Spectral Analyses of Graph Neural Networks

Explore the mathematical foundations of graph neural networks through spectral analysis in this 52-minute conference talk from the 2025 Mathematical and Scientific Foundations of Deep Learning Annual Meeting. Delve into the theoretical underpinnings of how graph neural networks process and learn from graph-structured data using spectral methods. Examine the connections between graph theory, spectral analysis, and deep learning architectures designed for non-Euclidean data structures. Gain insights into the mathematical frameworks that explain the behavior and performance of graph neural networks, including their ability to capture local and global graph properties through spectral decomposition techniques. Learn about the theoretical guarantees and limitations of these models from a spectral perspective, providing a deeper understanding of why and how graph neural networks work effectively on complex networked data.