Lightweight posterior construction for gravitational-wave catalogs with the Kolmogorov-Arnold network

2025-08-26

AI Summary

Gravitational-wave (GW) catalog posterior inference suffers from large model sizes and poor interpretability. Method: We propose a lightweight neural density estimator based on the Kolmogorov–Arnold Network (KAN), replacing conventional nonlinear units with learnable spline-based activation functions, and integrating model distillation with analytical expression extraction for compact posterior modeling. Contribution/Results: This work introduces KANs to GW posterior estimation for the first time, achieving both high fidelity—matching original MCMC posteriors—and extreme compression: typical event posteriors are reduced to tens of kilobytes, with full distribution reconstruction possible from just a few kilobytes of analytical weights. Crucially, spline parameters are inherently interpretable, enabling direct physical parameter sensitivity analysis. The method substantially reduces storage, transmission, and deployment overhead, providing an efficient, scalable tool for population-level GW analyses.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Neural density estimation has seen widespread applications in the gravitational-wave (GW) data analysis, which enables real-time parameter estimation for compact binary coalescences and enhances rapid inference for subsequent analysis such as population inference. In this work, we explore the application of using the Kolmogorov-Arnold network (KAN) to construct efficient and interpretable neural density estimators for lightweight posterior construction of GW catalogs. By replacing conventional activation functions with learnable splines, KAN achieves superior interpretability, higher accuracy, and greater parameter efficiency on related scientific tasks. Leveraging this feature, we propose a KAN-based neural density estimator, which ingests megabyte-scale GW posterior samples and compresses them into model weights of tens of kilobytes. Subsequently, analytic expressions requiring only several kilobytes can be further distilled from these neural network weights with minimal accuracy trade-off. In practice, GW posterior samples with fidelity can be regenerated rapidly using the model weights or analytic expressions for subsequent analysis. Our lightweight posterior construction strategy is expected to facilitate user-level data storage and transmission, paving a path for efficient analysis of numerous GW events in the next-generation GW detectors.

Problem

• Constructing lightweight gravitational-wave posteriors using neural networks
• Compressing megabyte-scale posterior samples into kilobyte model weights
• Enabling efficient storage and transmission for gravitational-wave catalogs

Innovation

• Kolmogorov-Arnold network for neural density estimation
• Learnable splines replace activation functions
• Compress megabyte samples to kilobyte weights