Deep Unfolded Variable Projection Networks

In this paper, we present a hybrid learning framework that integrates two model-driven AI paradigms: Deep unfolding and Variable Projections (VPs). The core idea is to unfold the iterations of VP solvers for separable nonlinear least squares (SNLLS) problems into trainable neural network layers. As a consequence, the network is capable of learning optimal nonlinear VP parameters during inference, which is a form of model-based meta-learning. Furthermore, the architecture incorporates prior knowledge of the underlying SNLLS problem, such as basis function expansions and signal structure, which enhance interpretability, reduce model size, and lower data requirements. As a case study, we adapt the proposed deep unfolded VPNet to learn ECG representations for the classification of five arrhythmias. Experimental results on the MIT-BIH Arrhythmia Database show that VPNet achieves performance comparable to state-of-the-art ECG classifiers, attaining  95% accuracy while maintaining a compact architecture. Its low computational complexity enables efficient training and inference, making it highly suitable for real-time, power-efficient edge computing applications. This is further validated through embedded implementation on STM32 microcontrollers.