# VPNet: Variable Projection Networks

arXiv: https://arxiv.org/abs/2006.15590 · HTML: https://mlsanity.com/paper/2006.15590/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Learning ECG Signal Features Without Backpropagation Using Linear Laws](https://mlsanity.com/paper/2307.01930/) (2023)
- [Rational Gaussian wavelets and corresponding model driven neural networks](https://mlsanity.com/paper/2502.01282/) (2025)
- [CVVNet: A Cross-Vertical-View Network for Gait Recognition](https://mlsanity.com/paper/2505.01837/) (2025)
- [Classification and detection of multiple UAVs using rational Gaussian wavelet neural networks](https://mlsanity.com/paper/2605.26310/) (2026)

## Abstract (arXiv)

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.