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Poster
in
Workshop: Physics for Machine Learning

Learning Deformation Trajectories of Boltzmann Densities

Bálint Máté · François Fleuret


Abstract: We introduce a training objective for continuous normalizing flows that can be used in the absence of samples but in the presence of an energy function. Our method relies on either a prescribed or a learnt interpolation ft of energy functions between the target energy f1 and the energy function of a generalized Gaussian f0(x)=||x/σ||pp. The interpolation of energy functions induces an interpolation of Boltzmann densities pteft and we aim to find a time-dependent vector field Vt that transports samples along the family pt of densities. The condition of transporting samples along the family pt can be translated to a PDE between Vt and ft and we optimize Vt and ft to satisfy this PDE.

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