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Found 5 papers, 0 papers with code
Variational Principles for Mirror Descent and Mirror Langevin Dynamics
Mirror descent, introduced by Nemirovski and Yudin in the 1970s, is a primal-dual convex optimization method that can be tailored to the geometry of the optimization problem at hand through the choice of a strongly convex potential function.
A mean-field theory of lazy training in two-layer neural nets: entropic regularization and controlled McKean-Vlasov dynamics
We first consider the mean-field limit, where the finite population of neurons in the hidden layer is replaced by a continual ensemble, and show that our problem can be phrased as global minimization of a free-energy functional on the space of probability measures over the weights.
Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit
In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small independent Gaussian perturbation.
Theoretical guarantees for sampling and inference in generative models with latent diffusions
We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the diffusion.
Local Optimality and Generalization Guarantees for the Langevin Algorithm via Empirical Metastability
For a particular local optimum of the empirical risk, with an arbitrary initialization, we show that, with high probability, at least one of the following two events will occur: (1) the Langevin trajectory ends up somewhere outside the $\varepsilon$-neighborhood of this particular optimum within a short recurrence time; (2) it enters this $\varepsilon$-neighborhood by the recurrence time and stays there until a potentially exponentially long escape time.
