# HLOB -- Information Persistence and Structure in Limit Order Books

arXiv: https://arxiv.org/abs/2405.18938 · HTML: https://mlsanity.com/paper/2405.18938/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 65 references that are in the map.
- First posted on arXiv 29 May 2024.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Universal features of price formation in financial markets: perspectives from Deep Learning](https://mlsanity.com/paper/1803.06917/) (2018)
- [Benchmark Dataset for Mid-Price Forecasting of Limit Order Book Data with Machine Learning Methods](https://mlsanity.com/paper/1705.03233/) (2017)
- [Temporal Attention augmented Bilinear Network for Financial Time-Series Data Analysis](https://mlsanity.com/paper/1712.00975/) (2017)
- [Facial Expression Analysis under Partial Occlusion: A Survey](https://mlsanity.com/paper/1802.08784/) (2018)
- [Using Deep Learning for price prediction by exploiting stationary limit order book features](https://mlsanity.com/paper/1810.09965/) (2018)
- [Deep Reinforcement Learning for Active High Frequency Trading](https://mlsanity.com/paper/2101.07107/) (2021)
- [Network Filtering for Big Data: Triangulated Maximally Filtered Graph](https://mlsanity.com/paper/1505.02445/) (2015)
- [Data Normalization for Bilinear Structures in High-Frequency Financial Time-series](https://mlsanity.com/paper/2003.00598/) (2020)
- [Parsimonious modeling with Information Filtering Networks](https://mlsanity.com/paper/1602.07349/) (2016)
- [Deep Learning modeling of Limit Order Book: a comparative perspective](https://mlsanity.com/paper/2007.07319/) (2020)
- [Temporal Logistic Neural Bag-of-Features for Financial Time series Forecasting leveraging Limit Order Book Data](https://mlsanity.com/paper/1901.08280/) (2019)
- [LOB-Based Deep Learning Models for Stock Price Trend Prediction: A Benchmark Study](https://mlsanity.com/paper/2308.01915/) (2023)
- [Deep Learning for Market by Order Data](https://mlsanity.com/paper/2102.08811/) (2021)
- [Multi-head Temporal Attention-Augmented Bilinear Network for Financial time series prediction](https://mlsanity.com/paper/2201.05459/) (2022)
- [Attention-based Neural Bag-of-Features Learning for Sequence Data](https://mlsanity.com/paper/2005.12250/) (2020)
- [Deep Limit Order Book Forecasting](https://mlsanity.com/paper/2403.09267/) (2024)
- [Topological regularization with information filtering networks](https://mlsanity.com/paper/2005.04692/) (2020)
- [Homological Neural Networks: A Sparse Architecture for Multivariate Complexity](https://mlsanity.com/paper/2306.15337/) (2023)
- [Limit Order Book Dynamics and Order Size Modelling Using Compound Hawkes Process](https://mlsanity.com/paper/2312.08927/) (2023)
- [Augmented Bilinear Network for Incremental Multi-Stock Time-Series Classification](https://mlsanity.com/paper/2207.11577/) (2022)
- [Axial-LOB: High-Frequency Trading with Axial Attention](https://mlsanity.com/paper/2212.01807/) (2022)
- [Homological Convolutional Neural Networks](https://mlsanity.com/paper/2308.13816/) (2023)

## Built on by (most cited first, 8 of 8)

- [DiffLOB: Diffusion Models for Counterfactual Generation in Limit Order Books](https://mlsanity.com/paper/2602.03776/) (2026)
- [Information Filtering Networks: Theoretical Foundations, Generative Methodologies, and Real-World Applications](https://mlsanity.com/paper/2505.03812/) (2025)
- [DiffVolume: Diffusion Models for Volume Generation in Limit Order Books](https://mlsanity.com/paper/2508.08698/) (2025)
- [Graph Regularized PCA](https://mlsanity.com/paper/2601.10199/) (2026)
- [Deep Learning Models Meet Financial Data Modalities](https://mlsanity.com/paper/2504.13521/) (2025)
- [An Efficient deep learning model to Predict Stock Price Movement Based on Limit Order Book](https://mlsanity.com/paper/2505.22678/) (2025)
- [Compositional Sparsity as an Inductive Bias for Neural Architecture Design](https://mlsanity.com/paper/2605.14764/) (2026)
- [The Inference-Compute Frontier and a Latency-Efficient Architecture for Limit Order Book Prediction](https://mlsanity.com/paper/2606.25986/) (2026)

## Abstract (arXiv)

We introduce a novel large-scale deep learning model for Limit Order Book mid-price changes forecasting, and we name it `HLOB'. This architecture (i) exploits the information encoded by an Information Filtering Network, namely the Triangulated Maximally Filtered Graph, to unveil deeper and non-trivial dependency structures among volume levels; and (ii) guarantees deterministic design choices to handle the complexity of the underlying system by drawing inspiration from the groundbreaking class of Homological Convolutional Neural Networks. We test our model against 9 state-of-the-art deep learning alternatives on 3 real-world Limit Order Book datasets, each including 15 stocks traded on the NASDAQ exchange, and we systematically characterize the scenarios where HLOB outperforms state-of-the-art architectures. Our approach sheds new light on the spatial distribution of information in Limit Order Books and on its degradation over increasing prediction horizons, narrowing the gap between microstructural modeling and deep learning-based forecasting in high-frequency financial markets.