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

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 ≤ 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.