F-ICL is an open benchmark and toolkit that exhaustively enumerates the 86 million valid programs of length 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.
Abstract
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.
This work measures the capability that role assumes and finds it lacking under the protocol the role is usually deployed with, one-shot greedy authoring with no test-time reasoning.
Wenhui Chen, Jianlin Chen, Ziyao Lin et al.· 0 citations
Evaluating uncertainty in AI-generated SQL queries requires estimating whether a query is correct, where correct means it executes to the same result as a human-written reference. We study which signals predict correctness on hard multi-table text-to-SQL, using AUROC to measure how well each ranks correct queries above incorrect ones. On BIRD and Spider, black-box signals such as string, structural, and execution self-consistency, a schema-relevance score, and query executability all fall between about 0.61 and 0.68 AUROC, with string self-consistency strongest at 0.675; white-box log-probability is similar (0.67). The signals that move past this ceiling are verification-based: an LLM judge scores from 0.72 (GPT-4o-mini) to 0.78 (Claude). Judges from different providers make different errors, so a two-provider ensemble reaches 0.82 AUROC with a well-calibrated probability (expected calibration error 0.03) and supports useful abstention frontiers (for example, answering 27% of questions at 24% selective risk) where self-consistency offers no valid low-risk subset. The pattern holds across two benchmarks, two generators, and two judge providers. We also ask whether a verifier can be trained. Fine-tuned verifiers, both encoder and generative, reach about 0.77 to 0.79 AUROC in-distribution but fall to about 0.66 on unseen schemas; scaling to 7B, adding schema diversity, distilling a strong judge's rationales, and cross-benchmark training all fail to close that gap. Cross-schema transfer appears to track model scale and reasoning rather than fine-tuning. In practice, correctness uncertainty for text-to-SQL lives in reasoning-based signals: a fine-tuned verifier is a good in-domain tool, but a verifier that generalizes across schemas currently means a large frozen reasoning model.
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
This work invert a family of test supermartingales and proposes several mixture querying rules that combine growth-oriented querying, prediction refinement, and uniform exploration, trying to mitigate the effects that slow the shrinkage rate.
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.
Omatharv Bharat Vaidya, C. Jerzak, Zayne Sprague et al.· 0 citations
When a language model must choose one answer from a large space of equally valid options, a format clause --"Reply with JSON only"-- changes which answer it chooses, and structured output is how software consumes language models.