samplingdb reference sets

Reference samples for the targets of samplingdb, a PyTorch library of unnormalised densities for benchmarking samplers. A sampler's output is scored against these sets. Each one comes from a long MCMC run on the target's own density, and was checked for convergence and independence before it was published here.

You do not need to download anything by hand. samplingdb fetches a set the first time it is used, checks its sha256, and keeps it in its cache. To look at a set first, open the dataset viewer above and pick the target in the subset menu.

Quick start

pip install git+https://github.com/h2o64/samplingdb

from samplingdb import build

target = build('lj55')
reference = target.test_samples(n=10000)   # downloads the set once (66 MB), then reads the cache
metrics = target.compute_metrics(samples)  # samples: your sampler's output, same shape

To fetch sets ahead of time, for example before a job on machines with no internet access:

import samplingdb

samplingdb.download_references(['lj55', 'aldp'])   # by catalog name
samplingdb.download_references()                   # every published set, 3.1 GB

The cache is ~/.cache/samplingdb, or the directory SAMPLINGDB_CACHE names. It is laid out like this repo, so a copy of the repo is a ready cache:

hf download h2o64/samplingdb --repo-type dataset --revision v1 --local-dir "$SAMPLINGDB_CACHE"

Without samplingdb, every file is a plain NumPy array:

import numpy as np
from huggingface_hub import hf_hub_download

path = hf_hub_download('h2o64/samplingdb', 'pt/dw4_6b739c6d.npy', repo_type='dataset', revision='v1')
x = np.load(path)   # (n_samples, dim)

Browsing, and loading with datasets

Each set also has a Parquet copy in viewer/, which is what the dataset viewer shows: one subset per target, named as in samplingdb.build, with one row per sample. The column x is the sample and log_prob is the samplingdb target's unnormalised log density at it, whose histogram the viewer draws above the column. For the particle systems, the peptides and the glass, log_prob is minus the energy in units of kT, so its histogram is the energy distribution, mirrored.

The same files load with the datasets library, under the split test:

from datasets import load_dataset

lj55 = load_dataset('h2o64/samplingdb', 'lj55', split='test')
rows = lj55.with_format('numpy')[:]
x, log_prob = rows['x'], rows['log_prob']   # (100352, 165) and (100352,)

The .npy files are what samplingdb reads and what the tag pins; the Parquet copies hold the same rows.

Files

Each row of an array is one sample, flattened, in the coordinates the samplingdb target's log_prob takes:

Folder	Targets	Coordinates
pt/	DW-4, LJ-13, LJ-55	particle positions; samplingdb removes the centre of mass when it reads them
swapmc/	ternary Kob-Andersen glass	particle positions in the periodic box, species in canonical order
md/	peptides	atom positions in nanometres, in the atom order of the released PDB
stan/	Bayesian posteriors	the unconstrained parameters, in samplingdb's order

A file is named <folder>/<target name>_<spec_id>.npy. The spec_id is a hash of the constants that define the density, so a set can never be read against a different density than the one it was drawn from. Next to every array, <same name>_manifest.json records the target, its spec_id, the full generation protocol with its diagnostics, and the array's sha256.

