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Title:
Mean field theory in Inverse Problems from Bayesian inference to overparameterization of networks

Abstract:
Bayesian sampling and neural networks are seemingly two different machine learning areas, but they both deal with many particle systems. In sampling, one evolves a large number of samples (particles) to match a target distribution function, and in optimizing over-parameterized neural networks, one can view neurons particles that feed each other information in the DNN flow. These perspectives allow us to employ mean-field theory, a powerful tool that translates dynamics of many particle system into a partial differential equation (PDE), so rich PDE analysis techniques can be used to understand both the convergence of sampling methods and the zero-loss property of over-parameterization of ResNets. We showcase the use of mean-field theory in these two machine learning areas, and we also invite the audience to brainstorm other possible applications.
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