CausalArena leaderboard · public release

One arena, many causal discovery regimes.

CausalArena evaluates tabular causal discovery with shared observational and mixed-interventional protocols across synthetic SCMs, semantic operational SCMs, formula-grounded scientific SCMs, and public real-data checks. The dashboard separates accuracy, structural error, intervention sensitivity, runtime, and graph-level inspection so that method behavior is visible beyond a single pooled score.

Open leaderboard Semantic/Formula Analysis Browse SCM Gallery

1,200 SCMsFull benchmark: 1000 synthetic, 100 semantic, 100 formula. Public release includes half of each family.

18Methods across control, search, functional, optimization, and pretrained families

600 releasedPublic release includes 500 synthetic, 50 semantic, and 50 formula SCMs

13 / 7Real-data checks: 13 obs-only views and 7 interventional datasets

What the arena is designed to test

CausalArena is built to test more than a single aggregate score. Its four design principles ask whether a benchmark is broad enough to stress different causal settings, grounded enough to make graph errors meaningful, inspectable enough to audit, and structured enough to support targeted analysis.

Coveragebroad causal settings and difficulty axes

Groundingdomain meaning plus executable mechanisms

Auditabilitytransparent SCMs, checks, and release governance

Analyzabilitydiagnostics beyond pooled leaderboard scores

How to read the dashboard

Use the three large entry points for the main leaderboard, semantic/formula case analysis, and SCM gallery. The tabs below provide complementary real-data checks, scaling curves, runtime summaries, diagnostics, and method metadata.

Leaderboardmain metrics and cost frontier

Sem/Formulacase-level graph inspection

SCM Galleryreleased grounded SCMs

Supporting viewsreal data, scaling, runtime, methods

Benchmark composition

Track	Scope	Ground truth	What it reveals
Synthetic SCMs	Controlled variation over graph families, mechanisms, root/noise distributions, dimensions, sample sizes, and intervention designs.	Executable DAG + mechanisms	How methods respond to isolated structural and statistical shifts.
Semantic operational SCMs	The 10 domains are cybersecurity/IT operations, education, finance/credit, government services/policy, healthcare delivery, housing/real estate, manufacturing, public health, urban transportation, and water/sanitation.	Executable DAG + variable/edge semantics	Whether methods recover meaningful operational chains, proxies, bottlenecks, and measurement channels.
Formula-grounded SCMs	Scientific and engineering equations across physics, biology, chemistry, earth/environmental systems, astronomy, materials, energy, and related domains.	Executable DAG + equations/ranges	Whether methods handle explicit scientific mechanisms, units, residuals, validity ranges, and equation-level interactions.
Real-data check	Public scored tabular sources: CD-CSG, Sachs flow cytometry, PetShop telemetry, and Causal Chamber physical systems.	Known directed graphs from sources	Whether wrappers still recover known graphs on public real tables outside the generated SCM arena.

Mechanism and distribution taxonomy

This section summarizes the actual category vocabulary present in the current release artifacts. Synthetic categories are read from the generated factor metadata; Semantic and Formula categories are read from the released grounded SCM records. Bars show proportions within the currently released subset where reliable per-category counts are available.

Synthetic SCMs

Controlled generated SCMs with explicit factor axes.

Graph families

bipartite layeredblock sparse layeredchaincollider richdense local moduleserlayeredscale freesmall worldtree

Dimensions

10203050100

10graph families

5dimensions

16edge mechanism families

14child-noise families

14root distributions

4root-dependency families

Edge mechanisms

activation additiveaggregation nonlineardiscretization assignmentexp loglinear additivelinear additive interactionmixture regimemultiplicativeneural randompiecewise threshold

Child noise

betacensoredexponentialgaussiangumbelheteroskedasticlaplacemixture outliermultiplicative lognormalquantized

Root distributions

bernoullibeta scaledcategorical ordinalexponentialgammagumbellognormalmixture normalmultinomial discretenormal

Root dependency

correlated normalindependent rootsrandom covariance normaluniform ball

All edge mechanisms (16)

activation additiveaggregation nonlineardiscretization assignmentexp loglinear additivelinear additive interactionmixture regimemultiplicativeneural randompiecewise thresholdpolynomial powerrational ratiorff gpsaturation cliptree basedtrig periodic

All noise families (14)

betacensoredexponentialgaussiangumbelheteroskedasticlaplacemixture outliermultiplicative lognormalquantizedrff heteroskedasticstudent ttarget r2 gaussianuniform

All root distributions (14)

bernoullibeta scaledcategorical ordinalexponentialgammagumbellognormalmixture normalmultinomial discretenormalpoissontruncated normaluniformzipf powerlaw

Semantic operational SCMs

Domain-grounded operational graphs; counts below are from released Semantic graph artifacts.

