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A Dance with the Langevin Equation


In this thesis, we shall discuss the Langevin equation. While the equation is well known in Statistical Physics, we show novel adaptions to the field of Machine Learning. In particular, we elaborate briefly on a recipe in an unsupervised learning scheme. That is, we introduce an irreversible Langevin sampler to accelerate Contrastive Divergence. This adjustment to the Langevin equation, as such, improves the convergence behavior towards the equilibrium by injecting a vector field C(x) satisfying some conditions derived from the Fokker-Planck equation. In particular, C(x) motivates the particles in the negative phase to dance such that convergence of system towards its thermal equilibrium state is accelerated. We illustrate an application in the form of learning a Gaussian-Bernoulli Restricted-Boltzmann machine.

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