Yang Li

Andreas Zimmerer, Claudius Kühn, Yang Li et al.

Modern data systems increasingly expose multi-modal large language models as semantic operators: SQL operators, including filters and joins, whose predicates are defined by a natural-language instruction. Query optimization in these systems still rests on the same foundations as in traditional databases$\unicode{x2013}$plan enumeration and cost models$\unicode{x2013}$yet faces new challenges, e.g., a larger plan space and the lack of efficient cardinality estimates. The elevated per-tuple costs of semantic operators make bad plan choices worse by orders of magnitude. Therefore, precise$\unicode{x2013}$but also fast and cheap$\unicode{x2013}$cardinality estimates for semantic filters and joins are of high importance for optimizing query plans that include semantic operators. In this paper, we introduce SemCEB, the first benchmark for cardinality estimation over semantic operators, based on a real-world dataset of (semi-)structured text and images with 102 hand-curated, diverse queries spanning a wide range of selectivities, assessing cardinality estimation for semantic filters and joins in isolation. We evaluate sampling-based algorithms and Semantic Histograms, a state-of-the-art cardinality estimation algorithm for semantic operators, with respect to their accuracy, cost, latency, and memory overhead. We show that, while sampling is robust across different predicate categories, it does not scale and comes with high costs. Our adaptation of Semantic Histograms, on the other hand, is limited in its applicability, and its performance appears sensitive to the predicate category.

Zihui Zhao, Yuanbo Tang, Yang Li

Dictionary learning has long been studied from both optimization and probabilistic perspectives. While formulations with element-wise sparsity regularization (e.g., L1-based sparse coding) admit well-established probabilistic interpretations, many structured variants that impose global constraints lack a clear and tractable generative view. In this paper, we revisit a class of practically effective yet theoretically under-explored dictionary learning methods that impose a simple global regularization on the number of activated dictionary atoms, which we term parsimoniously activated dictionary learning (PADL). We show that PADL admits an equivalent formulation as maximum a posteriori estimation under a structured generative model, with auxiliary latent variables that govern global activation patterns. This formulation allows us to derive generalization guarantees that are difficult to obtain under the original formulation. More importantly, it yields an analytical characterization of the tradeoff between sparsity, storage cost, and reconstruction accuracy, enabling data-driven estimation of optimal hyperparameters. Based on this connection, we develop an efficient and interpretable PADL algorithm that eliminates manual hyperparameter tuning, achieving improved reconstruction performance under comparable sparsity levels on visual benchmarks. We further demonstrate its practical utility in accelerating inference for vision-language models.