Machine learning (ML) and tensor-based methods have been of significant
interest for the scientific community for the last few decades. In a previous
work we presented a novel tensor-based system identification framework to ease
the computational burden of tensor-only architectures while still being able to
achieve exceptionally good performance. However, the derived approach only
allows to process real-valued problems and is therefore not directly applicable
on a wide range of signal processing and communications problems, which often
deal with complex-valued systems. In this work we therefore derive two new
architectures to allow the processing of complex-valued signals, and show that
these extensions are able to surpass the trivial, complex-valued extension of
the original architecture in terms of performance, while only requiring a
slight overhead in computational resources to allow for complex-valued
operations.

本文介绍两种新架构来处理复数信号，以提高系统识别性能，同时只需略微增加计算资源投入。

低秩张量分解下的复数自适应系统辨识

Complex-valued Adaptive System Identification via Low-Rank Tensor  Decomposition

Most deep learning pipelines are built on real-valued operations to deal with
real-valued inputs such as images, speech or music signals. However, a lot of
applications naturally make use of complex-valued signals or images, such as
MRI or remote sensing. Additionally the Fourier transform of signals is
complex-valued and has numerous applications. We aim to make deep learning
directly applicable to these complex-valued signals without using projections
into $\mathbb{R}^2$. Thus we add to the recent developments of complex-valued
neural networks by presenting building blocks to transfer the transformer
architecture to the complex domain. We present multiple versions of a
complex-valued Scaled Dot-Product Attention mechanism as well as a
complex-valued layer normalization. We test on a classification and a sequence
generation task on the MusicNet dataset and show improved robustness to
overfitting while maintaining on-par performance when compared to the
real-valued transformer architecture.

该论文旨在将深度学习直接应用于复值信号，提出了建立在变形器结构上的复值神经网络构建模块，并通过在 MusicNet 数据集上进行分类和序列生成任务的测试表明了该模型对于过拟合有更好的鲁棒性，同时维持了与实数传输器的性能相当水平。