# Testing General Relativity Through Gravitational Wave Classification: A Convolutional Neural Network Framework

arXiv: https://arxiv.org/abs/2605.02453 · HTML: https://mlsanity.com/paper/2605.02453/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 42 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Accelerated, Scalable and Reproducible AI-driven Gravitational Wave Detection](https://mlsanity.com/paper/2012.08545/) (2020)

## Built on by (most cited first, 1 of 1)

- [Identifiability Limits of Gravitational Wave Phase Deviations: Multiclass Classification with a Multihead Neural Network](https://mlsanity.com/paper/2609.31993/) (2026)

## Abstract (arXiv)

We present a machine learning framework for testing general relativity (GR) with gravitational wave signals from binary black hole mergers. Using the source parameters of 173 BBH events from the GWTC catalog as a realistic astrophysical population, we generate simulated GR waveforms and construct beyond GR (BGR) waveforms by applying controlled phase deformations. We introduce a response function formalism that provides a systematic framework for quantifying how any observable responds to modifications of GR. We train convolutional neural networks (CNNs) on two input representations: whitened waveforms and a response function type observable derived from the waveform mismatch, which isolates the effect of phase deviations from the bulk signal. Using response functions as the CNN input improves the classification sensitivity by a factor of approximately 33 compared to whitened waveforms, demonstrating that the choice of observable representation is as important as the classifier architecture. We study the fundamental limits of this classification through Bayes optimal error analysis, averaging methods that reveal coherent patterns hidden in noise, and a comparison between CNN accuracy and a single feature classifier as a proxy for human performance. At all deformation scales, the CNN outperforms the best single feature approach. We extend the framework to physically motivated theories using the parameterized post Einsteinian (ppE) formalism and apply it to massive gravity, where the classifier detects deviations for graviton masses of order mg ~ 10-23;eV/c2 with aLIGO design sensitivity.