# Residual Skill Optimization for Text-to-SQL Ensembles

arXiv: https://arxiv.org/abs/2605.21792 · HTML: https://mlsanity.com/paper/2605.21792/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 45 of its 53 references that are in the map.
- First posted on arXiv 20 May 2026.

## Builds on (most cited first, 30 of 45)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Can LLM Already Serve as A Database Interface? A BIg Bench for Large-Scale Database Grounded Text-to-SQLs](https://mlsanity.com/paper/2305.03111/) (2023)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [DIN-SQL: Decomposed In-Context Learning of Text-to-SQL with Self-Correction](https://mlsanity.com/paper/2304.11015/) (2023)
- [Text-to-SQL Empowered by Large Language Models: A Benchmark Evaluation](https://mlsanity.com/paper/2308.15363/) (2023)
- [SkillRL: Evolving Agents via Recursive Skill-Augmented Reinforcement Learning](https://mlsanity.com/paper/2602.08234/) (2026)
- [LEVER: Learning to Verify Language-to-Code Generation with Execution](https://mlsanity.com/paper/2302.08468/) (2023)
- [Spider 2.0: Evaluating Language Models on Real-World Enterprise Text-to-SQL Workflows](https://mlsanity.com/paper/2411.07763/) (2024)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [CodeS: Towards Building Open-source Language Models for Text-to-SQL](https://mlsanity.com/paper/2402.16347/) (2024)
- [CHESS: Contextual Harnessing for Efficient SQL Synthesis](https://mlsanity.com/paper/2405.16755/) (2024)
- [C3: Zero-shot Text-to-SQL with ChatGPT](https://mlsanity.com/paper/2307.07306/) (2023)
- [MAC-SQL: A Multi-Agent Collaborative Framework for Text-to-SQL](https://mlsanity.com/paper/2312.11242/) (2023)
- [MemSkill: Learning and Evolving Memory Skills for Self-Evolving Agents](https://mlsanity.com/paper/2602.02474/) (2026)
- [CHASE-SQL: Multi-Path Reasoning and Preference Optimized Candidate Selection in Text-to-SQL](https://mlsanity.com/paper/2410.01943/) (2024)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [CoEvoSkills: Self-Evolving Agent Skills via Co-Evolutionary Verification](https://mlsanity.com/paper/2604.01687/) (2026)
- [MCS-SQL: Leveraging Multiple Prompts and Multiple-Choice Selection For Text-to-SQL Generation](https://mlsanity.com/paper/2405.07467/) (2024)
- [Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems](https://mlsanity.com/paper/2505.15201/) (2025)
- [SkillClaw: Let Skills Evolve Collectively with Agentic Evolver](https://mlsanity.com/paper/2604.08377/) (2026)
- [The Dawn of Natural Language to SQL: Are We Fully Ready?](https://mlsanity.com/paper/2406.01265/) (2024)
- [Exploring Chain-of-Thought Style Prompting for Text-to-SQL](https://mlsanity.com/paper/2305.14215/) (2023)

## Abstract (arXiv)

Text-to-SQL ensembles improve over single-candidate generation by drawing multiple SQL candidates and selecting one, but their effectiveness is bounded by Pass@K, the probability that at least one of K candidates is correct. Existing methods source diversity heuristically through stochastic decoding or prompt variants, leaving candidate sets dominated by correlated failures. We present DivSkill-SQL, a residual skill optimization framework that builds complementary agentic Text-to-SQL ensembles without model fine-tuning: each new skill is optimized on examples the current skill ensemble fails on, provably targeting its marginal contribution to Pass@K. On Spider2-Lite, DivSkill-SQL improves selected accuracy by up to +11.1 points on Snowflake and +8.3 on BigQuery over the strongest ensemble baseline, with consistent gains across two base models (Opus-4.6 and GPT-5.4). Skills optimized on a single dialect transfer without retraining across dialects (Snowflake, BigQuery, SQLite) and to a different task formulation, such as BIRD-Critic (+2.6 pts). Error diagnostics show up to 3x fewer hallucinated schema references and function calls, indicating that gains come from genuinely reliable complementary skills rather than surface-form variation.