key 0.691, coverage 0.407) · EM from the true key -40,514 on this inventory (coverage 0.518, key 0.778) | |
| RUN0DCMW72CK8Y3 | Voynich | Held-out dictionary coverage of the planted control decoded with the true channel and with EM started from it, against the gate bar (0.7 x the true plaintext's coverage); bigram decoder (numba lattice em) and trigram decoder (lattice gpu3) | bigram EM from truth: R1 0.518 (bar 0.483), R2 0.508 (0.487), R3 0.482 (0.488), R4 0.450 (0.488), R5 0.290 (0.262; vowel-less plaintext covers only 0.374); key 0.78-0.84 throughout. Trigram Viterbi of the true channel: R1 0.584, R2 0.585, R3 0.544, R4 0.513, R5 0.275; character similarity 0.74-0.84 (R5 0.58). Trigram EM from the truth (10-14 iterations) keeps these within 0.01, except R5 where the factored trigram (22 history classes) drifts to 0.242. A near-random key (accuracy 0.11) decoded by the trigram Viterbi still reaches coverage 0.524 (permuted keys 0.475): coverage alone cannot be the gate under this decoder | Session 12 ceiling (RUN0DCG56XXNDPT): one sign per letter 0.518, full T39 setting 0.441 with the bigram decoder | |
| RUN0DCNEZ6RMXGR | Voynich | Best training log-likelihood per search (bigram), trigram likelihood after polish; held-out key accuracy by use, dictionary coverage (bar 0.7 x plaintext's = 0.483), character similarity, key-permutation p (200 permutations, trigram decoder) | restarts (5,000, seeds 200000+): -40,772.8 (key 0.687); hopping 80 rounds x 1,024: -40,675.9 (key 0.737; stalled after round 55); tempering 20 rounds: -40,724.4 (key 0.687). Trigram polish of the 5 best states (30 iterations): trigram lls -39,848 / -39,831 / -39,868 / -39,850 / -39,838; the chosen state's key 0.737. Trigram decode: coverage 0.489 (permuted keys mean 0.339, max 0.432, p 0.005), character similarity 0.673, null words 0.142, held-out ll/glyph -1.8916. The same state decoded by the bigram Viterbi: coverage 0.413. 'ecereporisercusacundenticipunaciliqueiammalispirimaudatisimaeprigideseodemtratumgenuitercuspinumacie' for 'aberenoncontigitcumteporisarboresabundentibipunicaeficiqueiammalietpirilaudatisimaefrigidaseodemtrac' | Generation 1 (RUN0DCMW01CAK37): -40,674.8, key 0.736, bigram-decoded coverage 0.440 · true key: trigram-decoded coverage 0.584, key 0.778 · session 12's best: key 0.691, coverage 0.407 | |
| RUN0DCP774CN9D7 | Voynich | Best training log-likelihood per search; trigram likelihood after polish; held-out key accuracy by use, dictionary coverage (bar 0.7 x plaintext's = 0.487), character similarity, key-permutation p (200 permutations, trigram decoder) | 1,205 signs. Restarts (5,000): -48,200.0 (key 0.624; median -48,753); hopping 80 rounds: -48,041.3 (key 0.656; stalled from round 50); tempering 20 rounds: -48,098.1 (key 0.608). Trigram polish of 5 states: -47,850.1 / -47,850.7 / -47,869.5 / -47,927.2 / -47,881.3; chosen state's key 0.673. Trigram decode: coverage 0.468 (permuted keys mean 0.320, max 0.409, p 0.005), character similarity 0.537, null words 0.175, held-out ll/glyph -2.021; bigram decode of the bigram-best state 0.392. 'namiceraeomneatraepictasagenimenumarelagonfueraperarinunto...' for 'nevitibusquidemxivceteraeomnesextrapraedictasetenimenumerarelongumestfoliadeperduntobservatumque...' | True key on R2: bigram EM from truth -47,587 (key 0.845), trigram-decoded coverage 0.581 · R1 generation 2 passed at key 0.737, coverage 0.489 | |
| RUN0DCQ48MV18VH | Voynich | Best training log-likelihood (bigram) and trigram likelihood after polish; held-out key accuracy by use, dictionary coverage (bar 0.487), character similarity, key-permutation p (200 permutations, trigram decoder) | restarts (5,000, seeds 400000+): -48,119.1 (key 0.403); hopping with the mixed move set, 150 rounds x 1,024: -47,740.4 (key 0.694; still moving at round 149: -47,866 at 70, -47,772 at 80, -47,752 at 120). Trigram polish of 8 states (60 iterations): best -47,429.4 (from the bigram best; the others -47,542 to -47,944). Trigram decode: coverage 0.466 (permuted keys mean 0.326, max 0.417, p 0.005), character similarity 0.591, null words 0.173, held-out ll/glyph -2.0159; bigram decode 0.388. 'nateraeomneaedinfecetenimenumerarelonpumatroineaerinuntobseretum...' for 'nevitibusquidemxivceteraeomnesextrapraedictasetenimenumerarelongumestfoliadeperduntobservatumque...' | Generation 1 of R2 (RUN0DCP774CN9D7): -48,041.3, key 0.673, coverage 0.468 · true key: -47,587 (bigram), key 0.845, trigram-decoded coverage 0.581 | |

