Title: Graph Variate Neural Networks
Primary area: learning on graphs and other geometries & topologies
Keywords: Temporal Graphs, Graph Neural Networks, Graph Variate Signal Analysis, Brain Computer Interfaces.

Abstract: 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 \textit{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 Graph-Variate Signal Analysis (GVSA) and tools from graph signal processing, we introduce \textbf{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.