# Identifiability Limits of Gravitational Wave Phase Deviations: Multiclass Classification with a Multihead Neural Network

arXiv: https://arxiv.org/abs/2609.31993 · HTML: https://mlsanity.com/paper/2609.31993/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 51 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 11 of 11)

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- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [An End-to-End Trainable Neural Network for Image-based Sequence Recognition and Its Application to Scene Text Recognition](https://mlsanity.com/paper/1507.05717/) (2015)
- [Efficient Object Localization Using Convolutional Networks](https://mlsanity.com/paper/1411.4280/) (2014)
- [Testing General Relativity Through Gravitational Wave Classification: A Convolutional Neural Network Framework](https://mlsanity.com/paper/2605.02453/) (2026)
- [Deep Learning Detection of Beyond-General-Relativity Deviations in Gravitational-Wave Signals: A Detection-Threshold Study with Real LIGO Noise](https://mlsanity.com/paper/2609.19416/) (2026)

## Abstract (arXiv)

We study how well gravitational-wave phase deviations can be identified using a neural network with classification and regression heads. The classification head distinguishes general relativity (GR) from six parametrized post-Einsteinian phase families with exponents b∈-7,-5,-3,-1,+1,+2; the regression head predicts the logarithm of the coupling magnitude, log10|β|. The network input is a response function quantifying the sensitivity of waveform mismatch to waveform deformations. We use stationary Gaussian noise with the Advanced LIGO design spectrum for 262 sources and a measured Hanford spectrum from the third observing run (O3) for 132 sources, and also test injections into recorded Hanford strain. On the two Gaussian datasets, the network identifies the exponent of deviations clearly above the noise with accuracies of 0.427 and 0.329. To interpret these results, we compare the network with an approximate classifier built from predicted waveform residuals for the six phase families and same sources. The two classifiers often confuse the same families. Examining residuals left by different phase corrections, we link these errors to similarities between the underlying deviations. On selected recorded Hanford strain, networks trained on simulated or recorded noise achieve overall classification accuracies close to those on simulated Hanford noise. Of thirteen neural-network variants tested on the Advanced LIGO design dataset, the recurrent network has the highest mean classification accuracy for loud deviations, although all variants remain below the approximate classifier. The network nearly matches that classifier's accuracy, indicating that identification is limited by similarities between neighboring phase families rather than by the network, for known intrinsic source parameters.