Physics Priors for Machine Learning and Machine Learning to Solve Physics
Max Welling - University of Amsterdam
Good neural architectures are rooted in good inductive biases (a.k.a. priors). Equivariance under symmetries is a prime example of a successful physics inspired prior which sometimes dramatically reduces the number of examples needed to learn predictive models. Diffusion based models, one of the most successful generative models, are rooted in nonequilbrium statistical mechanics. Reversely, ML methods have recently been used to solve PDEs for example in weather prediction, and to accelerate MD simulations by learning the (quantum mechanical) interactions between atoms and electrons.
In this work we will try to extend this thinking to more flexible priors in the hidden variables of a neural network. In particular, we will impose wavelike dynamics in hidden variables under transformations of the inputs, which relaxes the stricter notion of equivariance. We find that under certain conditions, wavelike dynamics naturally arises in these hidden representations. We formalize this idea in a VAE-over-time architecture where the hidden dynamics is described by a Fokker-Planck (a.k.a. drift-diffusion) equation. This in turn leads to a new definition of a disentangled hidden representation of input states that can easily be manipulated to undergo transformations. Joint work with Andy T. Keller and Yue Song.
Max Welling is a full professor and research chair in machine learning at the University of Amsterdam. He is a fellow at the Canadian Institute for Advanced Research (CIFAR) and the European Lab for Learning and Intelligent Systems (ELLIS) where he serves on the founding board. His previous appointments include Distinguished Scientist at MSR, VP at Qualcomm Technologies, professor at UC Irvine, postdoc at U. Toronto and UCL under supervision of prof. Geoffrey Hinton, and postdoc at Caltech under supervision of prof. Pietro Perona. He finished his PhD in theoretical high energy physics under supervision of Nobel laureate prof. Gerard ‘t Hooft. Max Welling has served as associate editor in chief of IEEE TPAMI from 2011-2015, he serves on the advisory board of the Neurips foundation since 2015 and has been program chair and general chair of Neurips in 2013 and 2014 respectively. He was also program chair of AISTATS in 2009 and ECCV in 2016 and general chair and co-founder of MIDL 2018. Max Welling is recipient of the ECCV Koenderink Prize in 2010 and the ICML Test of Time award in 2021.
Monday October 23rd, 16:00
Room 705, DIMA, Via Dodecaneso 35