Domains

Cybersecurity & It OperationsEducationFinance & CreditGovernment Services & Policy ImplementationHealthcare DeliveryHousing & Real EstateManufacturingPublic HealthUrban TransportationWater & Sanitation

Edge mechanism proportions

count or event process15%

stock flow or accumulation8.9%

piecewise or threshold8.8%

custom physical law7.4%

categorical or ordinal rule7.1%

mixture or regime switch6.5%

saturating response5.9%

min max or clamp logic5.4%

multiplicative product4.7%

bounded sigmoid index4.3%

ratio or normalization4.2%

deterministic formula3.9%

... plus 48 more categories

Node noise/distribution proportions

normal/Gaussian20%

lognormal15%

count/Bernoulli14%

mixture/zero-inflated10%

quantization/jitter/censoring9.3%

categorical/discrete8.7%

scenario-specific8.4%

beta/proportion8.2%

gamma/exponential2.3%

deterministic/none2.1%

heavy-tail/other continuous1.0%

measurement/calibration<1%

Frequent edge mechanisms

count or event process300stock flow or accumulation184piecewise or threshold181custom physical law152categorical or ordinal rule146mixture or regime switch134saturating response123min max or clamp logic111multiplicative product98bounded sigmoid index88ratio or normalization86deterministic formula80

Node noise/distributions

normal/Gaussian224lognormal176count/Bernoulli164mixture/zero-inflated118quantization/jitter/censoring107categorical/discrete100scenario-specific96beta/proportion94gamma/exponential26deterministic/none24

Root/intervenable distributions

categorical/discrete70normal/Gaussian57count/Bernoulli53beta/proportion49quantization/jitter/censoring49scenario-specific46mixture/zero-inflated44lognormal41deterministic/none15gamma/exponential12

All edge mechanism categories (60)

accumulation rate modifieractuation limitadditive compositionadditive indexaggregation group keyallocation with normalization and capattenuationbaseline headbeta binomial processbounded sigmoid indexcalibration gain offsetcapacity or constraintcategorical effectcategorical or ordinal rulecategorical to random effectcontrol couplingcontrol regimecount or event processcustom physical lawdeclared structural parentdeterministic formulaenvironmental amplificationenvironmental stressexponential decayexponential or logfirst order lagflow scalinghead requirementinteraction effectinteraction modulationlinear affinematerial fatiguemeasurement error modelmin max or clamp logicmixture or regime switchmultiplicative productnonlinear geometrynonmonotonic responseoffset referenceoperating point inertiapiecewise or thresholdpower lawpower scalingpricing policyprobabilistic logitrate reductionratio or normalizationresource constrained delaysampling latencysaturating responseselection censoring processseverity weight to mixturespatial spilloverstiffness increasestock flow or accumulationthrottling lossestriggered policy feedbacktrigonometric or periodicvulnerability amplificationwave propagation

Formula-grounded SCMs

Scientific equation-grounded graphs; counts below are from released Formula graph artifacts.

Scientific domains

Biology Physiology & EcologyCelestial Mechanics & AstronomyChemistry Kinetics & SolutionsClassical Mechanics & Fluid MechanicsEarth Science Hydrology & AtmosphereElectromagnetism & CircuitsEnergy Systems & Environmental EngineeringMaterials & Structural EngineeringOptics Waves & AcousticsThermodynamics & Heat Transfer

Edge mechanism proportions

deterministic formula20%

measurement error model11%

linear affine10%

custom physical law7.6%

calibration gain offset7.0%

ratio or normalization6.2%

piecewise or threshold5.1%

saturating response3.0%

categorical or ordinal rule2.9%

multiplicative product2.8%

min max or clamp logic2.4%

power law2.3%

... plus 75 more categories

Node noise/distribution proportions

normal/Gaussian25%

deterministic/none24%

scenario-specific12%

lognormal8.2%

quantization/jitter/censoring7.1%

categorical/discrete6.6%

heavy-tail/other continuous6.1%

beta/proportion5.1%

mixture/zero-inflated4.2%

count/Bernoulli1.6%

measurement/calibration<1%

gamma/exponential<1%

Frequent edge mechanisms

deterministic formula350measurement error model190linear affine174custom physical law130calibration gain offset120ratio or normalization106piecewise or threshold88saturating response51categorical or ordinal rule49multiplicative product48min max or clamp logic41power law40

