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

TL;DR

This paper introduces a lightweight, interpretable neural density estimator based on the Kolmogorov-Arnold network for efficient gravitational-wave catalog analysis, enabling rapid posterior reconstruction and data compression.

Contribution

It presents a novel KAN-based neural density estimator that compresses GW posterior samples into small model weights and analytic expressions, improving efficiency and interpretability.

Findings

KAN achieves higher accuracy and interpretability with learnable splines.

The method compresses GW posteriors into tens of kilobytes.

Rapid regeneration of GW posteriors facilitates efficient data analysis.

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.