The Manchester Centre for AI Fundamentals and Manchester's ELLIS Unit are co-hosting a series of seminars featuring expert researchers working in the fundamentals of AI. On 16 October, we are pleased to welcome Tolga Birdal from Imperial College London.
Abstract:
Deep neural networks (DNNs) exhibit remarkable generalization abilities, yet the mechanisms behind these capabilities remain poorly understood, defying the established wisdom of statistical learning theory. Recent research has revealed a compelling link between the fractal structures formed during iterative training and the resulting generalization performance. In this talk, Dr. Birdal sheds new light on these connections by presenting a novel framework that ties complexity measures to the topological properties of the training process.
The presentation begins by bounding the generalization error through the fractal dimension of training trajectories, practically computed using tools from persistent homology—introducing the 'persistent homology dimension' as a new, insightful proxy for generalization. Building on this, Dr. Birdal introduces more computationally efficient topological complexity measures that bypass the need for continuous training trajectories. These measures consistently show strong correlations with the generalization gap across diverse models, including transformers and graph networks. The findings hold transformative implications for both theory and practice, offering a new lens to study, understand and optimize the generalization power of modern AI systems.
Relevant Publications:
1 https://arxiv.org/abs/2111.13171 arxiv.org (NeurIPS 2021)
2 https://arxiv.org/abs/2407.08723 arxiv.org (Hopefully NeurIPS 2024 )
Bio:
Tolga Birdal is an assistant professor in the Department of Computing of Imperial College London. Previously, he was a Postdoctoral Research Fellow at Stanford University within the Geometric Computing Group of Prof. Leonidas Guibas. Tolga has defended his masters and Ph.D. theses at the Computer Vision Group under Chair for Computer Aided Medical Procedures, Technical University of Munich led by Prof. Nassir Navab. He was also a Doktorand at Siemens AG under supervision of Dr. Slobodan Ilic working on “Geometric Methods for 3D Reconstruction from Large Point Clouds”. His current foci of interest involve topological / geometric machine learning and 3D computer vision. More theoretical work is aimed at investigating and interrogating limits in geometric computing and non-Euclidean inference as well as principles of deep learning. Tolga is an AC for major vision conferences such as CVPR, ICCV, ECCV and 3DV and he has several publications at the well-respected venues such as NeurIPS, CVPR, ICCV, ECCV, ICLR, ICML, T-PAMI, IJCV, ICRA, IROS, ICASSP and 3DV. Aside from his academic life, Tolga has co-founded multiple companies including Befunky, a widely used web-based image editing platform.
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