This innovative practice full paper describes an AI-powered knowledge graph platform that connects SQL errors to conceptual gaps in undergraduate and graduate database systems courses. Students learning Structured Query Language (SQL) frequently struggle with semantic errors that reflect conceptual misunderstandings rather than syntax mistakes. A query may execute yet return incorrect results due to gaps spanning related concepts; misusing NATURAL JOIN in place of an explicit subquery reflects intertwined misunderstandings of JOIN, GROUP BY, and HAVING. Autograding systems detect correctness but provide surface-level feedback without connecting errors to the conceptual structure of the course. Educational knowledge graph research has shown the value of structured concept representations for curriculum analysis and adaptive learning, but these approaches have not been applied to diagnosing SQL misconceptions from student submissions. We present a platform that automatically extracts course concepts and relations from instructional materials, links them to student submission traces through a graph database, and classifies errors at the concept level. We evaluate the platform across two database systems courses at two universities, one using real student submissions and one using simulated submissions, through an expert study with five participants and an automated evaluation using an LLM as a judge. Results show that 95.7% of extracted nodes were rated as at least somewhat valid and 63.8% of triplets were rated fully correct. Expert feedback confirmed that the generated graphs align with instructor mental models and that mapping errors to course concepts provides actionable diagnostic insight; evaluating impact on student learning remains future work.
Despite the remarkable performance of large language models (LLMs) in text-to-SQL (SQL generation), correctly producing SQL queries remains challenging during initial generation. The SQL refinement task is subsequently introduced to correct syntactic and semantic errors in generated SQL queries. However, existing paradigms face two major limitations: (i) self-debugging becomes increasingly ineffective as modern LLMs rarely produce explicit execution errors that can trigger debugging signals; (ii) self-correction exhibits low detection precision due to the lack of explicit error modeling grounded in the question and schema, and suffers from severe hallucination that frequently corrupts correct SQLs. In this paper, we propose ErrorLLM, a framework that explicitly models text-to-SQL Errors within a dedicated LLM for text-to-SQL refinement. Specifically, we represent the user question and database schema as structural features, employ static detection to identify execution failures and surface mismatches, and extend ErrorLLM's semantic space with dedicated error tokens that capture categorized implicit semantic error types. Through a well-designed training strategy, we explicitly model these errors with structural representations, enabling the LLM to detect complex implicit errors by predicting dedicated error tokens. Guided by the detected errors, we perform error-guided refinement on the SQL structure by prompting LLMs. Extensive experiments demonstrate that ErrorLLM achieves the most significant improvements over backbone initial generation. Further analysis reveals that detection quality directly determines refinement effectiveness, and ErrorLLM addresses both sides by high detection F1 score while maintain refinement effectiveness.
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.
Text-to-SQL systems are typically evaluated by query-level execution correctness, but this terminal signal provides little guidance about which intermediate SQL decision caused success or failure. Token-level dense supervision is also ill-suited: SQL tokens do not align with complete semantic decisions, can penalize execution-equivalent queries, and are difficult to label reliably at scale. We therefore propose CAPER, which automatically derives clause-level supervision via counterfactual intervention on the SQL abstract syntax tree, enabling root-cause error localization for reward modeling; the resulting data is used to train CAPER-9B, a lightweight Clause-PRM that provides clause-boundary feedback for policy optimization and candidate verification. Experiments on BIRD and Spider show that clause-aligned supervision not only improves execution accuracy, achieving up to a 15.3% relative EX improvement over GPT-5.4, but also strengthens failure-localization capability, reaching 84.53% accuracy and 90.60% MRR on held-out failures. Our project page is at https://github.com/banrichard/RL-NL2SQL.