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 Markov chain run on the target's own density (MCMC, or replica-exchange molecular dynamics for the peptides), or from an exact sampler where the posterior allows one, and passed the convergence and independence checks below before it was published here. The repo also holds every target's default train split, the cheap and biased set a sampler may learn from, so that every user reads the same one.

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.

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
train = target.train_samples()             # the published train split, downloaded once
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', 'ace-a-nme-T300'])   # by catalog name
samplingdb.download_references()                   # every published set, 6.3 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 v5 --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_d9994289.npy', repo_type='dataset', revision='v5')
x = np.load(path)   # (n_samples, dim)

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
pt/	binary Kob-Andersen glass	particle positions in the periodic box, species in canonical order
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
exact/	the Brownian motion posterior	the unconstrained parameters, in samplingdb's order
train/	every target	the coordinates of the target's own folder above, or its log_prob's

A file is named <folder>/<target name>_<spec_id>.npy, and a train split train/<target name>_<spec_id>_<recipe>.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_d9994289.npy	dw4	102400	8	float32	3.3 MB	91% effective
pt/lj13_bd3bc3a0.npy	lj13	102400	39	float32	16.0 MB	98% effective
pt/lj55_01c56181.npy	lj55	100352	165	float32	66.2 MB	100% effective
pt/ka-binary-N64-T0.2_e60ecba4.npy	ka-binary-N64-T0.2	30720	128	float32	15.7 MB	91% effective
stan/seeds_f9a50f20.npy	seeds	100000	26	float64	20.8 MB	bulk ESS 96% of the draws
exact/brownian_45794097.npy	brownian	100000	32	float64	25.6 MB	exact independent 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	aaa-T310	100000	99	float32	39.6 MB	92% effective
md/aaaaaa-T310_08d2d916.npy	aaaaaa-T310	100005	189	float32	75.6 MB	98% effective
md/ace-a-nme-T300_54968005.npy	ace-a-nme-T300	100000	66	float32	26.4 MB	96% effective
md/ace-aaa-nme-T300_cda31701.npy	ace-aaa-nme-T300	100000	126	float32	50.4 MB	94% effective
swapmc/ka-ternary-N44-T0.32_d50e8a3f.npy	ka-ternary-N44-T0.32	131072	88	float32	46.1 MB	93% effective
swapmc/ka-ternary-N44-T1.0_c0f9b3b8.npy	ka-ternary-N44-T1.0	163840	88	float32	57.7 MB	92% effective
train/funnel_556b9f8f_uniform-neck.npy	funnel	100000	10	float64	8.0 MB	train split, recipe uniform-neck
train/manywell_30beb4d2_uniform-sides.npy	manywell	100000	32	float64	25.6 MB	train split, recipe uniform-sides
train/gmm40_a1f669cb_skewed-modes.npy	gmm40	100000	2	float64	1.6 MB	train split, recipe skewed-modes
train/mos_3d819321_skewed-modes.npy	mos	100000	2	float64	1.6 MB	train split, recipe skewed-modes
train/twomodes_0eddf6c9_skewed-modes.npy	twomodes	100000	2	float64	1.6 MB	train split, recipe skewed-modes
train/brackettwomodes_334746c8_skewed-modes.npy	brackettwomodes	100000	2	float64	1.6 MB	train split, recipe skewed-modes
train/manymodes-k3_edf2fcb2_skewed-modes.npy	manymodes-k3	100000	2	float64	1.6 MB	train split, recipe skewed-modes
train/eightgaussians_ae0110e3_skewed-modes.npy	eightgaussians	100000	2	float64	1.6 MB	train split, recipe skewed-modes
train/rings_5deb01ff_skewed-modes.npy	rings	100000	2	float64	1.6 MB	train split, recipe skewed-modes
train/checkerboard_9547623f_skewed-modes.npy	checkerboard	100000	2	float64	1.6 MB	train split, recipe skewed-modes
train/dw4_d9994289_hot-mala.npy	dw4	100000	8	float32	3.2 MB	train split, recipe hot-mala
train/lj13_bd3bc3a0_split-mala.npy	lj13	100000	39	float32	15.6 MB	train split, recipe split-mala
train/lj55_01c56181_split-mala.npy	lj55	100000	165	float32	66.0 MB	train split, recipe split-mala
train/seeds_f9a50f20_tempered-mala.npy	seeds	100000	26	float64	20.8 MB	train split, recipe tempered-mala
train/brownian_45794097_tempered-mala.npy	brownian	100000	32	float64	25.6 MB	train split, recipe tempered-mala
train/lgcp_cea6d9a6_tempered-mala.npy	lgcp	100000	1600	float64	1280.0 MB	train split, recipe tempered-mala
train/lgcp-whitened_30e98363_tempered-mala.npy	lgcp-whitened	100000	1600	float64	1280.0 MB	train split, recipe tempered-mala
train/ka-ternary-N44-T1.0_c0f9b3b8_hot-basin-mc.npy	ka-ternary-N44-T1.0	100000	88	float32	35.2 MB	train split, recipe hot-basin-mc
train/ka-ternary-N44-T0.32_d50e8a3f_hot-basin-mc.npy	ka-ternary-N44-T0.32	100000	88	float32	35.2 MB	train split, recipe hot-basin-mc
train/ka-binary-N64-T0.2_e60ecba4_hot-basin-mc.npy	ka-binary-N64-T0.2	100000	128	float32	51.2 MB	train split, recipe hot-basin-mc
train/ionosphere_d00109c3_tempered-mala.npy	ionosphere	100000	35	float64	28.0 MB	train split, recipe tempered-mala
train/sonar_52aa10ef_tempered-mala.npy	sonar	100000	61	float64	48.8 MB	train split, recipe tempered-mala
train/german-credit_3cfdf175_tempered-mala.npy	german-credit	100000	25	float64	20.0 MB	train split, recipe tempered-mala
train/breast-cancer_543f5f94_tempered-mala.npy	breast-cancer	100000	31	float64	24.8 MB	train split, recipe tempered-mala
train/ace-a-nme-T300_54968005_basin-md.npy	ace-a-nme-T300	100000	66	float32	26.4 MB	train split, recipe basin-md
train/ace-aaa-nme-T300_cda31701_basin-md.npy	ace-aaa-nme-T300	100000	126	float32	50.4 MB	train split, recipe basin-md
train/aaa-T310_e0bfbee3_basin-md.npy	aaa-T310	100000	99	float32	39.6 MB	train split, recipe basin-md
train/aaaaaa-T310_08d2d916_basin-md.npy	aaaaaa-T310	100000	189	float32	75.6 MB	train split, recipe basin-md

