Extended Corr2Cause: Advanced Causal Discovery

• The paper extends Corr2Cause by integrating multi-stage, structured causal discovery protocols using PC-style algorithms and knowledge graphs to enhance inference.
• It introduces a synthetic benchmark that scales from small to large graphs, increasing near-miss ambiguity and evaluating binary rejection accuracy.
• Empirical results demonstrate significant F1 improvements with modular pipelines over conventional models, underscoring benefits of externalized causal reasoning.

Extended Corr2Cause denotes an extension of the Corr2Cause line of work in two distinct but related senses. In one sense, Corr2Cause is extended in practice from a single-shot natural-language causal judgment task into a multi-stage, algorithmic causal discovery workflow executed in context by reasoning-specialist LLMs, including modular PC-style pipelines and structured knowledge-graph intermediates (Kadziolka et al., 31 Jul 2025, Sun et al., 23 May 2025). In the other sense, Extended Corr2Cause is an explicit synthetic benchmark that scales the original Corr2Cause setting from small graphs to larger structural causal models, intensifies near-miss observational ambiguity, and evaluates causal discrimination under increasing graph complexity (Roy et al., 26 May 2026). Across these uses, the central idea is the same: correlation- and independence-based textual premises are treated not merely as classification prompts, but as inputs to structured causal reasoning over Markov equivalence classes, candidate graphs, or interventionally distinguishable hypotheses.

1. Corr2Cause as the base problem

Corr2Cause is treated as a causal inference benchmark in natural language in which each instance contains a premise and a causal hypothesis. The premise is a textual description of correlations, marginal independencies, and conditional independencies among variables, and the hypothesis is a causal claim phrased in natural language (Kadziolka et al., 31 Jul 2025). In the formulation adopted for Corr2Cause, the underlying data-generating objects are directed graphical causal models, i.e. DAGs over variables $\mathcal{X}=\{X_1,\dots,X_N\}$, together with the Causal Markov condition and faithfulness (Kadziolka et al., 31 Jul 2025).

In the original benchmark formalization, DAGs are grouped into Markov equivalence classes (MECs), and hypotheses such as “Is-Parent,” “Is-Child,” “Is-Ancestor,” “Is-Descendant,” “Is-Confounder,” and “Is-Collider” are assigned binary labels depending on whether the relation holds in all DAGs in the MEC (Kadziolka et al., 31 Jul 2025). The task is therefore not limited to pairwise edge orientation; it is inference over equivalence classes from independence structure.

The benchmark is difficult for conventional LLMs. Reported original Corr2Cause results include GPT-4 with F1 $=29.08$, BART MNLI with F1 $=33.38$, and a random uniform baseline with F1 $=20.38$ (Kadziolka et al., 31 Jul 2025, Sun et al., 23 May 2025). The benchmark is also strongly imbalanced: one account describes roughly 85% “false” labels (Kadziolka et al., 31 Jul 2025), while another describes about 80% negative examples (Sun et al., 23 May 2025). Both descriptions agree that accuracy is misleading and that F1 on the positive class is the informative metric.

Generalization failures are central to the motivation for extending Corr2Cause. Fine-tuned models can achieve very high in-distribution performance and then collapse under paraphrasing or variable-name changes. Reported examples include RoBERTa-Large MNLI dropping from F1 $=94.74\%$ in distribution to $55.45\%$ under paraphrasing, and GPT-3 dropping from F1 $=85.52\%$ on original prompts to $46.96\%$ when variable names are refactored (Kadziolka et al., 31 Jul 2025). Another account summarizes this as “causal parroting,” namely reliance on shallow textual patterns rather than robust reasoning over causal structure (Sun et al., 23 May 2025).

2. Two forms of extension

A first form of extension leaves the Corr2Cause dataset unchanged but extends what the benchmark tests. In this usage, Corr2Cause becomes a testbed for staged, algorithmic, LLM-based causal discovery. The benchmark is no longer treated as a direct mapping from text to label; instead, the model is prompted to reconstruct a skeleton, identify v-structures, apply Meek’s rules, and evaluate hypotheses over a CPDAG or MEC (Kadziolka et al., 31 Jul 2025). A closely related variant replaces direct answer generation with a two-stage pipeline in which the model first builds a structured knowledge graph from correlational premises and then reasons over that graph to answer the hypothesis (Sun et al., 23 May 2025).

