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GwendalTsang/dimension-free-ald-reproduction

CPU reproduction of Dimension-Free Multimodal Sampling via Preconditioned ALD This is an independent reproduction bundle for arXiv:2602.01449 / OpenReview 3wMM5NEFvr. It uses the paper's analytic diagonal Gaussian-mixture scores and requires no trained model or dataset. Run The only runtime dependency is NumPy. python repro.py theory python -m unittest discover -s tests -v python repro.py experiment The default empirical command is a documented CPU-scaled sweep… See the full description on the dataset page: https://huggingface.co/datasets/GwendalTsang/dimension-free-ald-reproduction.

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CPU reproduction of Dimension-Free Multimodal Sampling via Preconditioned ALD

This is an independent reproduction bundle for arXiv:2602.01449 / OpenReview 3wMM5NEFvr. It uses the paper's analytic diagonal Gaussian-mixture scores and requires no trained model or dataset.

Run

The only runtime dependency is NumPy.

bash
python repro.py theory
python -m unittest discover -s tests -v
python repro.py experiment

The default empirical command is a documented CPU-scaled sweep with 512 samples per distribution and 4,000 Euler--Maruyama steps. To restore the paper's 2,500 samples and 20,000 steps:

bash
python repro.py experiment --paper-scale
python repro.py experiment --mode exact --paper-scale --workers 6 --k-values 20,50,80 --output artifacts/experiment
python repro.py experiment --mode score-error --paper-scale --workers 6 --k-values 20,50,80 --output artifacts/score-error
python repro.py aggregate-score-error artifacts/score-error*/ald_experiment_summary.json

Independent dimension/configuration runs use up to six local worker processes by default. Pass --workers 1 for serial execution or a different positive count to tune for the machine.

Outputs are written under artifacts/ as JSON, CSV, and self-contained HTML. The empirical run is deterministic from its recorded per-configuration seeds.

Scope

  • —Claims 1, 2, and 4 are independently audited using double-precision spectral partial sums through dimension 100,000.
  • —Claim 3's initialization, component-score, and annealing-bias terms are audited separately. The source states spectrum-dependent conditions; j^-3.5 is the paper's experimental admissible preconditioner, not a universal rate required by Proposition 4.3.
  • —Claim 5 is reproduced using the exact target, schedule, score, preconditioner, smoothing spectra, and kNN estimator described in Appendix I. The default run reduces samples and time steps for CPU cost; --paper-scale removes that reduction.
  • —Each empirical run reports the paper's estimator-robustness values at k=20,50,80 without repeating the expensive ALD integration.

The numerical audits support mathematical statements but do not replace their proofs.

Complete bundle and poster

  • —bundle/dimension-free-ald-reproduction.tar.gz is the self-contained archive recorded on the logbook Conclusion page (SHA-256 bce2a29df2fbac00adccb6df60853ba97b95f5b1ee70875cbc6e3d84f3cebda5).
  • —poster/poster.pdf and poster/poster.png are the print-ready Posterly render; poster/poster_embed.html is the self-contained interactive Trackio embed.
  • —poster/GATE_REPORT.json records passing strict preflight, style, geometry, and polish gates with zero warnings.
  • —The local suite contains nine unit/integration tests, including optimized-vs-general score agreement, finite-difference checks, NumPy/Torch parity, and an end-to-end Torch path executed on CPU.

The poster tooling comes from gradio-app/posterly, created by Ruishuo Chen.