Independence is the effective sample size as a fraction of the rows: measured on the stored chains for the tempered runs and the glass, and Stan's smallest bulk ESS for the posteriors, which exceeds 100% where successive NUTS draws are anticorrelated. The exact draws are independent by construction. A train split is biased on purpose, so its row says which recipe made it.

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 set is at least 90% independent; the binary glass, merged from shards, also shows no drift from its start, and its chains started from deep configurations and from a melt agree within 4 standard errors
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; each shard's energy agrees between the two halves of its run within 5 standard errors; the merged set is at least 90% independent on the pair distances and backbone torsions. The integrator is unadjusted: at 1 fs it puts Ace-A-Nme's mean energy about 0.1 kT above the zero-timestep limit
swapmc/	swap Monte Carlo on the GPU, 16 384 chains started from equilibrated configurations and stored at a fixed spacing	the merged set is at least 90% independent on the energy and the pair distances, with no drift from its start, 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
exact/	rejection sampling of the two log scales from their priors against the bounded marginal likelihood, then the locations from their exact Gaussian conditional	the factorised density equals samplingdb's up to a constant, to 1e-8 across 1000 random points; every proposal stays below the bound
train/	the target's own generate_train_samples at seed 0, 100 000 samples, on a GPU (gen/train/generate.py)	samplingdb's tests: every mode of the test split visited in the wrong proportions, and the test energies covered at both ends

Versions

samplingdb pins one tag of this repo and the sha256 of every file it reads, 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. A set regenerated for the same density keeps its file name and changes its bytes under a new tag; samplingdb refuses a cached copy from another tag.

Tag	Contents
v1	17 sets
v2	the Brownian posterior from an exact sampler, under exact/ in place of stan/; both ternary glass sets regenerated on the GPU; the three particle sets, unchanged, under new names, since the particle count joined their spec_id; the binary Kob-Andersen glass at T = 0.2, published for the first time; every set under the MIT License, in place of CC BY 4.0
v3	the default train split of every target, under train/; the reference sets of v2, unchanged
v4	the train splits of the particle systems and the glasses, with most chains far hotter than the target; everything else as in v3
v5	the train splits of LJ-13 and LJ-55, with nine chains in ten at one temperature above the target's and one in ten from 0.8 to 1 times it; everything else as in v4

License and attribution

The samples are released under the MIT License, like samplingdb. 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.
• The binary glass: the two-dimensional 80:20 Kob-Andersen mixture of Cheng et al. 2026, after Kob and Andersen 1995.