# Deep Unfolded Latent Optimally Partitioned-l2/l1 Networks for Data-driven Block-Sparse Recovery

arXiv: https://arxiv.org/abs/2606.12740 · HTML: https://mlsanity.com/paper/2606.12740/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 43 references that are in the map.
- First posted on arXiv 10 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Why gradient clipping accelerates training: A theoretical justification for adaptivity](https://mlsanity.com/paper/1905.11881/) (2019)
- [Improved Analysis of Clipping Algorithms for Non-convex Optimization](https://mlsanity.com/paper/2010.02519/) (2020)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [Deep Unfolding for Communications Systems: A Survey and Some New Directions](https://mlsanity.com/paper/1906.05774/) (2019)
- [RPCANet: Deep Unfolding RPCA Based Infrared Small Target Detection](https://mlsanity.com/paper/2311.00917/) (2023)
- [Deep Weight Factorization: Sparse Learning Through the Lens of Artificial Symmetries](https://mlsanity.com/paper/2502.02496/) (2025)
- [Smoothing the Edges: Smooth Optimization for Sparse Regularization using Hadamard Overparametrization](https://mlsanity.com/paper/2307.03571/) (2023)
- [Pattern-Coupled Sparse Bayesian Learning for Recovery of Block-Sparse Signals](https://mlsanity.com/paper/1311.2150/) (2013)
- [Deep Unfolding: Recent Developments, Theory, and Design Guidelines](https://mlsanity.com/paper/2512.03768/) (2025)
- [Deep Learning-based Channel Estimation for Wideband Hybrid MmWave Massive MIMO](https://mlsanity.com/paper/2205.05202/) (2022)
- [Perspective Functions: Proximal Calculus and Applications in High-Dimensional Statistics](https://mlsanity.com/paper/1610.01478/) (2016)
- [Escaping saddle points without Lipschitz smoothness: the power of nonlinear preconditioning](https://mlsanity.com/paper/2509.15817/) (2025)
- [Differentiable Sparsity via D-Gating: Simple and Versatile Structured Penalization](https://mlsanity.com/paper/2509.23898/) (2025)
- [A Convex-Nonconvex Framework for Enhancing Minimization Induced Penalties](https://mlsanity.com/paper/2407.14819/) (2024)
- [Theoretical Validation of the Latent Optimally Partitioned-ℓ2/ℓ1 Penalty with Application to Angular Power Spectrum Estimation](https://mlsanity.com/paper/2509.13745/) (2025)
- [WEEP: A Differentiable Nonconvex Sparse Regularizer via Weakly-Convex Envelope](https://mlsanity.com/paper/2507.20447/) (2025)

## Abstract (arXiv)

The convex Latent Optimal Partition (LOP)-l2/l1 approach enables block-sparse signal recovery with unknown partitions but relies on manual hyperparameter tuning. Additionally, numerical instability in differentiating its proximal operator prevents its automatic parameter tuning via Deep Unfolding (DU). To address these limitations, we propose two architectures: a stable framework utilizing implicit differentiation and a flexible variant leveraging Deep Weight Factorization (DWF). The DWF-based approach also supports nonconvex smooth data fidelity terms. Numerical experiments demonstrate that DU-LOP-l2/l1 yields competitive performance and high resilience against impulsive noise.