Graph Variate Neural Networks

2025-09-24

AI Summary

Modeling dynamic spatiotemporal signals is challenged by the absence or irrelevance of underlying graph structures. Method: We propose Graph-Varying Neural Networks (GVNNs), which introduce a signal-dependent dynamic connectivity tensor to jointly model long-term stable topology and instantaneous, data-driven functional connectivity; further, we design a sliding-window-free dynamic convolution mechanism enabling linear-time estimation of functional networks at each time step. GVNNs unify graph-varying signal analysis and graph signal processing, integrating stable support graphs, dynamic convolution, and a synergistic GNN–sequence modeling architecture. Results: On multivariate time-series forecasting benchmarks, GVNNs significantly outperform state-of-the-art graph-based models and match the performance of LSTM and Transformer baselines. In EEG-based motor imagery classification—a canonical dynamic functional connectivity task—GVNNs achieve state-of-the-art accuracy, demonstrating their effectiveness and promise for brain–computer interface and related applications.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Computational social science

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 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.

Problem

• Modeling dynamically evolving spatio-temporal signals with graph neural networks
• Capturing dynamic statistical interdependencies without sliding windows
• Handling cases where underlying graph structure may not exist

Innovation

• Signal-dependent connectivity tensor combining stable and instantaneous interactions
• Dynamic statistical interdependencies captured without sliding windows
• Linear complexity implementation for efficient sequence processing