Knowing When to Stop: Predicting Execution-Consistency Convergence in Text-to-SQL

Repeated LLM calls are the standard way to estimate how trustworthy a Text-to-SQL result is: run the pipeline multiple times, judge each SQL execution, and use the consistency of the verdicts as a confidence signal. The open question is when to stop, when the consistency has converged. We formulate this as a convergence-prediction problem and train a family of lightweight 1-D models that observe the running consistency trajectory and decide, at each step, whether further runs are unlikely to shift it materially, and we benchmark them against a principled Beta-Bernoulli stopping rule and a learned run-count baseline. On the BIRD benchmark and two production customer datasets, our method adapts its stopping point to each user question, halting sooner when consistency converges early and continuing longer when it converges late. We further show that the weak serial correlation between runs lets us permute their order as a training augmentation, controlled by a tunable shuffling weight. Performance stays consistent across the three datasets, and to mimic an imperfect production judge we inject noise into the correct/incorrect verdicts obtained by comparing the generated and ground-truth SQL results, showing that the method still predicts convergence reliably.

When to Truncate a Feature Ranking: A Residual-Overlap Stopping Rule for Subset Selection

Feature rankings are widely used in supervised feature selection because they are simple, scalable and easy to interpret. Variables are first ranked by a relevance score, and a subset is then obtained by retaining the top-ranked variables. Although the first stage has been extensively studied, the second is often governed by an arbitrary cardinality, an empirical threshold or cross-validation, without a direct interpretation. This raises a basic question: given a feature ranking, when is there enough accumulated class-separation evidence to stop selecting features? This paper develops a distributional framework for transforming supervised feature rankings into class-independent subsets through an explicit risk-calibrated stopping rule. For each variable and each pair of classes, marginal separation is measured by the Bhattacharyya coefficient between the corresponding class-conditional distributions. The proposed method selects a single global subset shared by all classes by retaining the shortest prefix of a ranking whose residual product overlap falls below a prescribed threshold for every relevant class contrast. We derive binary and multiclass Bayes-risk bounds for the labelled product marginal problem, and obtain prior-dependent and prior-free calibrations of the residual-overlap threshold from a target all-pairs risk level. An empirical comparison on high-dimensional genomic datasets illustrates that the rule can reduce tens of thousands of variables to a few dozen while maintaining predictive performance statistically comparable to the all-features baseline. As the stopping rule only requires one-dimensional marginal overlap estimates and scans a precomputed ranking, it is well suited to very high-dimensional settings where exhaustive subset search is infeasible and interpretable truncation of feature rankings is essential.