This work introduces CALVER (Causal Axiom-Level VERification), a training-free symbolic verifier that scores structured traces against Pearl's causal criteria, including -separation, backdoor adjustment, and intervention, and selects the highest-scoring candidate without consulting a reference answer.
Abstract
Self-consistency assumes the most frequent answer among sampled reasoning traces is the most reliable, but this can fail in causal reasoning: samples often repeat the same confounding error, and votes fragment across multiple valid answers, letting an invalid answer win despite a valid minority trace. We introduce CALVER (Causal Axiom-Level VERification), a training-free symbolic verifier that scores structured traces against Pearl's causal criteria, including -separation, backdoor adjustment, and intervention, and selects the highest-scoring candidate without consulting a reference answer. On CLEAR find-one-valid queries that admit multiple graph-valid answers, CALVER reaches 42.1% where plurality, a reward model, an LLM judge, and model confidence remain near 30% on identical frozen pools. Scaling the judge to 72B does not close the gap. In an audited clean-core subset, 11 of 21 graph-valid CALVER selections differ from the benchmark's listed answer while still satisfying the requested predicate. The advantage widens with the sampling budget and reproduces across ten published Bayesian networks, a second model family, and settings where the model must build the graph from text. CALVER also improves thresholded average-treatment-effect decisions against exact ground truth, generalizes to logic under a truth-table checker, and scores each candidate in milliseconds on CPU. CALVER needs only a causal structure, supplied outright or built from the text; wherever that holds, selection can aggregate via causal validity.
Mathematical chain of thought (CoT) evaluation is commonly reduced to whether the final answer matches a reference. This conflates producing a correct conclusion with producing a valid derivation an invalid chain can accidentally reach the right answer, while a valid calculation can be followed by a transcription error. We call this mismatch the reasoning answer consistency gap. This framework paper introduces the Reasoning Answer Faithfulness Score (RAFS), a reference free, instance level diagnostic of whether an emitted mathematical trace is locally credible, supports its answer, and is stable under resampling and targeted counterfactual interventions. RAFS combines step validity, reasoning to answer entailment and counterfactual sensitivity, answer consensus, and conditional reasoning stability. It evaluates transcript level agreement, not a models private computation and not factual correctness outside the tested mathematical setting. We retain a preregistered, results blind confirmatory study on GSM8K and MATH, with hypotheses, admissibility rules, calibration, and tests fixed before confirmatory outcomes are inspected. A separate feasibility pilot is specified to verify end to end execution and estimate interven tion coverage before that freeze numerical pilot claims are re ported only when trace level artifacts are available. We formalize four reasoning answer outcomes, justify the non compensatory aggregator, instantiate semantic trace distance, quantify compute and abstention tradeoffs, and define verifier independence and power analyses. RAFS is intended to complement mathematical answer accuracy with an auditable warning signal for silent reasoning failures and answer extraction errors
Vivek Shukla, Varun Shukla, Atul et al.· 0 citations
This paper introduces C LUE (Clustering and Experience-based Verification) , a training-free, non-parametric verifier that improves selection and reranking in Large Language Model outputs and finds that correct and incorrect solutions exhibit measurable geometric differences in their hidden-state trajectories.
Zhenwen Liang, Ruosen Li, Yujun Zhou et al.· Annual Meeting of the Associ...· 0 citations
Large language models (LLMs) are often asked whether something is absent from a record, list, or retrieved context. Yet non-observation licenses a negative answer only when evidence completely covers the query scope; otherwise, the answer should remain unknown. We call this completeness-sensitive negative reasoning. We introduce CROWN-QA, comprising CROWN-Synth, a controlled paired core that fixes the question and observed facts while varying only query-relative coverage, and CROWN-Real, a real-document contrast-set evaluation with controlled coverage variants. Across three LLM families, models show unstable closure judgments and substantial over-closure, failing to reliably distinguish a justified negative answer (Certified-Negative) from insufficient evidence (Unknown). The dominant CROWN-Synth failure is asymmetric: models often recognize implicitly complete evidence yet treat implicitly partial evidence as query-covering. Prompting redistributes errors between over- and under-closure rather than consistently resolving them. Structured certificate elicitation traces many errors to evidence-coverage mischaracterization. CROWN-Real shows that the core partial-coverage asymmetry persists on real-document content, while its strength and the balance between over- and under-closure vary by model, prompt, and source.
Byoungjae Min, Kennedy Edemacu, Sae-Hong Cho et al.· 0 citations
Large Reasoning Models produce diverse, sometimes inconsistent answers across repeated queries on the same problem, so multi-sample inference is a prerequisite for reliable deployment. Majority voting at k rollouts is the standard solution and the de facto accuracy target for this regime, but it is prohibitively expensive at the scale LRMs require. We introduce Funnel of Thoughts (FoT), an inference-time method that preserves the full 32-trajectory voted accuracy while halving its attention FLOPs, a 28.8% reduction in full-model inference cost. Across 115K reasoning trajectories from six LRMs, we find that unproductive trajectories often reveal themselves through repeated hesitation markers such as"Wait","Actually", and"perhaps."These trajectories are less likely to reach the correct answer and consume disproportionate attention FLOPs, degenerating into no-answer loops in the worst case. Built on this training-free lexical signal, FoT identifies the vocabulary that captures these pathological patterns and prunes affected trajectories before completion, reducing online generation attention FLOPs by 56.1% and wall time by 37.6% without any additional model inference; the same signal transfers without retuning across held-out architectures and out-of-domain tasks.
Chanhee Park, Sun Han, Jeongho Yoon et al.· 0 citations
A probe corpus of 42 retracted, fraudulent, and pseudoscientific papers is paired with a methodology for eliciting and scoring single-shot model engagement with each paper's framing, indicating an urgent need for guardrail infrastructure for scientific deployment of language models.
Whether large language models perform algorithmic inference or pattern completion is hard to test, because most benchmarks supply answers but no distributional reference for what the shown evidence licenses. F-ICL supplies one exactly: we exhaustively enumerate the 86 million valid programs of length at most 13 on a Turing-complete machine F, complement-symmetrised to remove output-polarity bias, and compute the exact posterior under a declared bounded Levin--Solomonoff prior. It is Bayes-optimal for that stated prior rather than universal, and models are never told it exists, so the score reads the inductive prior their served distribution already encodes. Across 105 serving configurations spanning open models from 0.8B to 675B and frontier systems, models answer up to 92% of queries correctly, yet 45 of the 46 exposing distributions sit farther from the F reference than a keystroke reference. This is not an artefact of task selection: on the bit coordinate, the half the length quota cannot distort, 69 of 80 runs stay below the anchor. Fidelity is inert to scale, which accuracy tracks; continuation improves late without converging; and models un-solve a solved task once per two gains, where the F reference does so once per nine and always repairs it. Because absolute distances are reference-dependent, we prove sequential bounds holding for rival priors: any predictor whose prior gives the reference positive weight has bounded cumulative excess loss, and, in a loss never invoking the reference, any Bayesian mixture giving the realised truth positive mass has a bounded truth-loss budget. On 23,998 trajectories, 86.7% already spend over 10 bits of it. Sequences ending by position nine cannot exclude an arbitrarily large finite constant, so these are lower bounds on what a rival prior must already pay. F-ICL is an open benchmark and toolkit.