# An Encoder-Decoder Network for Beamforming over Sparse Large-Scale MIMO Channels

arXiv: https://arxiv.org/abs/2510.02355 · HTML: https://mlsanity.com/paper/2510.02355/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Builds on (most cited first, 16 of 16)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Paraphrasing Complex Network: Network Compression via Factor Transfer](https://mlsanity.com/paper/1802.04977/) (2018)
- [Semi-Amortized Variational Autoencoders](https://mlsanity.com/paper/1802.02550/) (2018)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [Stabilizing Generative Adversarial Networks: A Survey](https://mlsanity.com/paper/1910.00927/) (2019)
- [High Dimensional Channel Estimation Using Deep Generative Networks](https://mlsanity.com/paper/2006.13494/) (2020)
- [Learning to Reflect and to Beamform for Intelligent Reflecting Surface with Implicit Channel Estimation](https://mlsanity.com/paper/2009.14404/) (2020)
- [Deep-Learning-based Millimeter-Wave Massive MIMO for Hybrid Precoding](https://mlsanity.com/paper/1901.06537/) (2019)
- [Deep Learning for Direct Hybrid Precoding in Millimeter Wave Massive MIMO Systems](https://mlsanity.com/paper/1905.13212/) (2019)
- [Unsupervised Deep Learning for Massive MIMO Hybrid Beamforming](https://mlsanity.com/paper/2007.00038/) (2020)
- [On Solution Functions of Optimization: Universal Approximation and Covering Number Bounds](https://mlsanity.com/paper/2212.01314/) (2022)
- [Near-Field Wideband Beamforming for Extremely Large Antenna Arrays](https://mlsanity.com/paper/2109.10054/) (2021)
- [Beamfocusing Optimization for Near-Field Wideband Multi-User Communications](https://mlsanity.com/paper/2306.16861/) (2023)
- [Near-field Hybrid Beamforming for Terahertz-band Integrated Sensing and Communications](https://mlsanity.com/paper/2309.13984/) (2023)

## Built on by (most cited first, 2 of 2)

- [A Semi-amortized Lifted Learning-to-Optimize Masked (SALLO-M) Transformer Model for Scalable and Generalizable Beamforming](https://mlsanity.com/paper/2510.13077/) (2025)
- [Self-Evolving In-Context Learning for Direct Pilot-to-Beamformer Design in MU-MISO Systems](https://mlsanity.com/paper/2607.11970/) (2026)

## Abstract (arXiv)

We develop an end-to-end deep learning framework for downlink beamforming in large-scale sparse MIMO channels. The core is a deep EDN architecture with three modules: (i) an encoder NN, deployed at each user end, that compresses estimated downlink channels into low-dimensional latent vectors. The latent vector from each user is compressed and then fed back to the BS. (ii) a beamformer decoder NN at the BS that maps recovered latent vectors to beamformers, and (iii) a channel decoder NN at the BS that reconstructs downlink channels from recovered latent vectors to further refine the beamformers. The training of EDN leverages two key strategies: (a) semi-amortized learning, where the beamformer decoder NN contains an analytical gradient ascent during both training and inference stages, and (b) knowledge distillation, where the loss function consists of a supervised term and an unsupervised term, and starting from supervised training with MMSE beamformers, over the epochs, the model training gradually shifts toward unsupervised using the sum-rate objective. The proposed EDN beamforming framework is extended to both far-field and near-field hybrid beamforming scenarios. Extensive simulations validate its effectiveness under diverse network and channel conditions.