When Many Answers Are Valid, Voting Fails: Symbolic Verification for Best-of-K Causal Reasoning in LLMs

Large language models reach 50 to 70% accuracy on causal reasoning benchmarks such as CLadder, but it is unclear whether this reflects structural reasoning or lexical pattern matching. We introduce Caliper, a controlled perturbation that replaces semantic variable names with placeholder tokens while preserving the causal graph and probabilistic specification of each question. Across nine instruction-tuned LLMs from 3.8B to 671B and three causal reasoning benchmarks, lexical anonymization yields robust accuracy drops of +7.6, +27.0, and +11.1 pp on a local 3.8B-14B set, rising to +29.6 and +18.0 pp on CRASS and e-CARE across nine frontier models spanning the 2024-2026 generations. Of 40 engaged model-by-benchmark cells, 39 show a positive gap, and the gap collapses by 17x on CLadder's pseudoword subset. Structured scaffolding and few-shot in-context learning each narrow the gap, but mainly by lowering P0 accuracy on smaller models rather than recovering P1. Current instruction-tuned LLMs, evaluated zero-shot, show little evidence of structural causal reasoning once lexical anchors are removed.

As large language models (LLMs) witness increasing deployment in complex, high-stakes decision-making scenarios, it becomes imperative to ground their reasoning in causality rather than spurious correlations. However, strong performance on traditional reasoning benchmarks does not guarantee true causal reasoning ability of LLMs, as high accuracy may still arise from memorizing semantic patterns instead of analyzing the underlying true causal structures. To bridge this critical gap, we propose a new causal reasoning benchmark, CausalFlip, designed to encourage the development of new LLM paradigm or training algorithms that ground LLM reasoning in causality rather than semantic correlation. CausalFlip consists of causal judgment questions built over event triples that could form different confounder, chain, and collider relations. Based on this, for each event triple, we construct pairs of semantically similar questions that reuse the same events but yield opposite causal answers, where models that rely heavily on semantic matching are systematically driven toward incorrect predictions. To further probe models' reliance on semantic patterns, we introduce a noisy-prefix evaluation that prepends causally irrelevant text before intermediate causal reasoning steps without altering the underlying causal relations or the logic of the reasoning process. We evaluate LLMs under multiple training paradigms, including answer-only training, explicit Chain-of-Thought (CoT) supervision, and a proposed internalized causal reasoning approach that aims to mitigate explicit reliance on correlation in the reasoning process. Our results show that explicit CoT can still be misled by spurious semantic correlations, where internalizing reasoning steps yields substantially improved causal grounding, suggesting that it is promising to better elicit the latent causal reasoning capabilities of base LLMs.

Causal discovery is a cornerstone of scientific reasoning, yet whether large language models can perform it reliably remains an open question. Recent benchmarks show that even fine-tuned models plateau on simple causal graphs and degrade as complexity grows, but why they fail has not been established. We prove the failure is fundamental: supervised fine-tuning, direct preference optimization, and in-context learning all produce predictors that cannot distinguish between causal graphs generating similar observational data, and any attempt to do so requires the model's internal representations to grow unboundedly, violating the very conditions under which these methods work. We formalize this as a kernel obstruction theorem, establishing that the limitation is intrinsic to the learning paradigm, \emph{not any particular model or dataset}. We propose Agentic Causal Bayesian Optimization (A-CBO), wherein a frozen language model serves as an interventional oracle answering targeted queries about intervention effects, while an external Bayesian loop concentrates beliefs over candidate graphs in logarithmically many rounds. Because the decision operates outside the space where the obstruction applies, A-CBO provably converges while the underlying model remains unchanged. On Corr2Cause, A-CBO matches fine-tuned baselines without any training. On Extended Corr2Cause, a new benchmark scaling to 24 variables with 18K test samples, A-CBO significantly outperforms both fine-tuning and preference optimization, with the advantage growing