  Gravitational wave science is a pioneering field with rapidly evolving data
analysis methodology currently assimilating and inventing deep learning
techniques. The bulk of the sophisticated flagship searches of the field rely
on the time-tested matched filtering principle within their core. In this
paper, we make a key observation on the relationship between the emerging deep
learning and the traditional techniques: matched filtering is formally
equivalent to a particular neural network. This means that a neural network can
be constructed analytically to exactly implement matched filtering, and can be
further trained on data or boosted with additional complexity for improved
performance. This fundamental equivalence allows us to define a "complexity
standard candle" allowing us to characterize the relative complexity of the
different approaches to gravitational wave signals in a common framework.
Additionally it also provides a glimpse of an intriguing symmetry that could
provide clues on how neural networks approach the problem of finding signals in
overwhelming noise. Moreover, we show that the proposed neural network
architecture can outperform matched filtering, both with or without knowledge
of a prior on the parameter distribution. When a prior is given, the proposed
neural network can approach the statistically optimal performance. We also
propose and investigate two different neural network architectures MNet-Shallow
and MNet-Deep, both of which implement matched filtering at initialization and
can be trained on data. MNet-Shallow has simpler structure, while MNet-Deep is
more flexible and can deal with a wider range of distributions. Our theoretical
findings are corroborated by experiments using real LIGO data and synthetic
injections. Finally, our results suggest new perspectives on the role of deep
learning in gravitational wave detection.