Node noise/distributions

normal/Gaussian286deterministic/none272scenario-specific138lognormal95quantization/jitter/censoring82categorical/discrete76heavy-tail/other continuous70beta/proportion59mixture/zero-inflated48count/Bernoulli18

Root/intervenable distributions

normal/Gaussian81categorical/discrete58scenario-specific38lognormal37heavy-tail/other continuous30quantization/jitter/censoring29beta/proportion24deterministic/none23mixture/zero-inflated4gamma/exponential2

Formula families

oxygen content CaO2 physiology1Fick First Law with Stokes Einstein and Beer Lambert1Hardy–Weinberg equilibrium (HWE) allele-to-genotype mapping1logistic growth1Monod growth kinetics with optical response and inverse calibration1Kepler third law with astrometric conversion and barycentric sum1Keplerian circular orbit relations with inverse-μ estimation1Newtonian gravity: escape velocity and surface gravity1Kepler’s third law (two-body) and mean orbital speed1photometric flux pipeline with stellar physics1

All edge mechanism categories (87)

activity correctionadditive indexaging driftalignment logicattenuation multiplicativeaveraging transformbaro alt conversionbeer lambertbeer lambert inversebounded power mapbounded sigmoid indexbuffer equilibriumcalibrated inverse mappingcalibration gaincalibration gain offsetcalibration offsetcapacity modelcategorical offsetcategorical or ordinal rulecontrol plant effectcount or event processcustom physical lawdecision ruledeterministic formuladeterministic physical lawdiagnostic score and flagsdifferencediurnal regime effectdynamic pressureeffective equilibriumelectrochemical nernstelectrode responseenvironmental context modelexponential or logfick first lawgeophysical correctiongradient estimationideal gasimpact stopping distance modelinstrument driftinstrument offsetionic strengthjunction potentialkinematic ratiolinear affinemagnitude transformmatrix effectmeasurement error modelmeasurement quantizationmeasurement saturationmin max or clamp logicmixing dilutionmixture empiricalmixture or regime switchmultiplicative productnonmonotonic responsephoton count processphysical boundpiecewise min controlpiecewise or thresholdpolicy couplingpower lawquadratic drag balancequantized triggerratioratio or normalizationregime mappingsaturating responseschedule arithmeticschedule constraintselection and mappingsigmoid mapsigmoid thresholdstate updatestock flowstock flow or accumulationstoichiometrystokes einsteintemperature effectthermodynamic propertythermodynamic relationthermodynamic transformtrigonometric or periodicunit conversionvalidity constraintweighted fusionwind advection projection

All formula families (50)

Aerodynamic power law (Betz-type, with explicit W→MW scaling)Arrhenius equation (local kinetic response)Beer–Lambert UV–Vis spectrophotometryCombined building heat-loss (transmission + ventilation sensible)Coulomb’s law (electrostatics)Darcy's law for saturated laminar porous flowEuler elastic buckling with rectangular-section geometry and slenderness diagnosticsFick First Law with Stokes Einstein and Beer LambertFourier 1D conduction parallel mergeHardy–Weinberg equilibrium (HWE) allele-to-genotype mappingHenderson–HasselbalchKepler third law with astrometric conversion and barycentric sumKeplerian circular orbit relations with inverse-μ estimationKepler’s third law (two-body) and mean orbital speedLC resonance law with temperature and DC-bias adjusted effective parametersLEFM stress intensity (Mode I) K = Y * sigma * sqrt(pi * a)Monod growth kinetics with optical response and inverse calibrationNOCT thermal model + linear PV temperature deratingNewtonian convection (Newton’s law) and lumped-capacitance transient coolingNewtonian gravity: escape velocity and surface gravityNormal-incidence diffraction grating law with imaging geometry (tan/atan) and inverse wavelength estimationOhm’s law (V = I·R), Joule heating (P = I^2·R), Energy accumulation (E = P·t)RC step response and time constantRL step response and time constantRational Method Q = C·i·A with Tc-coupled IDF and orifice capacity vs. storage attenuationSingle-slit diffraction minima (Fraunhofer)Snell’s law of refraction with Fresnel interface transmission and Beer–Lambert bulk attenuationStefan–Boltzmann longwave radiation and gray-body solar absorptionacoustic doppler effectbeam bending Euler Bernoullicentrifugal pump affinity lawseffectiveness NTU parallel brancheselectrochemistry nernst activityfirst order decay with arrhenius and beer lamberthydropower law with rating and weirhypsometric equation virtual temperaturehypsometric inverseideal projectile motion on level ground with inverse control orientationideal gas energy balancelinear elasticity (Hooke’s law) and strain definitionlinear thermal expansion two zonelogistic growthopen channel flow manningoxygen content CaO2 physiologyphotometric flux pipeline with stellar physicsquadratic drag terminal velocityrolling without slipping energy and geometrysimple harmonic oscillatorsimple pendulum small anglethin lens and magnification plus airy disk

