# On Generalization Bounds for Deep Compound Gaussian Neural Networks

arXiv: https://arxiv.org/abs/2402.13106 · HTML: https://mlsanity.com/paper/2402.13106/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [Unrolled Optimization with Deep Priors](https://mlsanity.com/paper/1705.08041/) (2017)
- [ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2103.11554/) (2021)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (2021)
- [Compressive Sensing and Neural Networks from a Statistical Learning Perspective](https://mlsanity.com/paper/2010.15658/) (2020)
- [DECONET: an Unfolding Network for Analysis-based Compressed Sensing with Generalization Error Bounds](https://mlsanity.com/paper/2205.07050/) (2022)
- [A Compound Gaussian Least Squares Algorithm and Unrolled Network for Linear Inverse Problems](https://mlsanity.com/paper/2305.11120/) (2023)
- [Deep Regularized Compound Gaussian Network for Solving Linear Inverse Problems](https://mlsanity.com/paper/2311.17248/) (2023)

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

- [How to warm-start your unfolding network](https://mlsanity.com/paper/2502.01854/) (2025)

## Abstract (arXiv)

Algorithm unfolding or unrolling is the technique of constructing a deep neural network (DNN) from an iterative algorithm. Unrolled DNNs often provide better interpretability and superior empirical performance over standard DNNs in signal estimation tasks. An important theoretical question, which has only recently received attention, is the development of generalization error bounds for unrolled DNNs. These bounds deliver theoretical and practical insights into the performance of a DNN on empirical datasets that are distinct from, but sampled from, the probability density generating the DNN training data. In this paper, we develop novel generalization error bounds for a class of unrolled DNNs that are informed by a compound Gaussian prior. These compound Gaussian networks have been shown to outperform comparative standard and unfolded deep neural networks in compressive sensing and tomographic imaging problems. The generalization error bound is formulated by bounding the Rademacher complexity of the class of compound Gaussian network estimates with Dudley's integral. Under realistic conditions, we show that, at worst, the generalization error scales O(n√ln(n)) in the signal dimension and O((Network Size)3/2) in network size.