Mean-field Langevin dynamics and energy landscape of neural networks
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Publication:2077356
DOI10.1214/20-AIHP1140zbMath1492.65023arXiv1905.07769MaRDI QIDQ2077356
Zhenjie Ren, David Šiška, Kaitong Hu, Lukasz Szpruch
Publication date: 25 February 2022
Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.07769
Applications of stochastic analysis (to PDEs, etc.) (60H30) Numerical solutions to stochastic differential and integral equations (65C30) PDEs in connection with mean field game theory (35Q89)
Related Items (9)
Unbiased Deep Solvers for Linear Parametric PDEs ⋮ Exponential entropy dissipation for weakly self-consistent Vlasov-Fokker-Planck equations ⋮ Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics ⋮ Stochastic gradient descent with noise of machine learning type. II: Continuous time analysis ⋮ Polyak-Łojasiewicz inequality on the space of measures and convergence of mean-field birth-death processes ⋮ Mean Field Analysis of Neural Networks: A Law of Large Numbers ⋮ Well-posedness and numerical schemes for one-dimensional McKean-Vlasov equations and interacting particle systems with discontinuous drift ⋮ Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: A stochastic control approach ⋮ A trajectorial approach to relative entropy dissipation of McKean-Vlasov diffusions: gradient flows and HWBI inequalities
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