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Gravitational wave science is a pioneering field with rapidly evolving dataanalysis methodology currently assimilating and inventing deep learningtechniques. The bulk of the sophisticated flagship searches of the field relyon the time-tested matched filtering principle within their core. In thispaper, we make a key observation on the relationship between the emerging deeplearning and the traditional techniques: matched filtering is formallyequivalent to a particular neural network. This means that a neural network canbe constructed analytically to exactly implement matched filtering, and can befurther trained on data or boosted with additional complexity for improvedperformance. Moreover, we show that the proposed neural network architecturecan outperform matched filtering, both with or without knowledge of a prior onthe parameter distribution. When a prior is given, the proposed neural networkcan approach the statistically optimal performance. We also propose andinvestigate two different neural network architectures MNet-Shallow andMNet-Deep, both of which implement matched filtering at initialization and canbe trained on data. MNet-Shallow has simpler structure, while MNet-Deep is moreflexible and can deal with a wider range of distributions. Our theoreticalfindings are corroborated by experiments using real LIGO data and syntheticinjections, where our proposed methods significantly outperform matchedfiltering at false positive rates above $5\times 10^{-3}\%$. The fundamentalequivalence between matched filtering and neural networks allows us to define a"complexity standard candle" to characterize the relative complexity of thedifferent approaches to gravitational wave signal searches in a commonframework. Finally, our results suggest new perspectives on the role of deeplearning in gravitational wave detection.

Generalized Approach to Matched Filtering using Neural Networks