TUTORIALS
Geometric and Topological Representation Learning
Organizers:
Semih Cantürk, Udem & Mila
Hamed Shirzad, UBC
Qi Yan, UBC
Guy Wolf, Udem & Mila
Renjie Liao, UBC & Vector Institute
Danica J. Sutherland, UBC & Amii
Abstract:
Real-world data in natural and social sciences typically exhibit intricate and complex relationships that are well-suited to be represented as graphs, point clouds and time series among other geometric and topological structures. Embedding appropriate inductive biases into deep learning models is thus essential in building systems that can learn and generalize from such data. Machine learning on graphs in particular has seen rapid development in recent years, owing much to advances in graph representation learning (GRL), a large family of methods with close connections to signal processing designed to encode sparse graph structured data into dense vector form in graph representations. Thanks to their ability to leverage data-intrinsic geometries, graph neural networks (GNN) have been in the forefront of GRL, while later work have built upon this foundation to arrive at a wide selection of complex and powerful GNN architectures addressing expressivity, multi-resolution signals, or implicit symmetries. These developments have collectively facilitated the use of GNNs in a variety of applications ranging from recommender systems and traffic forecasting to biochemistry and materials science, while also spawning novel subfields that extend these learning paradigms to even more complex structures in temporal graphs or simplicial complexes. In this tutorial, we aim to provide a bottom-up view of modern graph representation learning and its extensions to related topological structures. Our tutorial aims to appeal to a large audience including both newcomers into the field of geometric representation learning as well as research and industry experts.
Learning with Covariance Matrices: Foundations and Applications to Network Neuroscience
Organizers:
Saurabh Sihag, University at Albany SUNY
Gonzalo Mateos, University of Rochester
Elvin Isufi, Delft University of Technology
Alejandro Ribeiro, University of Pennsylvania
Abstract:
This tutorial will cover the wide gamut of traditional PCA approaches to coVariance neural networks in a unifying manner. Through rigorous formulations and intuitive reasoning, the content will be made accessible to SP researchers familiar with the basics of statistical analysis and machine learning (ML). The theoretical core of the tutorial consists of two key modules that focus on the stability and transferability of VNNs. Broadly, these modules address the robust generalization properties of VNN models to heterogeneous scenarios encountered in practice. We will ground the theoretical advances behind VNNs in first principles of statistical inference. In addition to its didactic value, this approach offers an enlightening perspective to the traditional PCA-driven statistcal approaches, from the lens of GNNs. Further, this tutorial will also include an application module discussing the problem of brain age prediction in neurodegenerative conditions. The conceptual clarity and explainable solution to this problem elucidated by VNN models will be highlighted. Overall, tutorial contents will span a broad spectrum of theoretical and use-inspired contributions that are relevant to the SP community.
Integration of Physics-Based and Data-Driven Models for Parameter Estimation with Applications to Image and Speech Signal Processing
Organizers:
Jie Chen, Northwestern Polytechnical University
Xiuheng Wang, CRAN, CNRS, Universite de Lorraine
Ziye Yang, Northwestern Polytechnical University
Abstract:
In the era of rapidly expanding data and computational power, data-driven models have gained tremendous momentum for tackling complex parameter estimation problems. However, purely data-driven approaches often face challenges such as low interpretability, risk of overfitting, and limited generalization when real-world data are scarce or unrepresentative. At the same time, physics-based methods provide transparent theoretical grounding and interpretability but may underperform when the physical environment is unknown, highly complex, or differs significantly from assumed models. Bridging these two complementary paradigms has therefore emerged as a crucial research direction in the signal processing community. The motivation behind such hybrid or integrated approaches is to leverage both domain knowledge (via physics-based constraints) and data-driven learning (via deep learning tools), resulting in systems that are more robust, explainable, and capable of capturing complex real-world phenomena. This tutorial is timely for both academic and industry stakeholders seeking to move beyond either purely model-driven or purely data-driven approaches. By understanding how to embed physical insights into deep learning architectures, or how to supplement traditional physics-based solutions with data-driven modules, researchers and engineers can develop models with improved performance, enhanced interpretability, and better generalization capabilities. As such, this topic has profound implications for a variety of fields, encompassing, but not limited to, computational imaging, remote sensing, or speech processing. Ultimately, this tutorial will offer a comprehensive roadmap for researchers to leverage the synergy between physics-based and data-driven approaches, which have emerged as the forefront of parameter estimation technologies in signal processing.