[2509.20311] Graph Variate Neural Networks

Computer Science > Machine Learning arXiv:2509.20311 (cs) [Submitted on 24 Sep 2025 (v1), last revised 24 Mar 2026 (this version, v2)] Title:Graph Variate Neural Networks Authors:Om Roy, Yashar Moshfeghi, Keith Smith View a PDF of the paper titled Graph Variate Neural Networks, by Om Roy and 2 other authors View PDF HTML (experimental) 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 ...