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Data Science and Biology - Speaker Series Hosted by Diversity in Data Science & CELLebrate Event Description Data Science and Biology - Speaker Series provides an exciting opportunity to […]
Dr. Grimshaw received his BA from UCSD in 1981, his PhD in Computer Science from the University of Illinois in 1988, and then joined the Department of Computer Science at […]
Join us for our annual Open House on August 31st at 3PM PDT (held virtually). The event will provide an in-depth look at our undergraduate and graduate data science talent and opportunities […]
What are the optimal algorithms for learning from data? Have we found them already, or are better ones out there to be discovered? Making these questions precise, and answering them, requires taking on the mathematically deep interplay between statistical and computational constraints. It also requires reconciling our theoretical toolbox with surprising new phenomena arising from practice, which seem to violate conventional rules of thumb regarding algorithm and model design. I will discuss progress along these lines: in terms of designing new algorithms for basic learning problems, controlling generalization in large statistical models, and understanding key statistical questions for generative modeling.
In this lecture we shall present some recent results on the interplay between control and Machine Learning, and more precisely, Supervised Learning and Universal Approximation. We adopt the perspective of the simultaneous or ensemble control of systems of Residual Neural Networks (ResNets). Roughly, each item to be classified corresponds to a different initial datum for the Cauchy problem of the ResNets, leading to an ensemble of solutions to be driven to the corresponding targets, associated to the labels, by means of the same control. We present a genuinely nonlinear and constructive method, allowing to show that such an ambitious goal can be achieved, estimating the complexity of the control strategies. This property is rarely fulfilled by the classical dynamical systems in Mechanics and the very nonlinear nature of the activation function governing the ResNet dynamics plays a determinant role. It allows deforming half of the phase space while the other half remains invariant, a property that classical models in mechanics do not fulfill. The turnpike property is also analyzed in this context, showing that a suitable choice of the cost functional used to train the ResNet leads to more stable and robust dynamics. This lecture is inspired in joint work, among others, with Borjan Geshkovski (MIT), Carlos Esteve (Cambridge), Domènec Ruiz-Balet (IC, London) and Dario Pighin (Sherpa.ai).
