Authors: Turan Orujlu, Jordan Matelsky, Martin V. Butz, Charley M. Wu, Konrad P. Kording
Abstract
Here we introduce Partially Observed Structural Causal Models (POSCMs) as an extension of structural causal models (SCMs) to settings where upstream contexts co-determine both the interaction structure and downstream mechanisms on observed variables. POSCMs thus provide a self-contained causal modeling framework for endogenous graphs, allowing for an intervention hierarchy spanning node- and edge-level contexts and endogenous variable interventions. To define edge interventions, we separate node mechanisms into edge-local transmission channels that can be modified without changing the source node or the rest of the target mechanism. We provide an identifiability theory that clarifies which intervention families would suffice to disentangle structure formation from mechanisms. We then empirically validate these theoretical results in two external simulators: a biophysically detailed virtual human retina and a gene-regulatory analogue. The experiments reproduce non-identifiability under latent context, expose structure-mechanism confounding under latent edges, and recover pathway-level input-output relationships under targeted interventions, consistent with our positive Markov kernel identifiability results. Together, POSCMs provide an intervention-oriented framework for causal systems in which contexts, graph structure, mechanisms, and measurements are jointly generated and only partially observed.
Causal discovery, the problem of inferring the direction of causality, is generally ill-posed. We use the language of structural causal models (SCM) to show that assuming that the causal relations are acyclic and invariant across multiple environments (e.g., the way minimum wage affects employment rate is stable across different geographical regions), \textit{only} two auxiliary environments are sufficient to infer the causal graph for arbitrary nonlinear mechanisms. Moreover, we demonstrate that this implies identifiability of the SCM functional mechanisms: as a corollary, we show that \textit{two} auxiliary environments are sufficient to guarantee correct counterfactual inference. We empirically support our theoretical results on synthetic data.
An artificial intelligence must have a model of its environment that is causal, supporting reasoning about interventions and counterfactuals, and also combinatorial, supporting generalization to unseen combinations of objects. In this work, we formally study when and how such a model can be learned. We develop relational structural causal models, extending structural causal models (Pearl 2009) to settings where objects and their relations vary. First, we show how answers to not only causal but also observational queries about unseen combinations of objects can not be identified without further assumptions. To enable such identification--including in the presence of unobserved confounding--we define relational causal graphs and derive symbolic identification criteria. Finally, we propose relational neural causal models, a provably correct approach that outperforms non-relational baselines on simulated traffic scenes with varying cars, signals, and pedestrians.
Most causal benchmarks for language models score local answers or graph structure. We introduce ReplaySCM, a 1,300 item benchmark for executable causal mechanism induction from finite interventional evidence. Each item contains binary worlds generated by a latent fully observed acyclic Boolean structural causal model (SCM). A system must output a mechanism map in a restricted Boolean DSL; the submission is parsed, checked for legality and acyclicity, and replayed on training and held-out intervention worlds. Scoring uses replay behavior rather than formula strings, so syntactically different mechanisms receive credit when they behave correctly. ReplaySCM varies the structural information disclosed to the model through Ordered, Block-order, Hidden-order, and Hidden-roots settings, and includes Alternative-SCM tasks that supply a valid reference SCM and ask for a semantically distinct alternative that fits the training worlds, together with a separating intervention and witness. Frontier LLMs infer parts of the functional-parent structure, but held-out replay drops sharply when order or root structure is hidden. We also evaluate a matched support-audit ladder: Original, Extra Worlds, and Counterexample Audit (CEx), that raises mean local predecessor-pattern coverage from 0.8949 to 0.9815 to 1.0; under the audited searches, no discovered semantic alternative remains consistent with the training worlds. The Ordered/Hidden-order gap persists under this stronger evidence. ReplaySCM complements answer-level causal reasoning and graph-discovery benchmarks by evaluating executable replay generalization from finite interventional evidence, without claiming unique identification of the latent SCM.