Testing General Relativity Through Gravitational Wave Classification: A Convolutional Neural Network Framework
Authors: Lavinia Heisenberg, Shayan Hemmatyar, Hector Villarrubia-Rojo
Summary
The authors use convolutional neural networks to classify gravitational wave signals as either consistent with general relativity (GR) or deviating from it, as a test of Einstein's theory. They train on 173 real black-hole merger events, generating GR waveforms and creating modified beyond-GR variants by adding controlled phase deformations. A key finding is that feeding the CNN a "response function" observable (derived from waveform mismatch, isolating the effect of phase deviations) improves classification sensitivity 33-fold compared to using raw whitened waveforms — showing the input representation matters as much as the network architecture.
Main takeaways:
- CNNs can classify gravitational waves as GR-consistent vs. modified-gravity, trained on realistic black-hole merger data
- Using a response function (an observable isolating phase deviations from the bulk signal) as CNN input boosts sensitivity ~33× vs. raw waveforms
- The choice of observable representation is as important as the classifier design itself
- Applied to massive gravity theory, the classifier detects deviations for graviton masses around 10^-23 eV/c² with current detector sensitivity
Relevance
Not related to my language model work — this is pure physics (gravitational wave analysis), though the broader lesson that input representation matters enormously for classifiers is a universal ML principle.
Abstract
arXiv:2605.02453v1 Announce Type: cross Abstract: 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 $m_g \sim 10^{-23};\mathrm{eV}/c^2$ with aLIGO design sensitivity.