# Theoretical Analysis of Learned Database Operations under Distribution Shift through Distribution Learnability

arXiv: https://arxiv.org/abs/2411.06241 · HTML: https://mlsanity.com/paper/2411.06241/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 9 Nov 2024.

## Builds on (most cited first, 13 of 13)

- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [The Case for Learned Index Structures](https://mlsanity.com/paper/1712.01208/) (2017)
- [Optimal approximation of piecewise smooth functions using deep ReLU neural networks](https://mlsanity.com/paper/1709.05289/) (2017)
- [Optimal approximation of continuous functions by very deep ReLU networks](https://mlsanity.com/paper/1802.03620/) (2018)
- [Learned Cardinalities: Estimating Correlated Joins with Deep Learning](https://mlsanity.com/paper/1809.00677/) (2018)
- [Deep Unsupervised Cardinality Estimation](https://mlsanity.com/paper/1905.04278/) (2019)
- [FITing-Tree: A Data-aware Index Structure](https://mlsanity.com/paper/1801.10207/) (2018)
- [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)
- [Are We Ready For Learned Cardinality Estimation?](https://mlsanity.com/paper/2012.06743/) (2020)
- [One Network Fits All? Modular versus Monolithic Task Formulations in Neural Networks](https://mlsanity.com/paper/2103.15261/) (2021)
- [On Distribution Dependent Sub-Logarithmic Query Time of Learned Indexing](https://mlsanity.com/paper/2306.10651/) (2023)
- [Are Updatable Learned Indexes Ready?](https://mlsanity.com/paper/2207.02900/) (2022)

## Built on by (most cited first, 4 of 4)

- [In-Context Adaptation to Concept Drift for Learned Database Operations](https://mlsanity.com/paper/2505.04404/) (2025)
- [Mathematical Foundations of Poisoning Attacks on Linear Regression over Cumulative Distribution Functions](https://mlsanity.com/paper/2603.00537/) (2026)
- [Lower Bounds for the Algorithmic Complexity of Learned Indexes](https://mlsanity.com/paper/2601.06629/) (2026)
- [Selectivity Estimation for Linear Queries via Online Learning](https://mlsanity.com/paper/2607.02895/) (2026)

## Abstract (arXiv)

Use of machine learning to perform database operations, such as indexing, cardinality estimation, and sorting, is shown to provide substantial performance benefits. However, when datasets change and data distribution shifts, empirical results also show performance degradation for learned models, possibly to worse than non-learned alternatives. This, together with a lack of theoretical understanding of learned methods undermines their practical applicability, since there are no guarantees on how well the models will perform after deployment. In this paper, we present the first known theoretical characterization of the performance of learned models in dynamic datasets, for the aforementioned operations. Our results show novel theoretical characteristics achievable by learned models and provide bounds on the performance of the models that characterize their advantages over non-learned methods, showing why and when learned models can outperform the alternatives. Our analysis develops the distribution learnability framework and novel theoretical tools which build the foundation for the analysis of learned database operations in the future.