Research on learned cardinality estimation has made significant progress in recent years. However, existing methods still face distinct challenges that hinder their practical deployment in production environments. We define these challenges as the “Trilemma of Cardinality Estimation”, where learned cardinality estimation methods struggle to balance generality, accuracy, and updatability. To address these challenges, we introduce DistJoin, a join cardinality estimator based on efficient distribution prediction using multi-autoregressive models. Our contributions are threefold: (1) We propose a method to estimate join cardinality by leveraging the probability distributions of individual tables in a decoupled manner. (2) To meet the re quirements of efficiency for DistJoin, we develop Adaptive Neural Predicate Modulation (ANPM), a high-throughput distribution estimation model. (3) We demonstrate that an existing similar approach suffers from variance accumulation issues by formal variance analysis. To mitigate this problem, DistJoin employs a selectivity-based approach to infer join cardinality, effectively reducing variance. In summary, DistJoin not only represents the first data-driven method to support both equi and non-equi joins simultaneously but also demonstrates superior accuracy while enabling fast and flexible updates. The experimental results demonstrate that DistJoin achieves the highest accuracy, robustness to data updates, generality, and comparable update and inference speed relative to existing methods.

Learned cardinality estimation methods have achieved high precision compared to traditional methods. Among learned methods, query-driven approaches have faced the work-load drift problem for a long time. Although both data-driven and hybrid methods are proposed to avoid this problem, most of them suffer from high training and estimation costs, limited scalability, instability, and long-tail distribution problems on high-dimensional tables, which seriously affects the practical application of learned cardinality estimators. In this paper, we prove that most of these problems are directly caused by the widely used progressive sampling. We solve this problem by introducing predicate information into the autoregressive model and propose Duet, a stable, efficient, and scalable hybrid method to estimate cardinality directly without sampling or any non-differentiable process, which can not only reduce the inference complexity from$O(n)$to$O(1)$compared to Naru and UAE but also achieve higher accuracy on high cardinality and high-dimensional tables. Experimental results show that Duet can achieve all the design goals above and be much more practical. Besides, Duet even has a lower inference cost on CPU than that of most learned methods on GPU.