BUFF: Boosted Decision Tree based Ultra-Fast Flow matching (2404.18219v1)

Abstract: Tabular data stands out as one of the most frequently encountered types in high energy physics. Unlike commonly homogeneous data such as pixelated images, simulating high-dimensional tabular data and accurately capturing their correlations are often quite challenging, even with the most advanced architectures. Based on the findings that tree-based models surpass the performance of deep learning models for tasks specific to tabular data, we adopt the very recent generative modeling class named conditional flow matching and employ different techniques to integrate the usage of Gradient Boosted Trees. The performances are evaluated for various tasks on different analysis level with several public datasets. We demonstrate the training and inference time of most high-level simulation tasks can achieve speedup by orders of magnitude. The application can be extended to low-level feature simulation and conditioned generations with competitive performance.

• The paper introduces BUFF, a novel framework that integrates boosted decision trees with conditional flow matching for rapid simulation of high-dimensional physics data.
• It employs small, lightweight GBT models with high-order numerical solvers to reduce computational costs while maintaining high generative accuracy.
• The model demonstrates high fidelity by effectively capturing complex distributions, improving simulation speed and accuracy in high energy physics tasks.

Exploration of Tree-Based Conditional Flow Matching for High-Dimension Simulations in High Energy Physics

Introduction

The paper introduced an innovative generative modeling framework, Boosted Decision Tree based Ultra-Fast Flow matching (BUFF), integrating Gradient Boosted Trees (GBT) with conditional flow matching for rapid and efficient simulation of complex high-dimensional data commonly found in high energy physics (HEP). This approach leverages the strengths of tree-based models for tabular data, which often surpass deep learning models in performance for specific tasks. The novel framework, termed flowBDT, is analyzed across various tasks using public datasets, demonstrating significant improvements in training and inference speeds with robust performance metrics.

Methodological Enhancements and Dataset Description

Model Design and Setup

The tree-based conditional flow matching approach modifies the traditional setup by employing small, lightweight GBT models instead of neural networks. Each model operates at an independent time step, making the system suitable for parallel processing and significantly reducing computational costs. Utilizing high-order numerical solvers like the Midpoint and Dormand-Prince methods, the flowBDT model achieves enhanced generative performance with a reduced number of time steps.

Experiments and Datasets

The BUFF framework was tested across several datasets:

• JetNet Dataset: Involves simulating particle jets with topological variations, deriving high-level features to reflect interactions within subjets.
• CaloChallenge Dataset: Focuses on simulating calorimeter responses to particle showers, capturing intricate energy distributions and interactions within the calorimeter.
• Jet Datasets for Unfolding: Targets the unfolding of event-level observables affected by detector distortions to their true particle-level quantities.
• Schrödinger Bridge Refinement: Aims to refine electron shower simulations by conditioning on parameterized fast simulation outputs.

Performance Analysis

High-Level Feature Simulation

With applications in simulating high-level features like jet substructure and kinematics, BUFF demonstrates an ability to capture complex, multi-modal distributions efficiently. The metrics such as f-divergence and Earth Mover's Distance indicate an excellent alignment between the generated and target distributions, suggesting high fidelity in simulation.

Low-Level Detailed Simulations

For detailed simulations such as individual calorimeter cells or jet constituents, BUFF shows promising results by effectively managing very high dimensions up to several hundreds. The model faithfully reproduces key physical properties, including energy distributions and spatial shower patterns.

Conditional Generation and Unfolding

Conditional generation approaches show substantial improvements in capturing dependencies and correlations in data, particularly useful in tasks like data unfolding where maintaining underlying physical relationships is crucial. This model's ability to utilize conditions derived from data itself or approximations enhances its flexibility and accuracy in generation tasks.

Conclusions and Future Work

The BUFF model, facilitated by the flowBDT setup, presents a compelling alternative to traditional generative models in HEP, providing a swift and accurate simulation across various simulation levels and conditions. Future enhancements will focus on expanding its application spectrum in HEP tasks such as anomaly detection and further optimization of computational efficiency, potentially broadening its applicability in other fields requiring rapid simulation of complex, high-dimensional data. The integration of tree-based models within a flow matching framework presents a significant advance, particularly in handling tabular data, setting a robust foundation for future exploratory works in simulation and data analysis within computational and experimental physics.

Acknowledgements

The research team extends gratitude towards collaborators and fellow researchers, whose insights and discussions have been invaluable in refining the techniques and applications presented in this paper. Their contributions towards evaluating the practical implications and performance across various datasets have been crucial in advancing the BUFF framework's development.