Graph Variate Neural Networks
This addresses the problem of modeling dynamic spatio-temporal signals for applications like forecasting and brain-computer interfaces, representing a novel method for a known bottleneck.
The paper tackles the challenge of modeling dynamically evolving spatio-temporal signals in Graph Neural Networks by introducing Graph-Variate Neural Networks (GVNNs), which combine stable long-term support with instantaneous data-driven interactions to capture dynamic interdependencies without sliding windows. The results show GVNNs outperform graph-based baselines in forecasting benchmarks, achieve competitive performance with LSTMs and Transformers, and demonstrate strong accuracy in EEG motor-imagery classification.
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.