Aggregate leaderboard

The leaderboard reports aggregate F1/SHD/SID/nSHD together with appendix metrics including precision, recall, AUROC, and AP. Use the controls to sort by the metric of interest; hover details indicate whether a method supports observation-only evaluation, mixed-interventional evaluation, or both.

Slice-level behavior

The same method can move substantially across benchmark family and data regime. This heatmap uses the same metric family as the aggregate leaderboard, but keeps Synthetic, Semantic, and Formula slices separate.

Per-SCM Semantic/Formula analyzer

Select any released Semantic or Formula SCM and inspect how all methods behave on that particular graph. The table reports replicate-averaged metrics for the selected graph; ΔF1 is method-centered, so positive values mean the method performs better on this SCM than on its own average over released Semantic/Formula SCMs in the same regime.

This is an interactive SCM picker, not a fixed example.Choose a benchmark family, regime, metric, and scenario; the graph, ranking, and error-mode panels update together.

Select SCM below

Benchmark Regime Metric Search Selected SCM scenario

Real-data check

Sources: six CD-CSG observation-only datasets, Sachs flow-cytometry, four PetShop telemetry scenarios, and two Causal Chamber physical-system benchmarks. Obs-only additionally includes observation-only conversions of the seven interventional tables.

Per-dataset real-data check

Dataset-level view across CD-CSG, Sachs, PetShop, and Causal Chamber sources. Means are coarse because real-data cases are few and heterogeneous.

Inspect one real dataset.Choose a regime, dataset, and metric; the ranking plot and method table update together.

Dataset-level ranking

Regime Dataset Metric

Sample-size sensitivity

Synthetic SCMs are fixed at d=30 while observation-only sample size varies. All methods are shown by default; toggle buttons can hide or restore individual curves.

Intervention-protocol sensitivity

The synthetic SCM pool is fixed at d=30; only the intervention design changes. F1 SD summarizes protocol stability.

Protocol profiles

Paper figure summarizing held-out intervention designs and their F1/SHD shifts.

Runtime and cost

For pretrained/amortized wrappers, the table uses fitted per-graph cost after the one-time model load. For other wrappers, it uses end-to-end per-graph runtime on the synthetic main benchmark.

Pretrained runtime fit

Fixed-load plus per-graph fit used to separate checkpoint loading from amortized inference time.

Synthetic factor diagnostics

These analysis figures explain where methods differ across graph, mechanism, noise, root, and dimensional factors, rather than serving as generic manuscript illustrations.

Graph-family interactions

Self-centered shifts by graph topology after accounting for method and category difficulty.

Dimension scaling

How relative method behavior changes as graph dimension increases.

Mechanism interactions

Child-mechanism-level shifts, useful for separating linear, nonlinear, multiplicative, and other mechanism effects.

Noise interactions

Noise-family-level shifts that reveal sensitivity to non-Gaussian or heteroscedastic settings.

Graph-level factors

Additional graph-level covariates after difficulty centering.

Root dependency

Relative behavior under independent and dependent root-variable generation.

Root source

Self-centered shifts by root distribution/source family.

Prior-support and construction diagnostics

These figures connect benchmark coverage, pretraining-support auditing, and the agentic construction pipeline.

Documented prior coverage

Audited support coverage over synthetic factor axes.

OOD relative gains

Relative gains on categories outside documented pretraining support.

Construction ablation

Quality scores across reference grounding, planning, and graph review stages.

Method metadata

Parameter counts are meaningful for fixed pretrained checkpoints. Classical and per-dataset optimization methods do not have a single benchmark-wide parameter count.