Technical Summary: ReplaySCM

Problem Statement

Current causal reasoning benchmarks for large language models (LLMs) predominantly evaluate local outputs, such as answers to specific causal questions, predicted counterfactual values, or individual graph edges. While useful, these tasks do not verify whether a system can synthesize a reusable, executable causal model capable of generalizing under new, unseen interventions.

This paper introduces ReplaySCM, a benchmark designed to evaluate executable causal mechanism induction from finite interventional evidence. The core challenge is to induce a Structural Causal Model (SCM) that, when "replayed" on both training and held-out intervention worlds, produces behavior semantically identical to the ground truth, regardless of the syntactic form of the induced formulas.

Methodology

Benchmark Design

ReplaySCM consists of 1,300 items generated from small, finite, binary, fully observed, acyclic Boolean SCMs.

• Latent SCM: Each problem is grounded in a latent SCM where endogenous mechanisms are Boolean expressions over observed roots and other endogenous variables.
• Intervention Worlds: The benchmark provides multiple training worlds generated by executing the latent SCM under hard interventions (clamping variables to specific values). A set of held-out worlds is withheld for evaluation.
• Output Format: Models must output a mechanism map in a restricted Boolean Domain Specific Language (DSL) containing operators not, and, or, xor, and iff.
• Evaluation Protocol: The evaluator parses the submission, checks for legality and acyclicity, and replays the submitted SCM on the training and held-out worlds.
  • Scoring: Credit is assigned based on semantic replay behavior, not string matching. Any executable SCM that induces the correct truth table on the scored worlds is considered correct, even if its Boolean formulas differ syntactically from the gold standard.

Structural Disclosure Ladder

The benchmark varies the structural information disclosed to the model to isolate specific reasoning capabilities:

1. Ordered (Ord-Full): Reveals the full topological order.
2. Block-order: Reveals coarse precedence blocks but hides intra-block order.
3. Hidden-order: Reveals the root/endogenous partition but hides the endogenous order.
4. Hidden-roots: Hides both the order and the root set, requiring the model to predict the root set first.

Ambiguity Reduction and Support-Audit

To address the under-constrained nature of finite evidence, the authors employ a three-level support-audit ladder:

• Original: Standard training worlds.
• Extra Worlds: Adds 3–4 gold-simulated training worlds to increase local predecessor-pattern coverage (from ~0.89 to ~0.98).
• Counterexample Audit (CEx): Further adds worlds to achieve full local coverage (1.0) and specifically targets discovered semantic alternatives. In CEx, no discovered alternative from LLMs, symbolic exact search, or bnlearn+DSL searches remains consistent with the training worlds.

Supplementary Tasks

• Alternative-SCM: Given a valid reference SCM, the model must find a semantically distinct alternative that fits the training worlds and provide a separating intervention and witness.
• Non-LLM Baselines: Includes bnlearn+DSL (structure proposal + exact Boolean fitting) and symbolic exact-search (direct search for Boolean mechanisms) to calibrate task difficulty.

Key Contributions

1. Executable SCM Induction Benchmark: Introduces a publicly released benchmark evaluated by exact replay on training and held-out worlds, moving beyond local answer scoring.
2. Matched Revealed-Structure Ladder: Organizes the benchmark to isolate the impact of structural disclosure (Ordered vs. Hidden-order vs. Hidden-roots) on the same latent SCMs.
3. Ambiguity Control: Implements a generator that filters trivial shortcuts and tracks residual ambiguity through support filters, bounded audits, and the three-level support-audit ladder (Original, Extra Worlds, CEx).
4. Comprehensive Evaluation: Benchmarks frontier LLMs against shared evaluators and non-LLM baselines, providing a calibrated view of the difficulty of executable mechanism induction.

Results

Executive Mechanism Induction Remains Unsolved

Frontier LLMs (e.g., GPT-5.4, Claude Opus 4.6, Gemini 3.1 Pro) perform well below perfect exact replay.

• TrainExact vs. HeldoutExact: While some models achieve high validity and partial parent-structure inference, HeldoutExact (strict replay on all held-out worlds) remains low, particularly in Hidden-order settings.
• The "Train-Exact" Gap: Responses that fail to fit training worlds almost invariably fail on held-out worlds. However, even responses that are TrainExact (fit all training worlds exactly) often fail on held-out worlds, indicating that fitting the observed data does not guarantee the correct underlying mechanism.

Impact of Structural Information

Performance degrades significantly as structural information is withheld:

• Ordered vs. Hidden-order: There is a substantial drop in performance when the topological order is hidden. For example, on the Hidden-order pool, GPT-5.4 achieves a TrainExact of 0.628 but drops to 0.292 on HeldoutExact.
• Hidden-roots: Performance collapses when the root set is hidden, as the model must simultaneously predict the root set and induce mechanisms.

Semantic Structure vs. Exact Mechanism

• Partial Inference: Models often infer informative functional-parent relationships (high Parent F1) but fail to match the exact parent map or local mechanisms required for full replay.
• Alternative-SCM: When a valid reference SCM is supplied, performance on finding semantically distinct alternatives is significantly higher than inferring the SCM from scratch. This suggests that local editing of a causal object is easier than global inference from intervention data.

Support-Audit Findings

• Extra Worlds: Increasing training data improves held-out replay and reduces the train-to-held-out gap, but the Ordered/Hidden-order performance gap persists.
• Counterexample Audit (CEx): Even after adding worlds to eliminate all discovered alternatives from LLMs and symbolic search, the Hidden-order setting remains harder than Ordered. This indicates that the difficulty is not solely due to finite-sample ambiguity but reflects a fundamental challenge in inferring hidden structure.

Significance and Claims

The paper claims that ReplaySCM complements existing answer-level and graph-discovery benchmarks by evaluating the generalization of executable causal objects.

• Separation of Capabilities: The benchmark demonstrates a clear separation between "describing causal structure" (inferring dependencies) and "constructing a causal object that can be executed" (synthesizing mechanisms that generalize). Models can produce plausible explanations or edge sets yet fail when their proposed mechanisms are replayed under new interventions.
• Hidden Structure is Hard: The primary empirical finding is that inferring hidden structure (order or roots) is significantly harder than producing a valid answer object or fitting isolated local mechanisms.
• No Claim of Uniqueness: The authors explicitly state that ReplaySCM does not claim to prove the unique identification of the latent SCM. Instead, it provides a controlled testbed for evaluating executable replay generalization from finite interventional evidence, using bounded ambiguity audits to rule out easy finite-sample shortcuts.

The work suggests that while frontier LLMs can infer partial dependency structures, they struggle to assemble the exact parent maps and Boolean mechanisms necessary for robust causal simulation, a gap that persists even with stronger evidence and structural priors.