# CoLSE: A Lightweight and Robust Hybrid Learned Model for Single-Table Cardinality Estimation using Joint CDF

arXiv: https://arxiv.org/abs/2512.12624 · HTML: https://mlsanity.com/paper/2512.12624/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 66 references that are in the map.
- First posted on arXiv 14 Dec 2025.

## Builds on (most cited first, 21 of 21)

- [Transformer in Transformer](https://mlsanity.com/paper/2103.00112/) (2021)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Learned Cardinalities: Estimating Correlated Joins with Deep Learning](https://mlsanity.com/paper/1809.00677/) (2018)
- [Bao: Learning to Steer Query Optimizers](https://mlsanity.com/paper/2004.03814/) (2020)
- [Deep Unsupervised Cardinality Estimation](https://mlsanity.com/paper/1905.04278/) (2019)
- [Cardinality Estimation in DBMS: A Comprehensive Benchmark Evaluation](https://mlsanity.com/paper/2109.05877/) (2021)
- [Lero: A Learning-to-Rank Query Optimizer](https://mlsanity.com/paper/2302.06873/) (2023)
- [Deep Archimedean Copulas](https://mlsanity.com/paper/2012.03137/) (2020)
- [FLAT: Fast, Lightweight and Accurate Method for Cardinality Estimation](https://mlsanity.com/paper/2011.09022/) (2020)
- [Flow-Loss: Learning Cardinality Estimates That Matter](https://mlsanity.com/paper/2101.04964/) (2021)
- [A Unified Deep Model of Learning from both Data and Queries for Cardinality Estimation](https://mlsanity.com/paper/2107.12295/) (2021)
- [DeepDB: Learn from Data, not from Queries!](https://mlsanity.com/paper/1909.00607/) (2019)
- [Are We Ready For Learned Cardinality Estimation?](https://mlsanity.com/paper/2012.06743/) (2020)
- [A Survey on Advancing the DBMS Query Optimizer: Cardinality Estimation, Cost Model, and Plan Enumeration](https://mlsanity.com/paper/2101.01507/) (2021)
- [FactorJoin: A New Cardinality Estimation Framework for Join Queries](https://mlsanity.com/paper/2212.05526/) (2022)
- [ALECE: An Attention-based Learned Cardinality Estimator for SPJ Queries on Dynamic Workloads (Extended)](https://mlsanity.com/paper/2310.05349/) (2023)
- [QuickSel: Quick Selectivity Learning with Mixture Models](https://mlsanity.com/paper/1812.10568/) (2018)
- [PRICE: A Pretrained Model for Cross-Database Cardinality Estimation](https://mlsanity.com/paper/2406.01027/) (2024)
- [COOOL: A Learning-To-Rank Approach for SQL Hint Recommendations](https://mlsanity.com/paper/2304.04407/) (2023)
- [Glue: Adaptively Merging Single Table Cardinality to Estimate Join Query Size](https://mlsanity.com/paper/2112.03458/) (2021)
- [LpBound: Pessimistic Cardinality Estimation using ℓp-Norms of Degree Sequences](https://mlsanity.com/paper/2502.05912/) (2025)

## Abstract (arXiv)

Cardinality estimation (CE), the task of predicting the result size of queries is a critical component of query optimization. Accurate estimates are essential for generating efficient query execution plans. Recently, machine learning techniques have been applied to CE, broadly categorized into query-driven and data-driven approaches. Data-driven methods learn the joint distribution of data, while query-driven methods construct regression models that map query features to cardinalities. Ideally, a CE technique should strike a balance among three key factors: accuracy, efficiency, and memory footprint. However, existing state-of-the-art models often fail to achieve this balance. To address this, we propose CoLSE, a hybrid learned approach for single-table cardinality estimation. CoLSE directly models the joint probability over queried intervals using a novel algorithm based on copula theory and integrates a lightweight neural network to correct residual estimation errors. Experimental results show that CoLSE achieves a favorable trade-off among accuracy, training time, inference latency, and model size, outperforming existing state-of-the-art methods.