Deep Unfolding: Recent Developments, Theory, and Design Guidelines
Nir Shlezinger, Santiago Segarra, Yi Zhang, Dvir Avrahami, Zohar Davidov, Tirza Routtenberg, Yonina C. Eldar
TL;DR
This tutorial surveys deep unfolding, a framework that turns iterative optimization into trainable neural architectures to combine interpretability and guarantees from model-based methods with data-driven flexibility. It formalizes optimization for inference versus learning, introduces four unfolding paradigms (learning hyperparameters, learning objective parameters, learning correction terms, and dnn inductive bias), and discusses training strategies and theoretical guarantees. The work analyzes convergence and generalization for unfolded optimizers, compares paradigms qualitatively and quantitatively (via a RPCA-based study), and outlines open challenges. The findings underscore deep unfolding as a principled, scalable pathway to design efficient, robust, and domain-aware inference models with controllable latency and complexity.
Abstract
Optimization methods play a central role in signal processing, serving as the mathematical foundation for inference, estimation, and control. While classical iterative optimization algorithms provide interpretability and theoretical guarantees, they often rely on surrogate objectives, require careful hyperparameter tuning, and exhibit substantial computational latency. Conversely, machine learning (ML ) offers powerful data-driven modeling capabilities but lacks the structure, transparency, and efficiency needed for optimization-driven inference. Deep unfolding has recently emerged as a compelling framework that bridges these two paradigms by systematically transforming iterative optimization algorithms into structured, trainable ML architectures. This article provides a tutorial-style overview of deep unfolding, presenting a unified perspective of methodologies for converting optimization solvers into ML models and highlighting their conceptual, theoretical, and practical implications. We review the foundations of optimization for inference and for learning, introduce four representative design paradigms for deep unfolding, and discuss the distinctive training schemes that arise from their iterative nature. Furthermore, we survey recent theoretical advances that establish convergence and generalization guarantees for unfolded optimizers, and provide comparative qualitative and empirical studies illustrating their relative trade-offs in complexity, interpretability, and robustness.