One World Seminar Series on the
Mathematics of Machine Learning
The One World Seminar Series on the Mathematics of Machine Learning is an online platform for research seminars, workshops and seasonal schools in theoretical machine learning. The focus of the series lies on theoretical advances in machine learning and deep learning as a complement to the one world seminars on probability, on Information, Signals and Data (MINDS), on methods for arbitrary data sources (MADS), and on imaging and inverse problems (IMAGINE).
The series was started during the Covid-19 epidemic in 2020 to bring together researchers from all over the world for presentations and discussions in a virtual environment. It follows in the footsteps of other community projects under the One World Umbrella which originated around the same time.
We welcome suggestions for speakers concerning new and exciting developments and are committed to providing a platform also for junior researchers. We recognize the advantages that online seminars provide in terms of flexibility, and we are experimenting with different formats. Any feedback on different events is welcome.
Asymptotic Analysis of Deep Residual Networks
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature: one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. The scaling regime one ends up with depends on certain features of the network architecture, such as the smoothness of the activation function. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit. In the case where the scaling limit is a stochastic differential equation, the deep network limit is shown to be described by a system of forward-backward stochastic differential equations. Joint work with: Alain-Sam Cohen (InstaDeep Ltd), Alain Rossier (Oxford), RenYuan Xu (University of Southern California).
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Seminars are held online on Zoom. The presentations are recorded and video is made available on our youtube channel. A list of past seminars can be found here. All seminars, unless otherwise stated, are held on Wednesdays at 12 noon ET. The invitation will be shared on this site before the talk and distributed via email.