Measure Learning at Steady State: A BIRD-SQL Formula 1 Case Study

Recent advances in in-context learning (ICL) text-to-SQL have substantially improved execution accuracy on public benchmarks by assembling increasingly elaborate pipelines around the base generator, yet existing studies typically report aggregate end-to-end accuracy, without quantifying the marginal accuracy-cost contribution of individual design choices. Consequently, providing a unified, paradigm-level cost-accuracy quantification remains a critical challenge for understanding and configuring modern text-to-SQL. To address this, we instantiate 17 paradigm-level configurations across five recurring modules of the ICL text-to-SQL pipeline under a single controlled implementation, and attribute each paradigm's marginal contribution and incurred cost across all four backbones spanning diverse capability levels and reasoning styles. Our analysis reveals that execution-feedback refinement is the only paradigm whose benefit holds universally at consistently low cost, while most other modules help only under backbone-dependent conditions. Token accounting shows that input demand is more closely tied to pipeline structure, whereas output demand is more sensitive to backbone generation behavior. Cross-module analysis further shows that stacking improves accuracy on most backbones, although how the gains compose varies with backbone capability. We also find that a fixed budget is often better spent engineering a more elaborate pipeline over a mid-tier backbone than upgrading to a frontier model with a lean pipeline. These findings distill into an actionable, cost-aware tiered guideline that transfers to five additional backbones without per-paradigm search.

In-context learning (ICL) is an emerging paradigm that employs the semantic information inherent in large language models (LLMs) for generating answers to user queries. While the remarkable performance of ICL has been widely known, a general modeling and a rigorous theoretical analysis of this paradigm are still lacking. This work presents a probabilistic model for ICL and derives the performance of ICL for both general parametric distributions and exponential families. Based on the derived results, the work explains the impact of multiple factors such as the number of demonstrations, the sensitivity of the probabilistic model to the variation of its parameters, as well as the similarity between the demonstrations and the query on the performance of ICL.

While recent advancements in inference-time learning have improved LLM reasoning on Text-to-SQL tasks, current solutions still struggle to perform well on the most challenging tasks in the Bird-Bench (BIRD) benchmark. This is due to inadequate solution space exploration, which is necessary to uncover promising candidate queries that can be further refined to produce the correct output. To address this challenge, we introduce CA-SQL, a novel Text-to-SQL pipeline that utilizes the estimated difficulty of a task to dynamically scale the breadth of the exploration for generating solution candidates. In addition, we use a custom prompt seeding method, based on principles of evolutionary search, to further elicit exploratory behavior from the base LLM and a novel voting method to select the best candidate solution at the end of the search. Experiments demonstrate that our solution achieves a state-of-the-art score of 51.72% on the "challenging" tier of BIRD development set problems, using only GPT-4o-mini, out-performing other in-context learning approaches, even those that leverage larger models. Overall, our method attains a competitive 61.06% execution accuracy and 68.77% Soft F1 score on the BIRD development dataset.