Dataset distillation has emerged as a powerful approach for reducing data requirements in deep learning. Among various methods, distribution matching-based approaches stand out for their balance of computational efficiency and strong performance. However, existing distance metrics used in distribution matching often fail to accurately capture distributional differences, leading to unreliable measures of discrepancy. In this paper, we reformulate dataset distillation as a minmax optimization problem and introduce Neural Characteristic Function Discrepancy (NCFD), a comprehensive and theoretically grounded metric for measuring distributional differences. NCFD leverages the Characteristic Function (CF) to encapsulate full distributional information, employing a neural network to optimize the sampling strategy for the CF’s frequency arguments, thereby maximizing the discrepancy to enhance distance estimation. Simultaneously, we minimize the difference between real and synthetic data under this optimized NCFD measure. Our approach, termed Neural Characteristic Function Matching (NCFM), inherently aligns the phase and amplitude of neural features in the complex plane for both real and synthetic data, achieving a balance between realism and diversity in synthetic samples. Experiments demonstrate that our method achieves significant performance gains over state-of-the-art methods on both low- and high-resolution datasets. Notably, we achieve a 22.9% accuracy boost on ImageSquawk. Our method also reduces GPU memory usage by over 300× and achieves 20× faster processing speeds compared to state-of-the-art methods. To the best of our knowledge, this is the first work to achieve lossless compression of CIFAR-100 on a single NVIDIA 2080 Ti GPU using only 2.3 GB of memory. The code for this work is publicly available at: https://github.com/gszfwsb/NCFM.

State-of-the-art Text-to-SQL models rely on fine-tuning or few-shot prompting to help LLMs learn from training datasets containing mappings from natural language (NL) queries to SQL statements. Consequently, the quality of the dataset can greatly affect the accuracy of these Text-to-SQL models. Unlike other NL tasks, Text-to-SQL datasets are prone to errors despite extensive manual efforts due to the subtle semantics of SQL. Our study has found a non-negligible (>30%) portion of incorrect NL to SQL mapping cases exists in popular datasets Spider and BIRD. This paper aims to improve the quality of Text-to-SQL training datasets and thereby increase the accuracy of the resulting models. To do so, we propose a necessary correctness condition called execution consistency. For a given database instance, an NL to SQL mapping satisfies execution consistency if the execution result of an NL query matches that of the corresponding SQL. We develop SQLDriller to detect incorrect NL to SQL mappings based on execution consistency in a best-effort manner by crafting database instances that likely result in violations of execution consistency. It generates multiple candidate SQL predictions that differ in their syntax structures. Using a SQL equivalence checker, SQLDriller obtains counterexample database instances that can distinguish non-equivalent candidate SQLs. It then checks the execution consistency of an NL to SQL mapping under this set of counterexamples. The evaluation shows SQLDriller effectively detects and fixes incorrect mappings in the Text-to-SQL dataset, and it improves the model accuracy by up to 13.6%.

Proving the equivalence between SQL queries is a fundamental problem in database research. Existing solvers model queries using algebraic representations and convert such representations into first-order logic formulas so that query equivalence can be verified by solving a satisfiability problem. The main challenge lies in "unbounded summations", which appear commonly in a query's algebraic representation in order to model common SQL features, such as projection and aggregate functions. Unfortunately, existing solvers handle unbounded summations in an ad-hoc manner based on heuristics or syntax comparison, which severely limits the set of queries that can be supported. This paper develops a new SQL equivalence prover called SQLSolver, which can handle unbounded summations in a principled way. Our key insight is to use the theory of LIA^*, which extends linear integer arithmetic formulas with unbounded sums and provides algorithms to translate a LIA^* formula to a LIA formula that can be decided using existing SMT solvers. We augment the basic LIA^* theory to handle several complex scenarios (such as nested unbounded summations) that arise from modeling real-world queries. We evaluate SQLSolver with 359 equivalent query pairs derived from the SQL rewrite rules in Calcite and Spark SQL. SQLSolver successfully proves 346 pairs of them, which significantly outperforms existing provers.

Query rewriting transforms a relational database query into an equivalent but more efficient one, which is crucial for the performance of database-backed applications. Such rewriting relies on pre-specified rewrite rules. In existing systems, these rewrite rules are discovered through manual insights and accumulate slowly over the years. In this paper, we present WeTune, a rule generator that automatically discovers new rewrite rules. Inspired by compiler superoptimization, WeTune enumerates all valid logical query plans up to a certain size and tries to discover equivalent plans that could potentially lead to more efficient rewrites. The core challenge is to determine which set of conditions (aka constraints) allows one to prove the equivalence between a pair of query plans. We address this challenge by enumerating combinations of "interesting" constraints that relate tables and their attributes between each pair of queries. We also propose a new SMT-based verifier to verify the equivalence of a query pair under different enumerated constraints. To evaluate the usefulness of rewrite rules discovered by WeTune, we apply them on the SQL queries collected from the 20 most popular open-source web applications on GitHub. WeTune successfully optimizes 247 queries that existing databases cannot optimize, resulting in substantial performance improvements.