Translating natural language questions into SQL has become a core challenge in enabling non-technical users to query databases. While recent work has explored large-scale synthetic data generation to improve model performance through post-training, most efforts emphasize cross-domain generalization. This leaves a gap for real-world enterprise scenarios, where models need to specialize to a single database schema and organizations require to be able to evaluate their Text-to-SQL systems on their own databases. To address this, we introduce SING-SQL, a fully automated two-stage framework for generating high-quality, high-coverage synthetic Text-to-SQL data for any target database, without relying on SQL logs or manual annotations. Our approach hierarchically partitions a database schema into sub-schemas, synthesizes SQL queries across multiple complexity levels, and applies a quality-aware pipeline that includes LLM-as-a-judge validation, executability checks, automatic repair, and column balancing. We further release SingSQL-LM, a family of compact language models fine-tuned on the synthetic data, achieving strong in-domain generalization. On the subset of the BIRD benchmark, SingSQL-LM-3B-R64 reaches 82.87% Soft F1 and 73.03% EX upper bound with 32 candidates, outperforming the best 3B-scale baseline by +16.21 in Soft F1 and +12.36 in EX. At the 1.5B scale, SingSQL-LM-1.5B-R64 improves over prior systems by +9.30 in Soft F1 and +4.49 in EX. On synthetic evaluation sets, SingSQL-LMs exceed prior systems by wide margins, establishing state-of-the-art performance among open models at comparable scales. Our study of context management strategies reveals that schema-free fine-tuning combined with schema-only inference provides the most robust results. These findings establish SING-SQL as a scalable, database-agnostic paradigm for producing and evaluating enterprise-grade Text-to-SQL systems.

Developing custom reasoning models via Reinforcement Learning (RL) that can incorporate organization-specific knowledge has great potential to address problems faced by enterprise customers. In many of these problems, the reward function is verifiable, a setting termed RL with Verifiable Rewards (RLVR). We apply RLVR to a popular data science benchmark called BIRD that measures the ability of an AI agent to convert a natural language query for a database to SQL executions. We apply a simple and general-purpose training recipe involving careful prompt and model selection, a warm-up stage using our offline RL approach called TAO, followed by rigorous online RLVR training. With no additional training data beyond the BIRD training set and no use of proprietary models, our very first submission to the BIRD leaderboard reached state-of-the-art accuracy on the private test set: 73.56% without self-consistency and 75.68% with self-consistency. In the latter case, our model also required fewer generations than the second-best approach. While BIRD is only a proxy task, the simplicity of our framework makes it broadly applicable to enterprise domains such as business intelligence, data science, and coding.

We present the Neural Satisfiability Network (NSNet), a general neural framework that models satisfiability problems as probabilistic inference and meanwhile exhibits proper explainability. Inspired by the Belief Propagation (BP), NSNet uses a novel graph neural network (GNN) to parameterize BP in the latent space, where its hidden representations maintain the same probabilistic interpretation as BP. NSNet can be flexibly configured to solve both SAT and #SAT problems by applying different learning objectives. For SAT, instead of directly predicting a satisfying assignment, NSNet performs marginal inference among all satisfying solutions, which we empirically find is more feasible for neural networks to learn. With the estimated marginals, a satisfying assignment can be efficiently generated by rounding and executing a stochastic local search. For #SAT, NSNet performs approximate model counting by learning the Bethe approximation of the partition function. Our evaluations show that NSNet achieves competitive results in terms of inference accuracy and time efficiency on multiple SAT and #SAT datasets.