Learning and Interpreting Gravitational-Wave Features from CNNs with a Random Forest Approach

TL;DR

This work tackles the interpretability challenge of CNN-based gravitational-wave detection by introducing a hybrid CNN-RF architecture that extracts four physically meaningful features from the final CNN layer and feeds them, along with the CNN probability, into a Random Forest classifier. The approach delivers a significant detection performance boost on long-duration data, including improved sensitivity at a fixed false-alarm rate of 10 events per month and enhanced low-SNR signal recovery, while enabling feature-level interpretability via RF importance. Feature attribution shows both CNN-derived and handcrafted features contribute meaningfully, with variance and CNN probability among the top contributors, highlighting the value of physically motivated post-processing of CNN features. While the method adds computational overhead and currently focuses on a two-detector setup, it offers a flexible path toward interpretable, robust GW detection and can be extended to multi-detector networks and additional source classes in future work.

Abstract

Convolutional neural networks (CNNs) have become widely adopted in gravitational wave (GW) detection pipelines due to their ability to automatically learn hierarchical features from raw strain data. However, the physical meaning of these learned features remains underexplored, limiting the interpretability of such models. In this work, we propose a hybrid architecture that combines a CNN-based feature extractor with a random forest (RF) classifier to improve both detection performance and interpretability. Unlike prior approaches that directly connect classifiers to CNN outputs, our method introduces four physically interpretable metrics - variance, signal-to-noise ratio (SNR), waveform overlap, and peak amplitude - computed from the final convolutional layer. These are jointly used with the CNN output in the RF classifier to enable more informed decision boundaries. Tested on long-duration strain datasets, our hybrid model outperforms a baseline CNN model, achieving a relative improvement of 21\% in sensitivity at a fixed false alarm rate of 10 events per month. Notably, it also shows improved detection of low-SNR signals (SNR $\le$ 10), which are especially vulnerable to misclassification in noisy environments. Feature attribution via the RF model reveals that both CNN-extracted and handcrafted features contribute significantly to classification decisions, with learned variance and CNN outputs ranked among the most informative. These findings suggest that physically motivated post-processing of CNN feature maps can serve as a valuable tool for interpretable and efficient GW detection, bridging the gap between deep learning and domain knowledge.

Figures (7)

• Figure 1: Architecture of the CNN-RF model. The raw input data is first processed by a fixed CNN. Features are then extracted from the output of its final convolutional layer, from which four handcrafted features are computed. These features, along with the $\mathbf{CNN\ probability}$, are concatenated and fed into an RF classifier for the final classification decision.
• Figure 2: Trigger count distribution per cluster for the background and injected signals. All values are normalized using max-normalization. The red line corresponds to the background set, and the blue line represents the injected signals.
• Figure 3: The input data and the first two feature maps from the convolutional layers. The input contains four types of data: the first is simulated GW waveform, the second is synthetic GW signal, the third is pure noise, and the fourth is glitch. The blue and orange lines in input represent the H1 detector and the L1 detector, respectively. The feature maps in each convolutional layer correspond to the four types of data.
• Figure 4: The histogram of the four extracted features across three types of data is presented in four panels labeled (a), (b), (c), and (d). Each panel represents the frequency distribution of one of the extracted features for GW signals (blue), Noise (orange), and Glitches (green).
• Figure 5: The ROC curves corresponding to each class in the CNN-RF model. The blue curve corresponds to GW signals, the orange to noise, and the green to glitches. The black curve labeled ‘luck’ represents the ROC curve of a random classifier (i.e., random guessing), which yields an expected AUC of 0.5.