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TILOS Fireside Chat on "Theory in the age of modern AI", which will be a conversation led by TILOS team members: Misha Belkin (UCSD), Arya Mazumdar (moderator, UCSD), Tara Javidi (UCSD), Visheeth Vishnoi (Yale U). The focus will be on the implications to, and the roles played by theory, in modern AI (especially with the recent exciting […]
TILOS Seminar: Towards Foundation Models for Graph Reasoning and AI 4 Science Michael Galkin, Research Scientist at AI Lab HDSI 123 and Zoom: https://ucsd.zoom.us/j/99334315002 Abstract: Foundation models in graph learning are hard to design due to the lack of common invariances that transfer across different structures and domains. In this talk, I will give an overview […]
In this talk I will discuss the challenges and opportunities for using deep learning in medical image reconstruction. Contemporary techniques in this field rely on convolutional architectures that are limited by the spatial invariance of their filters and have difficulty modeling long-range dependencies. To remedy this, I will discuss our work on designing new transformer-based architectures called HUMUS-Net that lead to state of the art performance and do not suffer from these limitations. In the next part of the talk I will report on techniques to significantly reduce the required data for training. Finally, I will briefly discuss our recent attempts to develop rigorous theory for simple end-to-end training methods used in image reconstruction problems which is surprisingly quite challenging even for simple target functions. Notability, our theory will be in the rich (or beyond NTK regime) that conforms with practical choice of hyperparameters. Time permitting I will discuss other exciting directions for the use of deep learning in MR.
Abstract: The principle of Optimism in the Face of Uncertainty (OFU) is one of the foundational algorithmic design choices in Reinforcement Learning and Bandits. Optimistic algorithms balance exploration and exploitation by deploying data collection strategies that maximize expected rewards in plausible models. This is the basis of celebrated algorithms like the Upper Confidence Bound (UCB) for multi-armed bandits. For nearly a decade, the analysis of optimistic algorithms, including Optimistic Least Squares, in the context of rich reward function classes has relied on the concept of eluder dimension, introduced by Russo and Van Roy in 2013. In this talk we shed light on the limitations of the eluder dimension in capturing the true behavior of optimistic strategies in the realm of function approximation. We remediate these by introducing a novel statistical measure, the “dissimilarity dimension”. We show it can be used to provide sharper sample analysis of algorithms like Optimistic Least Squares by establishing a link between regret and the dissimilarity dimension. To illustrate this, we will show that some function classes have arbitrarily large eluder dimension but constant dissimilarity. Our regret analysis draws inspiration from graph theory and may be of interest to the mathematically minded beyond the field of statistical learning theory. This talk sheds new light on the fundamental principle of optimism and its algorithms in the function approximation regime, advancing our understanding of these concepts.