# Sig2Model: A Boosting-Driven Model for Updatable Learned Indexes

arXiv: https://arxiv.org/abs/2509.20781 · HTML: https://mlsanity.com/paper/2509.20781/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 73 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Builds on (most cited first, 30 of 37)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Measuring Catastrophic Forgetting in Neural Networks](https://mlsanity.com/paper/1708.02072/) (2017)
- [Highway Networks](https://mlsanity.com/paper/1505.00387/) (2015)
- [Search on the Replay Buffer: Bridging Planning and Reinforcement Learning](https://mlsanity.com/paper/1906.05253/) (2019)
- [The Case for Learned Index Structures](https://mlsanity.com/paper/1712.01208/) (2017)
- [Convergence Analysis of Two-layer Neural Networks with ReLU Activation](https://mlsanity.com/paper/1705.09886/) (2017)
- [Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery](https://mlsanity.com/paper/2305.06144/) (2023)
- [HoloDetect: Few-Shot Learning for Error Detection](https://mlsanity.com/paper/1904.02285/) (2019)
- [RadixSpline: A Single-Pass Learned Index](https://mlsanity.com/paper/2004.14541/) (2020)
- [FITing-Tree: A Data-aware Index Structure](https://mlsanity.com/paper/1801.10207/) (2018)
- [Learning Multi-dimensional Indexes](https://mlsanity.com/paper/1912.01668/) (2019)
- [Tsunami: A Learned Multi-dimensional Index for Correlated Data and Skewed Workloads](https://mlsanity.com/paper/2006.13282/) (2020)
- [SOSD: A Benchmark for Learned Indexes](https://mlsanity.com/paper/1911.13014/) (2019)
- [Qd-tree: Learning Data Layouts for Big Data Analytics](https://mlsanity.com/paper/2004.10898/) (2020)
- [A Method for Evaluating Hyperparameter Sensitivity in Reinforcement Learning](https://mlsanity.com/paper/2412.07165/) (2024)
- [Updatable Learned Index with Precise Positions](https://mlsanity.com/paper/2104.05520/) (2021)
- [Analysis of Stochastic Processes through Replay Buffers](https://mlsanity.com/paper/2206.12848/) (2022)
- [CARMI: A Cache-Aware Learned Index with a Cost-based Construction Algorithm](https://mlsanity.com/paper/2103.00858/) (2021)
- [LIDER: An Efficient High-dimensional Learned Index for Large-scale Dense Passage Retrieval](https://mlsanity.com/paper/2205.00970/) (2022)
- [WISK: A Workload-aware Learned Index for Spatial Keyword Queries](https://mlsanity.com/paper/2302.14287/) (2023)
- [Updatable Learned Indexes Meet Disk-Resident DBMS -- From Evaluations to Design Choices](https://mlsanity.com/paper/2305.01237/) (2023)
- [Approximate Denial Constraints](https://mlsanity.com/paper/2005.08540/) (2020)
- [Shift-Table: A Low-latency Learned Index for Range Queries using Model Correction](https://mlsanity.com/paper/2101.10457/) (2021)
- [The Case for Learned In-Memory Joins](https://mlsanity.com/paper/2111.08824/) (2021)
- [Accelerating String-Key Learned Index Structures via Memoization-based Incremental Training](https://mlsanity.com/paper/2403.11472/) (2024)
- [Approximate Inference in Structured Instances with Noisy Categorical Observations](https://mlsanity.com/paper/1907.00141/) (2019)
- [Record fusion: A learning approach](https://mlsanity.com/paper/2006.10208/) (2020)

## Abstract (arXiv)

Learned Indexes (LIs) represent a paradigm shift from traditional index structures by employing machine learning models to approximate the cumulative distribution function (CDF) of sorted data. While LIs achieve remarkable efficiency for static datasets, their performance degrades under dynamic updates: maintaining the CDF invariant (sum of F(k) equals 1) requires global model retraining, which blocks queries and limits the queries-per-second (QPS) metric. Current approaches fail to address these retraining costs effectively, rendering them unsuitable for real-world workloads with frequent updates. In this paper, we present Sig2Model, an efficient and adaptive learned index that minimizes retraining cost through three key techniques: (1) a sigmoid boosting approximation technique that dynamically adjusts the index model by approximating update-induced shifts in data distribution with localized sigmoid functions while preserving bounded error guarantees and deferring full retraining; (2) proactive update training via Gaussian mixture models (GMMs) that identifies high-update-probability regions for strategic placeholder allocation to speed up updates; and (3) a neural joint optimization framework that continuously refines both the sigmoid ensemble and GMM parameters via gradient-based learning. We evaluate Sig2Model against state-of-the-art updatable learned indexes on real-world and synthetic workloads, and show that Sig2Model reduces retraining cost by up to 20x, achieves up to 3x higher QPS, and uses up to 1000x less memory.