  We introduce VPNet, a novel model-driven neural network architecture based on
variable projection (VP). Applying VP operators to neural networks results in
learnable features, interpretable parameters, and compact network structures.
This paper discusses the motivation and mathematical background of VPNet and
presents experiments. The VPNet approach was evaluated in the context of signal
processing, where we classified a synthetic dataset and real electrocardiogram
(ECG) signals. Compared to fully connected and one-dimensional convolutional
networks, VPNet offers fast learning ability and good accuracy at a low
computational cost of both training and inference. Based on these advantages
and the promising results obtained, we anticipate a profound impact on the
broader field of signal processing, in particular on classification, regression
and clustering problems.

Machine Learning;Signal Processing;Machine Learning