# Deep Unfolding with Approximated Computations for Rapid Optimization

arXiv: https://arxiv.org/abs/2509.00782 · HTML: https://mlsanity.com/paper/2509.00782/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2025.

## Built on by (most cited first, 1 of 1)

- [Deep Unfolding: Recent Developments, Theory, and Design Guidelines](https://mlsanity.com/paper/2512.03768/) (2025)

## Abstract (arXiv)

Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high computational cost per iteration. While deep unfolding has emerged as a powerful paradigm for converting iterative algorithms into learned models that operate with a fixed number of iterations, it does not inherently address the cost of each iteration. In this paper, we introduce a learned optimization framework that jointly tackles iteration count and per-iteration complexity. Our approach is based on unfolding a fixed number of optimization steps, replacing selected iterations with low-complexity approximated computations, and learning extended hyperparameters from data to compensate for the introduced approximations. We demonstrate the effectiveness of our method on two representative problems: (i) hybrid beamforming; and (ii) robust principal component analysis. These fundamental case studies show that our learned approximated optimizers can achieve state-of-the-art performance while reducing computational complexity by over three orders of magnitude. Our results highlight the potential of our approach to enable rapid, interpretable, and efficient decision-making in real-time systems.