A second form of extension changes the benchmark itself. Extended Corr2Cause, or Extended C2C, is described as a synthetic benchmark designed to stress-test causal discovery from correlational information at larger graph scales than the original Corr2Cause (Roy et al., 26 May 2026). In this version, instances correspond to SCMs over $d$ variables with $d\in\{7,\dots,24\}$ in the primary evaluation region, with additional released data up to 28 variables (Roy et al., 26 May 2026). Premise length scales as $=29.08$0, and the benchmark is explicitly tuned so that near-miss DAGs with almost identical observational patterns become more prevalent as $=29.08$1 grows (Roy et al., 26 May 2026).

These two extensions are methodologically aligned. The practical extension emphasizes structured reasoning protocols for observational premises, whereas the explicit benchmark extension emphasizes the scaling limits of observational discrimination and the need for procedures that go beyond end-to-end text classification (Kadziolka et al., 31 Jul 2025, Sun et al., 23 May 2025, Roy et al., 26 May 2026). This suggests that “Extended Corr2Cause” is best understood as a family of extensions centered on structured, graph-based, and increasingly adversarial causal reasoning from correlation and conditional independence statements.

3. Explicit Extended Corr2Cause benchmark

In its explicit benchmark sense, Extended Corr2Cause is built from standard SCM ingredients. Variables are $=29.08$2, the causal structure is a DAG $=29.08$3, and structural equations take the form

$=29.08$4

with interventional distributions induced by $=29.08$5 (Roy et al., 26 May 2026). The benchmark is constructed so that observational distributions of distinct candidate graphs can be very similar, while their interventional responses differ.

A canonical near-miss pair highlighted in the construction is the chain

$=29.08$6

versus the fork

$=29.08$7

which share the same conditional independence pattern $=29.08$8 and thus identical textual premises at the level of pairwise correlations and CI statements (Roy et al., 26 May 2026). Extended Corr2Cause scales this idea so that the observational “gap” between the true and closest false hypothesis shrinks as $=29.08$9, and the near-miss kernel similarity parameter satisfies $=33.38$0 (Roy et al., 26 May 2026).

The evaluation subset reported for Extended Corr2Cause contains 18,000 test samples, obtained as 1,000 test instances per depth for $=33.38$1 (Roy et al., 26 May 2026). An appendix-level dataset description gives a fuller view: graph sizes $=33.38$2, total samples 2,171,400, train/dev/test splits for $=33.38$3–24, and raw JSON for $=33.38$4–28 for training only (Roy et al., 26 May 2026). The average number of tokens per premise grows from 112 at $=33.38$5 to about 1,150 at $=33.38$6, reflecting the $=33.38$7 growth in premise length (Roy et al., 26 May 2026).

A distinctive design choice is the test formulation. Whereas original Corr2Cause is described as a multi-class task over six causal relation templates, the Extended Corr2Cause test split is described as all-negative, so evaluation reduces to binary rejection accuracy (Roy et al., 26 May 2026). Each instance still consists of a premise $=33.38$8, a hypothesis $=33.38$9, and a label $=20.38$0, where $=20.38$1 means that the hypothesis is entailed by all DAGs consistent with $=20.38$2, but on the extended test split all labels are $=20.38$3 (Roy et al., 26 May 2026).

4. Modular and structured reasoning over Corr2Cause

The practical extension of Corr2Cause in reasoning-oriented work is built around the PC algorithm and related structured intermediates. One implementation embeds the entire PC causal discovery algorithm into a single zero-shot prompt and instructs the model to build the skeleton, identify v-structures, apply Meek’s rules, and decide whether the hypothesis is supported by the resulting causal structure, returning JSON of the form {"hypothesis_answer": true/false} (Kadziolka et al., 31 Jul 2025). This turns Corr2Cause into an in-context simulation of causal discovery rather than a direct textual entailment problem.

