PatternBoost Multi-Level Experiments

Code and exact certificates for Towards Learning-Guided Discovery of Extremal Geometric Constructions: A PatternBoost Study (ALENEX 2027).

The final study contains 27 configurations for each of three problems:

Problem	Objective	Recorded best	Original RNG seed
MISR	Rectangle independent-set clique-LP gap	3/2	5381899176938748427
Unit-square stabbing	Line-stabbing set-cover LP gap	20/13	2072069136256961140
Guillotine	Destroyed fraction under optimal recursive cuts	1/3	4475353812576049258

All 81 recorded seeds, per-row runtime settings, and certificate hashes are committed in the seed manifest. The complete runtime matrix combines the historical matrix rows with their saved launch settings. Generated searches go in the Git-ignored runs/ directory; the committed certificates and compact data are under docs/assets/.

Install

Use Python 3.11 or 3.12 in a virtual environment:

git clone https://github.com/rishigajjala/patternboost-multilevel.git
cd patternboost-multilevel
python3 -m venv .venv
source .venv/bin/activate
python -m pip install -e . -r requirements.txt

The exact verifiers use NumPy, SciPy/HiGHS, and the bundled combinatorial solvers. No commercial solver is required. Install PyTorch for guided searches:

python -m pip install -r requirements-torch.txt

Per-run dependency versions are recorded in the seed manifest and certificates. The headline unit-square run used PyTorch 2.7.1, while retained MISR and guillotine runs record 2.8.0+cu128. Use a separate matching environment when comparing a historical run. The default optional requirements select 2.8.0.

Verify the reported constructions

These commands work without PyTorch:

python reproduce.py --mode verify
python reproduce.py --mode smoke

Verification recomputes the scores of all 81 stored certificates. The smoke mode checks the small-example scoring pipeline. Neither is a repeated-seed search experiment.

Re-run a paper configuration

Inspect a complete recorded configuration before launching it:

python reproduce.py --mode single --problem unit_square --dry-run

A normal single run uses that configuration's recorded seed and historical 24-hour budget / 1,000,000-generation cap:

python reproduce.py --mode single --problem unit_square

Use --problem misr or --problem guillotine for their headline cells. --paper-seeds is accepted explicitly; --seed INTEGER selects a different single-run seed, and --fresh-seeds generates and records new seeds. Every invocation writes its effective matrix in an isolated run directory. For a deliberately shorter comparison, both overrides change the matrix row:

python reproduce.py --mode single --problem misr --iterations 200 --budget-seconds 3600

Short runs and changed seeds may not reach a paper record. Generation counts are not interchangeable across different populations or training schedules. Fixed seeds also do not guarantee bitwise agreement across library versions, hardware, or source revisions. Historical source revisions are recorded per row; this entry point runs the checked-out harness with the recorded settings.

The three historical cohorts

Cohort	Rows	Initial n / grid	Population / elite	Initial pool / immigrants per generation	Train interval
Retained July 9	36 (12 per problem)	8 / 8	32 / 6	32 / 0	7
Main July 11 replacements	42	MISR/guillotine: 12 / 8; unit-square: 20 / 16	16 / 4	16 / 0	10
Unit-square follow-up	3	20 / 16	32 / 12	128 / 4, resolution diversity enabled	10

Both headline MISR and guillotine records belong to the retained cohort. Assigning one setting tuple per problem loses this distinction. The ordinary multilevel.cli matrix --stage main command generates the older design and fresh seeds; use the committed final runtime matrix for the paper's final grid.

Full matrix and HPC

Preview or run the same 81 per-row configurations locally:

python reproduce.py --mode full --parallel 4 --dry-run
python reproduce.py --mode full --parallel 4

For Slurm, check out the project and keep the results on the cluster's scratch filesystem. With the project environment activated, generate a 25-hour array:

python -m multilevel.cli make-slurm \
  --matrix docs/assets/replacement_81_final_20260712/data/final_81_runtime.jsonl \
  --out runs/paper_81_array.slurm \
  --project-dir "$PWD" \
  --results-dir "$SCRATCH/patternboost-results" \
  --time 25:00:00 --partition compute --cpus-per-task 4 --mem 16G \
  --runner patternboost

The PatternBoost Slurm fallback cap is 1,000,000 generations. Explicit matrix fields take precedence over launcher defaults. To submit shorter jobs, create rows with explicitly reduced iteration and wall-clock budgets instead of assuming a CLI fallback overrides the paper matrix.

Read ARTIFACT_EVALUATION.md for evaluation modes, source provenance, analysis regeneration, output locations, and limitations. docs/HPC_JUBAIL.md documents cluster-specific setup. Sync helpers require an explicit account, for example REMOTE=NETID@jubail.abudhabi.nyu.edu scripts/sync_to_hpc.sh.

Data, reports, and development

• Final 81-cell evidence
• Full report PDF and analysis guide
• Recorded implementation details
• Model-capacity study
• Exploratory appendix tasks
• Separate FormulaBoost prototype

For regression checks:

python -m pip install pytest
python -m pytest -q

This public Git repository is versioned but its default branch can change. An immutable publication requires a separately deposited, versioned archive; no DOI is claimed here.