File	build name	Samples	dim	dtype	Size	Independence
pt/dw4_6b739c6d.npy	dw4	102400	8	float32	3.3 MB	91% effective
pt/lj13_6a0a72c4.npy	lj13	102400	39	float32	16.0 MB	98% effective
pt/lj55_dc3f6b7e.npy	lj55	100352	165	float32	66.2 MB	100% effective
stan/seeds_f9a50f20.npy	seeds	100000	26	float64	20.8 MB	bulk ESS 96% of the draws
stan/brownian_45794097.npy	brownian	100000	32	float64	25.6 MB	bulk ESS 92% of the draws
stan/lgcp_cea6d9a6.npy	lgcp	100000	1600	float64	1280.0 MB	bulk ESS 90% of the draws
stan/lgcp-whitened_30e98363.npy	lgcp-whitened	100000	1600	float64	1280.0 MB	bulk ESS 98% of the draws
stan/breast-cancer_543f5f94.npy	breast-cancer	100000	31	float64	24.8 MB	bulk ESS 102% of the draws
stan/german-credit_3cfdf175.npy	german-credit	100000	25	float64	20.0 MB	bulk ESS 110% of the draws
stan/ionosphere_d00109c3.npy	ionosphere	100000	35	float64	28.0 MB	bulk ESS 96% of the draws
stan/sonar_52aa10ef.npy	sonar	100000	61	float64	48.8 MB	bulk ESS 108% of the draws
md/aaa-T310_e0bfbee3.npy	trialanine	100000	99	float32	39.6 MB	92% effective
md/aaaaaa-T310_08d2d916.npy	hexaalanine	100005	189	float32	75.6 MB	98% effective
md/ace-a-nme-T300_54968005.npy	aldp	100000	66	float32	26.4 MB	96% effective
md/ace-aaa-nme-T300_cda31701.npy	ala4	100000	126	float32	50.4 MB	94% effective
swapmc/ka-ternary-N44-T0.32_d50e8a3f.npy	ka-ternary-T0.32	105600	88	float32	37.2 MB	20 relaxation times apart
swapmc/ka-ternary-N44-T1.0_c0f9b3b8.npy	ka-ternary-T1.0	102400	88	float32	36.0 MB	20 relaxation times apart

Independence is the effective sample size as a fraction of the rows: measured on the stored chains for the tempered runs, and Stan's smallest bulk ESS for the posteriors, which exceeds 100% where successive NUTS draws are anticorrelated. For the glass it is the spacing between stored configurations of one chain, in structural relaxation times.

The rows are interleaved across chains, so the first n rows of a file span every chain of the run that produced it, and test_samples(n=...) can read a prefix.

How the sets were made

Every set was generated by a script in the gen/ folder of the samplingdb repository, which documents each protocol and its acceptance checks in docs/reference-sets.md.

Folder	Sampler	Checked before writing
pt/	non-reversible parallel tempering with HMC moves	every chain makes 10 round trips and every pair of adjacent levels accepts at least 5% of its swaps; the merged set is at least 90% independent, with no drift from its start
md/	replica-exchange molecular dynamics with solute tempering, BAOAB at 1 fs	every replica makes a round trip and every pair of adjacent levels accepts at least 5% of its swaps; the merged set is at least 90% independent on the pair distances and backbone torsions, with no drift from its start
swapmc/	swap Monte Carlo: 100 relaxation times of equilibration, then one configuration every 20	consecutive configurations of a chain have decorrelated, and the specific heat agrees between the two halves of the run
stan/	Stan's NUTS, on models written in samplingdb's own coordinates	Stan's log density equals samplingdb's to 1e-9; R-hat below 1.01, bulk ESS above 90% of the draws, no divergences

Not published yet

Two catalogued targets have no set in this release. A later release will add them under a new tag.

• ka-binary-T0.2, the binary Kob-Andersen glass of Cheng et al. 2026. Its parallel-tempering replicas that crystallise stay trapped at intermediate temperatures, and the set generated so far is not stationary.
• chignolin. Its folding equilibrium is expensive to sample, and the planned 10 000-structure set has not been run yet.

Versions

samplingdb pins one tag of this repo and the sha256 of every file it reads. A release adds files under a new tag and never replaces a published one, so every samplingdb version keeps reading the exact bytes it was tested against. A density change gets a new spec_id, and therefore a new file.

Tag	Contents
v1	the 17 sets above

License and attribution

The samples are released under CC BY 4.0. They are draws from densities that others defined, so please also credit the sources of the densities you use:

• DW-4, LJ-13 and LJ-55: the potentials of Köhler et al. 2020, as implemented in bgflow.
• The logistic regressions: the Ionosphere, Sonar, Statlog (German Credit) and Breast Cancer Wisconsin (Diagnostic) datasets of the UCI Machine Learning Repository, under CC BY 4.0. Seeds: the data of Crowder 1978. Brownian: the model of inference_gym. LGCP: the Finnish pines data of Møller et al. 1998.
• The peptides: the systems of the Sequential Boltzmann Generators data (Tan et al. 2025), with the Amber ff99SB-ILDN and ff14SB force fields and OBC implicit solvent, evaluated with OpenMM.
• The ternary glass: the swap-friendly Kob-Andersen mixture of Jung et al. 2023, after Kob and Andersen 1995.