The central modular version decomposes the process into four stages: skeleton estimation, v-structure identification, Meek-rules orientation, and hypothesis evaluation over the MEC (Kadziolka et al., 31 Jul 2025). In the skeleton stage, the model starts with edges for correlated pairs and removes an edge $=20.38$4 if any independence statement says $=20.38$5, marginally or conditionally (Kadziolka et al., 31 Jul 2025). In the v-structure stage, the model extracts separation sets from the premise and orients triples $=20.38$6 as colliders when $=20.38$7 and $=20.38$8 are non-adjacent, $=20.38$9 and $=94.74\%$0 are present, and $=94.74\%$1 is absent from all conditioning sets that separate $=94.74\%$2 and $=94.74\%$3 (Kadziolka et al., 31 Jul 2025). In the third stage, the model applies Meek’s rules to obtain a PDAG or CPDAG while preserving v-structures, avoiding directed cycles, and orienting only compelled edges (Kadziolka et al., 31 Jul 2025). In the fourth stage, the hypothesis is declared true only if it holds in every valid DAG completion consistent with the CPDAG and the independence constraints (Kadziolka et al., 31 Jul 2025).

A parallel structured approach replaces PC-style graph orientation with knowledge-graph construction. Here the model first extracts a KnowledgeGraph(nodes: List[Node], edges: List[Edge]) from the premise, with edge labels such as "correlates with", "independent of", or "independent given A and B" (Sun et al., 23 May 2025). The schema is enforced using a Pydantic model, an OpenAI-style tool specification, and a regex-constrained decoder via RegexLogitsProcessor, so that generated outputs must match the JSON schema (Sun et al., 23 May 2025). The resulting KG is converted into DOT/Graphviz, and the second-stage prompt asks the model to answer the causal query using the original premise, the hypothesis, and the graph representation (Sun et al., 23 May 2025).

These structured variants share a common logic. They separate premise comprehension from inference, externalize intermediate objects, and constrain output to machine-readable forms (Kadziolka et al., 31 Jul 2025, Sun et al., 23 May 2025). A plausible implication is that the essential extension is not merely longer prompting, but the conversion of Corr2Cause into a piecewise causal reasoning workflow with inspectable artifacts such as skeletons, separation sets, CPDAGs, or knowledge graphs.

5. Empirical results and diagnostic findings

On unchanged Corr2Cause, reasoning-specialist models and structured pipelines substantially improve over earlier baselines. In a single-prompt PC setup, reported zero-shot results include DeepSeek-R1-70B with F1 $=94.74\%$4, DeepSeek-R1 API with F1 $=94.74\%$5, and OpenAI o3-mini with F1 $=94.74\%$6, compared with the best original Corr2Cause baseline BART MNLI at F1 $=94.74\%$7 (Kadziolka et al., 31 Jul 2025). In the four-stage modular pipeline, performance rises further: DeepSeek-R1-70B reaches F1 $=94.74\%$8, DeepSeek-R1 API reaches F1 $=94.74\%$9, and OpenAI o3-mini reaches F1 $55.45\%$0 (Kadziolka et al., 31 Jul 2025). The authors describe this as “up to a three-fold F1 improvement” (Kadziolka et al., 31 Jul 2025).

Stage-wise analysis localizes where reasoning remains difficult. Reported stage-wise F1 values show near-perfect performance for skeleton discovery and v-structure identification in the strongest models, while Meek’s rules and hypothesis evaluation are harder. For OpenAI o3-mini, the reported stage-wise F1 values are 1.00 for skeleton, 0.99 for v-structures, 0.95 for Meek’s Rules, and 0.84 for hypothesis evaluation (Kadziolka et al., 31 Jul 2025). This establishes Corr2Cause as a diagnostic decomposition of causal discovery subtasks rather than merely an end metric.

The structured knowledge-graph approach also yields large gains. On the Corr2Cause test subset with Qwen3-32B, direct zero-shot prompting gives F1 $55.45\%$1, precision $55.45\%$2, recall $55.45\%$3, and accuracy $55.45\%$4, whereas the structured approach gives F1 $55.45\%$5, precision $55.45\%$6, recall $55.45\%$7, and accuracy $55.45\%$8 (Sun et al., 23 May 2025). The paper characterizes this as a 47.5% relative F1 increase and a 93.4% increase in recall, without fine-tuning (Sun et al., 23 May 2025).

