Modelling dynamically evolving spatio-temporal signals is a prominent challenge in the Graph Neural Network (GNN) literature. Notably, GNNs assume an existing underlying graph structure. While this underlying structure may not always exist or is derived independently from the signal, a temporally evolving functional network can always be constructed from multi-channel data. Graph Variate Signal Analysis (GVSA) defines a unified framework consisting of a network tensor of instantaneous connectivity profiles against a stable support usually constructed from the signal itself. Building on GVSA and tools from graph signal processing, we introduce Graph-Variate Neural Networks (GVNNs): layers that convolve spatio-temporal signals with a signal-dependent connectivity tensor combining a stable long-term support with instantaneous, data-driven interactions. This design captures dynamic statistical interdependencies at each time step without ad hoc sliding windows and admits an efficient implementation with linear complexity in sequence length. Across forecasting benchmarks, GVNNs consistently outperform strong graph-based baselines and are competitive with widely used sequence models such as LSTMs and Transformers. On EEG motor-imagery classification, GVNNs achieve strong accuracy highlighting their potential for brain-computer interface applications.

翻译：对动态演化的时空信号进行建模是图神经网络（GNN）文献中的一项重要挑战。值得注意的是，GNN假设存在一个潜在的基础图结构。虽然这种基础结构可能并不总是存在，或者是从信号中独立推导出来的，但多通道数据总能构建出一个随时间演化的功能网络。图变分信号分析（GVSA）定义了一个统一框架，该框架由一个瞬时连接性配置的网络张量和一个通常由信号自身构建的稳定支撑构成。基于GVSA和图信号处理工具，我们引入了图变分神经网络（GVNN）：这些层利用信号相关的连接张量对时空信号进行卷积，该张量将稳定的长期支撑与即时的数据驱动交互相结合。这种设计无需采用滑动窗口即可捕获每个时间步的动态统计依赖关系，并且能够实现序列长度线性复杂度的有效计算。在预测基准测试中，GVNN持续优于基于图的强基线模型，并与LSTM和Transformer等广泛使用的序列模型性能相当。在EEG运动想象分类任务中，GVNN取得了高准确率，突显了其在脑机接口应用中的潜力。