This talk explores modern machine learning through high-dimensional statistics, using random matrix theory to analyze learning models. The speaker, Denny Wu from University of Toronto and the Vector Institute, presents two examples: hyperparameter selection in overparameterized models and gradient-based representation learning in neural networks. The analysis reveals insights such as the possibility of negative optimal ridge penalty and the advantages of feature learning over random features. Why it matters: This research provides a deeper theoretical understanding of deep learning phenomena, with potential implications for optimizing training and improving model performance in the region.
A DeepMind researcher presented work on incorporating symmetries into machine learning models, with applications to lattice-QCD and molecular dynamics. The work includes permutation and translation-invariant normalizing flows for free-energy estimation in molecular dynamics. They also presented U(N) and SU(N) Gauge-equivariant normalizing flows for pure Gauge simulations and its extensions to incorporate fermions in lattice-QCD. Why it matters: Applying symmetry principles to generative models could improve AI's ability to model complex physical systems relevant to materials science and other fields in the region.
Pascal Fua from EPFL presented an approach to implementing convolutional neural nets that output complex 3D surface meshes. The method overcomes limitations in converting implicit representations to explicit surface representations. Applications include single view reconstruction, physically-driven shape optimization, and bio-medical image segmentation. Why it matters: This research advances geometric deep learning by enabling end-to-end trainable models for 3D surface mesh generation, with potential impact on various applications in computer vision and biomedical imaging in the region.
This talk discusses the asymptotic study of large asymmetric spiked tensor models. It explores connections between these models and equivalent random matrices constructed through contractions of the original tensor. Mohamed El Amine Seddik, currently a senior researcher at TII in Abu Dhabi, presented the work. Why it matters: The research provides theoretical foundations relevant to machine learning algorithms that leverage low-rank tensor structures, potentially impacting AI research and applications in the region.
MBZUAI Professor Fakhri Karray and co-authors from the University of Waterloo have published "Elements of Dimensionality Reduction and Manifold Learning," a textbook on methods for extracting useful components from large datasets. The book addresses the challenge of the "curse of dimensionality," where growth in datasets complicates their use in machine learning. Karray developed the material from a popular course he taught at Waterloo. Why it matters: The textbook provides a unified resource for students and researchers in machine learning and AI, addressing a foundational challenge in processing high-dimensional data, relevant to diverse applications in the region.
This article discusses approximating a high-dimensional distribution using Gaussian variational inference by minimizing Kullback-Leibler divergence. It builds upon previous research and approximates the minimizer using a Gaussian distribution with specific mean and variance. The study details approximation accuracy and applicability using efficient dimension, relevant for analyzing sampling schemes in optimization. Why it matters: This theoretical research can inform the development of more efficient and accurate AI algorithms, particularly in areas dealing with high-dimensional data such as machine learning and data analysis.
KAUST Professor Peter Markowich discusses the role of mathematics in football, describing a match as a random process with a drift. The randomness stems from player conditions, referee decisions, weather, and more, while the drift represents the higher probability of the better team winning. He notes that the complexity arising from 11 players on each side increases the randomness compared to sports like tennis. Why it matters: This perspective highlights the interplay of chance and skill in sports, offering a mathematical lens for understanding game dynamics.
Emilio Porcu from Khalifa University presented on temporally evolving generalized networks, where graphs evolve over time with changing topologies. The presentation addressed challenges in building semi-metrics and isometric embeddings for these networks. The research uses kernel specification and network-based metrics and is illustrated using a traffic accident dataset. Why it matters: This work advances the application of kernel methods to dynamic graph structures, relevant for modeling evolving relationships in various domains.