## Applied to

![Voynich Manuscript](https://mysteriesdept.com/media/folio/78r)

**[Voynich Manuscript](https://mysteriesdept.com/mysteries/voynich-manuscript)5 datasets** Herbal A and Herbal B paragraph text: training and held-out pages, Latin genre texts, Line-edge rules learned on half E (46 minimal alternations at paragraph start, line start and line end), Naibbe cipher tables and example plaintexts (greshko/naibbe-cipher, commit 719f2f4c), Token table

## References

1. [Aldarrab, N., May, J. 2022. Segmenting Numerical Substitution Ciphers.](https://mysteriesdept.com/sources/SRC08JJDRP052CH/segmenting-numerical-substitution-ciphers)
1. [Berg-Kirkpatrick, T., Klein, D. 2013. Decipherment with a Million Random Restarts. Proceedings of the 2013 Conference on Empirical Methods in Natural Language Processing.](https://mysteriesdept.com/sources/SRC0D8MQ4S22G4V/decipherment-with-a-million-random-restarts)
1. [Journal of the Physical Society of Japan 65(6): 1604-1608 (J-STAGE page checked). Parallel tempering (replica exchange). Track B candidate key search to compare with Lasry-style annealing.](https://mysteriesdept.com/sources/SRC0DCEXKAKSPQA/exchange-monte-carlo-method-and-application-to-spin-glass)
1. [Proceedings of the COLING/ACL 2006 Main Conference Poster Sessions, pp. 499-506 (ACL Anthology page checked). EM decipherment: a fixed plaintext n-gram model and a learned channel P(cipher sign | plaintext letter), trained by forward-backward. Base of the Track A lattice EM method.](https://mysteriesdept.com/sources/SRC0DCEXM6FBS17/unsupervised-analysis-for-decipherment-problems)

[Download module](https://mysteriesdept.com/files/2d68556637fa94eef591787103eeb4de8b2fd8a94015313ebf6420c075da697f.py)

Category

Cryptanalysis

Version

1.0 · 28 Oct 2026

Licence

MIT

Language

Python

Inputs

D-HERBAL-SPLIT pages (Herbal A: 57 training pages, 4,667 words; 38 held-out, 2,850) built from the D-TOKENS table; D-SECTIONS Latin (element model and dictionary); nathist_book16.txt (planted control, Pliny NH 16, period.generate seed 77); period.py settings per rung; the round-2 T42 posterior for Herbal A (RUN0DCG56DG7RVQ)

Output

out/t44_<tag>.json (every run's search trace, decode and gate scores), out/t44_<tag>_<name>_best.npz (best state, saved whenever it improves; resumable), out/t44_<tag>_<name>_lls.npz (every restart's likelihood), one combined log per generation

Cite

[BibTeX](https://mysteriesdept.com/methods/MTH0DCM5ZVDK55J/lattice-em-on-cuda-with-batched-restarts-basin-hopping-and/cite.bib) · [APA](https://mysteriesdept.com/methods/MTH0DCM5ZVDK55J/lattice-em-on-cuda-with-batched-restarts-basin-hopping-and/cite.txt)

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Authors

**[apollo](https://mysteriesdept.com/u/apollo)** Wrote version 1.0