Simons Institute Courses

A Local Graph Limits Perspective on Sampling-Based GNNs

Explore how local graph limits provide theoretical foundations for understanding sampling-based graph neural networks and their scalability across large graphs.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

Size (OOD) Generalization of Neural Models via Algorithmic Alignment

Explore how neural models achieve size generalization through algorithmic alignment, covering theoretical foundations and practical applications in geometric optimization problems.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Mathematical Connections of Some Local-to-Global Expressivity Results Over Geometric Graphs and Geometric Rigidity

Explore mathematical connections between geometric graph expressivity and rigidity theory, linking MPGNN invariants to classical geometric problems and future research directions.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Homomorphism Indistinguishability - Graph Learning and Theoretical Computer Science

Explore the theoretical foundations of homomorphism indistinguishability and its applications in graph learning, quantum information, and computational complexity analysis.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Mapping Multisets to Vectors

Explore neural networks that map multisets to vectors using permutation invariant operations, analyzing injectivity and bi-Lipschitzness properties with sorting-based approaches.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

ML for Discrete Optimization - Theoretical Foundations

Discover how calibrated machine learning predictions enhance discrete optimization algorithms by bridging reliability and efficiency in decision-making under uncertainty.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Recent Trends in Combinatorial Optimization Augmented Machine Learning - A Graph Learning Perspective

Explore cutting-edge integration of machine learning and operations research for data-driven optimization problems with combinatorial structures in industrial settings.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Understanding ReLU Networks Through Graph Problems and Polyhedra

Explore the theoretical foundations of ReLU networks using polyhedral geometry, graph theory, and combinatorial optimization to understand representable functions and complexity.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Szemerédi Regularity Lemma in Graph Machine Learning

Discover how the Szemerédi Regularity Lemma from graph theory provides theoretical foundations for Graph Neural Networks, enabling better generalization bounds and scalable designs for large graphs.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Toward Universal Graph Representations - Foundations and Frontiers of Graph Foundation Models

Explore graph foundation models and universal representations, examining positional vs structural embeddings, invariances in statistical tests, and applications to algorithmic reasoning in network optimization.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Exact Performance Verification of First-Order Methods in Parametric Convex Optimization

Discover a computational framework for quantifying finite-iteration performance of first-order optimization methods through fixed-length computational graphs and verification.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Graph Machine Learning and Random Graph Models

Explore graph machine learning and GNN behavior on large random graphs through geometric models, convergence analysis, and stability insights for deep architectures.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Higher Order Graph Neural Networks with P-Tensors

Explore advanced graph neural networks using P-tensors to overcome message passing limitations while maintaining equivariance and improving expressiveness for complex graph structures.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Boot Camp on Combinatorial Optimization and Graph Learning

Dive into combinatorial optimization and graph learning fundamentals with expert insights from Cornell Tech's Andrea Lodi in this comprehensive bootcamp session.

• YouTube
• 1 hour 32 minutes
• Self-Paced
• Free Video

Bootcamp on Geometry and Graph Learning

Discover geometric principles and graph learning techniques in this comprehensive bootcamp covering theoretical foundations and practical applications.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video