Deep Unfolded Variable Projection Networks

Bognár, Gergő and Feindert, Manuel and Huber, Christian and Lunglmayr, Michael and Huemer, Mario and Kovács, Péter (2025) Deep Unfolded Variable Projection Networks. INTERNATIONAL JOURNAL OF NEURAL SYSTEMS, 35 (13). No. 2550053. ISSN 0129-0657

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Abstract

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.

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