On the explicit Extended Corr2Cause benchmark, results are framed around binary rejection accuracy and, in some tables, per-class F1 mapped back to the six original relation templates (Roy et al., 26 May 2026). A-CBO, an agentic interventional framework discussed below, substantially outperforms zero-shot prompting and trained baselines. For example, on Extended C2C, Qwen3-30B$55.45\%$9 improves from zero-shot F1 $=85.52\%$0, accuracy $=85.52\%$1, to A-CBO F1 $=85.52\%$2, accuracy $=85.52\%$3, and GLM-5.1$=85.52\%$4 improves from zero-shot F1 $=85.52\%$5, accuracy $=85.52\%$6, to A-CBO F1 $=85.52\%$7, accuracy $=85.52\%$8 (Roy et al., 26 May 2026). Fine-tuned RoBERTa-Large baselines collapse as graph size increases: SFT accuracy falls from $=85.52\%$9 at $46.96\%$0–10 to $46.96\%$1 at $46.96\%$2–24, while DPO falls to $46.96\%$3 at the highest depth range (Roy et al., 26 May 2026).

Failure analysis in the modular Corr2Cause work attributes part of the improvement to iterative re-evaluation. When comparing LLaMA 3.3-70B-Instruct with DeepSeek-R1-70B on the skeleton stage, the reasoning model performs many micro-steps in its internal reasoning trace, with mean about 66 micro-steps and maximum about 135, and often revisits doubtful edges using self-correction cues such as “Wait…” or “Hold on…” (Kadziolka et al., 31 Jul 2025). The more often the reasoning model revisits an edge, the more likely the conventional model is to misclassify it (Kadziolka et al., 31 Jul 2025). This suggests that structured external pipelines partly mimic an internal rechecking mechanism.

6. Theory, limitations, and conceptual scope

The large-scale Extended Corr2Cause benchmark is explicitly tied to a theoretical claim about observational causal discrimination. A kernel obstruction theorem states that supervised fine-tuning, direct preference optimization, and in-context learning produce bounded-norm kernel-type predictors that cannot maintain a non-vanishing margin between sufficiently similar near-miss premise–hypothesis pairs as $46.96\%$4 (Roy et al., 26 May 2026). Because Extended Corr2Cause is designed so that $46.96\%$5, the benchmark serves as an empirical stress test for this claim (Roy et al., 26 May 2026).

The proposed escape route is Agentic Causal Bayesian Optimization (A-CBO). In this framework, a frozen LLM is used only as a binary oracle for local interventional questions such as “Does $46.96\%$6 change under $46.96\%$7?”, while an external Bayesian loop maintains posterior mass over candidate graphs and selects the next intervention by maximizing expected information gain (Roy et al., 26 May 2026). Under an oracle reliability assumption, the convergence bound

$46.96\%$8

depends on the number of hypotheses $46.96\%$9 and oracle noise $d$0, but not on the near-miss parameter $d$1 (Roy et al., 26 May 2026). This sharply contrasts with purely observational LLM paradigms on the extended benchmark.

The practical extensions of Corr2Cause also have clear limitations. The four-stage PC pipeline increases token usage substantially; for o3-mini, one report gives about 4k tokens per sample for the single-prompt baseline and about 11k for the pipeline, while DeepSeek-R1 API increases from about 8k to about 25k (Kadziolka et al., 31 Jul 2025). The knowledge-graph approach requires one extra LLM call per example together with regex-constrained decoding and JSON parsing, and graph-construction errors can cascade into wrong final judgments (Sun et al., 23 May 2025). Both approaches also remain tied to faithfulness and accurate independence information, because the core reasoning procedures inherit the assumptions of PC-style discovery (Kadziolka et al., 31 Jul 2025).

A further conceptual limitation is terminological. The phrase “Extended Corr2Cause” does not appear as a dataset name in the modular PC paper; there it is an interpretive description of how Corr2Cause is used rather than a new benchmark identity (Kadziolka et al., 31 Jul 2025). By contrast, in the A-CBO work, Extended Corr2Cause is an explicit named dataset with enlarged graphs and all-negative test labels (Roy et al., 26 May 2026). A precise reading therefore distinguishes between extended use of Corr2Cause and Extended Corr2Cause as a benchmark.

Taken together, these strands define Extended Corr2Cause as a broader research program around causal reasoning from correlational text under structured representations, larger graph regimes, and stronger adversarial ambiguity. The benchmark-centered strand emphasizes scaling and near-miss hardness (Roy et al., 26 May 2026). The prompt- and pipeline-centered strand emphasizes modular in-context discovery over MECs, CPDAGs, and graph intermediates (Kadziolka et al., 31 Jul 2025, Sun et al., 23 May 2025). Their shared significance is that Corr2Cause is no longer only a binary natural-language classification task; it becomes a vehicle for studying how LLMs reconstruct, manipulate, and validate causal structure under observational constraints.