# Harnessing Tensor Structures -- Multi-Mode Reservoir Computing and Its Application in Massive MIMO

arXiv: https://arxiv.org/abs/2102.09322 · HTML: https://mlsanity.com/paper/2102.09322/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 45 references that are in the map.
- First posted on arXiv 25 Jan 2021.

## Builds on (most cited first, 12 of 12)

- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [What Can ResNet Learn Efficiently, Going Beyond Kernels?](https://mlsanity.com/paper/1905.10337/) (2019)
- [Learning to Detect](https://mlsanity.com/paper/1805.07631/) (2018)
- [Blessing of dimensionality: mathematical foundations of the statistical physics of data](https://mlsanity.com/paper/1801.03421/) (2018)
- [Adaptive Neural Signal Detection for Massive MIMO](https://mlsanity.com/paper/1906.04610/) (2019)
- [Artificial Intelligence-Enabled Cellular Networks: A Critical Path to Beyond-5G and 6G](https://mlsanity.com/paper/1907.07862/) (2019)
- [RCNet: Incorporating Structural Information into Deep RNN for MIMO-OFDM Symbol Detection with Limited Training](https://mlsanity.com/paper/2003.06923/) (2020)
- [Learning for Integer-Constrained Optimization through Neural Networks with Limited Training](https://mlsanity.com/paper/2011.05399/) (2020)
- [Learning with Knowledge of Structure: A Neural Network-Based Approach for MIMO-OFDM Detection](https://mlsanity.com/paper/2012.00711/) (2020)

## Abstract (arXiv)

In this paper, we introduce a new neural network (NN) structure, multi-mode reservoir computing (Multi-Mode RC). It inherits the dynamic mechanism of RC and processes the forward path and loss optimization of the NN using tensor as the underlying data format. Multi-Mode RC exhibits less complexity compared with conventional RC structures (e.g. single-mode RC) with comparable generalization performance. Furthermore, we introduce an alternating least square-based learning algorithm for Multi-Mode RC as well as conduct the associated theoretical analysis. The result can be utilized to guide the configuration of NN parameters to sufficiently circumvent over-fitting issues. As a key application, we consider the symbol detection task in multiple-input-multiple-output (MIMO) orthogonal-frequency-division-multiplexing (OFDM) systems with massive MIMO employed at the base stations (BSs). Thanks to the tensor structure of massive MIMO-OFDM signals, our online learning-based symbol detection method generalizes well in terms of bit error rate even using a limited online training set. Evaluation results suggest that the Multi-Mode RC-based learning framework can efficiently and effectively combat practical constraints of wireless systems (i.e. channel state information (CSI) errors and hardware non-linearity) to enable robust and adaptive learning-based communications over the air.