  In scientific and engineering scenarios, a recurring task is the detection of
low-dimensional families of signals or patterns. A classic family of
approaches, exemplified by template matching, aims to cover the search space
with a dense template bank. While simple and highly interpretable, it suffers
from poor computational efficiency due to unfavorable scaling in the signal
space dimensionality. In this work, we study TpopT (TemPlate OPTimization) as
an alternative scalable framework for detecting low-dimensional families of
signals which maintains high interpretability. We provide a theoretical
analysis of the convergence of Riemannian gradient descent for TpopT, and prove
that it has a superior dimension scaling to covering. We also propose a
practical TpopT framework for nonparametric signal sets, which incorporates
techniques of embedding and kernel interpolation, and is further configurable
into a trainable network architecture by unrolled optimization. The proposed
trainable TpopT exhibits significantly improved efficiency-accuracy tradeoffs
for gravitational wave detection, where matched filtering is currently a method
of choice. We further illustrate the general applicability of this approach
with experiments on handwritten digit data.
