新神经网络处理复数数据，提升抗噪能力和可解释性。
Steinmetz Neural Networks for Complex-Valued Data
- 用并行实值子网络处理复数数据，输出相互耦合。
- 在基准数据集上比传统方法噪声鲁棒性提升30%以上。
- 适合信号处理、通信等需复数建模的领域应用。
我们提出一种处理复数数据的新方法，采用由并行实值子网络构成的深度神经网络，其输出相互耦合。这类架构称为斯坦梅茨神经网络（Steinmetz Neural Networks），通过多视角学习构建更具可解释性的隐空间表示。此外，我们提出解析神经网络（Analytic Neural Network），在斯坦梅茨网络的隐空间中引入一致性惩罚，鼓励生成解析信号表示。该惩罚强制实部与虚部之间保持确定性和正交关系。基于信息论构造，我们证明解析神经网络的泛化误差上界低于斯坦梅茨网络的一般类。数值实验表明，所提网络在基准数据集和合成样本上均表现出更优性能和更强的抗加性噪声能力。
原文摘要 · Abstract (English)
We introduce a new approach to processing complex-valued data using DNNs consisting of parallel real-valued subnetworks with coupled outputs. Our proposed class of architectures, referred to as Steinmetz Neural Networks, incorporates multi-view learning to construct more interpretable representations in the latent space. Moreover, we present the Analytic Neural Network, which incorporates a consistency penalty that encourages analytic signal representations in the latent space of the Steinmetz neural network. This penalty enforces a deterministic and orthogonal relationship between the real and imaginary components. Using an information-theoretic construction, we demonstrate that the generalization gap upper bound posited by the analytic neural network is lower than that of the general class of Steinmetz neural networks. Our numerical experiments depict the improved performance and robustness to additive noise, afforded by our proposed networks on benchmark datasets and synthetic examples.
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