Fetching the paper…
Reading the bibliography…
As an example of the nonlinear Fokker-Planck equation, the mean field Langevin dynamics recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide neural networks in the mean field regime, and hence the convergence property of the dynamics is of great theoretical interest.
Analysis of a two-layer neural network via displacement convexity
Javanmard, A., Mondelli, M., and Montanari, A. (2019) · 1901
Earlier work this paper cites.
Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit
Mei, S., Misiakiewicz, T., and Montanari, A. (2019) · 1902
Earlier work this paper cites.
Mean-field langevin dynamics and energy landscape of neural networks
Hu, K., Ren, Z., Siska, D., and Szpruch, L. (2019) · 1905
Earlier work this paper cites.
Guillin, A., Liu, W., Wu, L., and Zhang, C. (2019) · 1909
Earlier work this paper cites.
Mean-field neural odes via relaxed optimal control
Jabir, J.-F., Šiška, D., and Szpruch, Ł. (2019) · 1912
Earlier work this paper cites.
Convex Analysis
Rockafellar, R. T. (1970) · 1970
Earlier work this paper cites.
Diffusions hypercontractives in sem. probab. xix lnm 1123
Bakry, D. and Émery, M. (1985) · 1985
Earlier work this paper cites.
Logarithmic sobolev inequalities and stochastic ising models
Holley, R. and Stroock, D. (1987) · 1987
Earlier work this paper cites.
Sample estimate of the entropy of a random vector
Kozachenko, L. and Leonenko, N. N. (1987) · 1987
Earlier work this paper cites.
The variational formulation of the fokker–planck equation
Jordan, R., Kinderlehrer, D., and Otto, F. (1998) · 1998
Earlier work this paper cites.
A generalized neural tangent kernel analysis for two-layer neural networks
Chen, Z., Cao, Y., Gu, Q., and Zhang, T. (2020a) · 2002
Earlier work this paper cites.
On the convergence of langevin monte carlo: The interplay between tail growth and smoothness
Erdogdu, M. A. and Hosseinzadeh, R. (2020) · 2005
Earlier work this paper cites.
Ergodicity of the underdamped mean-field langevin dynamics
Kazeykina, A., Ren, Z., Tan, X., and Yang, J. (2020) · 2007
Earlier work this paper cites.
A dynamical central limit theorem for shallow neural networks
Chen, Z., Rotskoff, G. M., Bruna, J., and Vanden-Eijnden, E. (2020b) · 2008
Earlier work this paper cites.
Convergence of unadjusted hamiltonian monte carlo for mean-field models
Bou-Rabee, N. and Schuh, K. (2020) · 2009
Earlier work this paper cites.
Hypocoercivity
Villani, C. (2009) · 2009
Earlier work this paper cites.
Convex analysis and monotone operator theory in Hilbert spaces
Bauschke, H. H., Combettes, P. L., et al. (2011) · 2011
Cited alongside, same era.
Analysis and geometry of Markov diffusion operators
Bakry, D., Gentil, I., and Ledoux, M. (2013) · 2013
Cited alongside, same era.
Stochastic numerics for mathematical physics
Milstein, G. N. and Tretyakov, M. V. (2013) · 2013
Cited alongside, same era.
Theoretical guarantees for approximate sampling from smooth and log-concave densities
Dalalyan, A. S. (2014) · 2014
Cited alongside, same era.
Poincaré and logarithmic sobolev inequalities by decomposition of the energy landscape
Menz, G. and Schlichting, A. (2014) · 2014
Cited alongside, same era.
Stochastic runge-kutta accelerates langevin monte carlo and beyond
Li, X., Wu, Y., Mackey, L., and Erdogdu, M. A. (2019) · 2019
Later among the works it cites.
Global convergence of neuron birth-death dynamics
Rotskoff, G. M., Jelassi, S., Bruna, J., and Vanden-Eijnden, E. (2019) · 2019
Later among the works it cites.
Adaptivity of deep relu network for learning in besov and mixed smooth besov spaces: optimal rate and curse of dimensionality
Suzuki, T. (2019) · 2019
Later among the works it cites.
Rapid convergence of the unadjusted langevin algorithm: Isoperimetry suffices
Vempala, S. and Wibisono, A. (2019) · 2019
Later among the works it cites.
Regularization matters: Generalization and optimization of neural nets vs their induced kernel
Wei, C., Lee, J. D., Liu, Q., and Ma, T. (2019) · 2019
Later among the works it cites.
Mean field analysis of neural networks: A central limit theorem
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Dalalyan, A. S. (2017) · 2017
Cited alongside, same era.
Nonasymptotic convergence analysis for the unadjusted langevin algorithm
Durmus, A. and Moulines, E. (2017) · 2017
Cited alongside, same era.
Long-time behaviour and propagation of chaos for mean field kinetic particles
Monmarché, P. (2017) · 2017
Cited alongside, same era.
Stochastic particle gradient descent for infinite ensembles
Nitanda, A. and Suzuki, T. (2017) · 2017
Cited alongside, same era.
Stability and generalization of learning algorithms that converge to global optima
Charles, Z. and Papailiopoulos, D. (2018) · 2018
Cited alongside, same era.
On the global convergence of gradient descent for over-parameterized models using optimal transport
Chizat, L. and Bach, F. (2018) · 2018
Cited alongside, same era.
Neural tangent kernel: Convergence and generalization in neural networks
Jacot, A., Gabriel, F., and Hongler, C. (2018) · 2018
Cited alongside, same era.
Sirignano, J. and Spiliopoulos, K. (2020) · 2020
Later among the works it cites.
Mirror descent algorithms for minimizing interacting free energy
Ying, L. (2020) · 2020
Later among the works it cites.
On learnability via gradient method for two-layer relu neural networks in teacher-student setting
Akiyama, S. and Suzuki, T. (2021) · 2021
Later among the works it cites.
Mixing time guarantees for unadjusted hamiltonian monte carlo
Bou-Rabee, N. and Eberle, A. (2021) · 2021
Later among the works it cites.
Convergence of langevin monte carlo in chi-squared and rényi divergence
Erdogdu, M. A., Hosseinzadeh, R., and Zhang, M. S. (2021) · 2021
Later among the works it cites.
The kinetic fokker-planck equation with mean field interaction
Guillin, A., Liu, W., Wu, L., and Zhang, C. (2021) · 2021
Later among the works it cites.
Frank-wolfe methods in probability space
Kent, C., Blanchet, J., and Glynn, P. (2021) · 2021
Later among the works it cites.
Particle dual averaging: Optimization of mean field neural networks with global convergence rate analysis
Nitanda, A., Wu, D., and Suzuki, T. (2021) · 2021
Later among the works it cites.
Mean-field langevin dynamics: Exponential convergence and annealing
Chizat, L. (2022) · 2022
Closest in time.
Particle stochastic dual coordinate ascent: Exponential convergent algorithm for mean field neural network optimization
Oko, K., Suzuki, T., Nitanda, A., and Wu, D. (2022) · 2022
Closest in time.
Sampling as optimization in the space of measures: The langevin dynamics as a composite optimization problem
Wibisono, A. (2018) · 2093
Closest in time.