Mean Field Analysis of Neural Networks: A Law of Large Numbers
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Publication:5219306
DOI10.1137/18M1192184zbMath1440.60008arXiv1805.01053OpenAlexW3010825589WikidataQ114847156 ScholiaQ114847156MaRDI QIDQ5219306
Justin A. Sirignano, Konstantinos V. Spiliopoulos
Publication date: 11 March 2020
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.01053
Computational methods for problems pertaining to probability theory (60-08) Strong limit theorems (60F15) Neural nets and related approaches to inference from stochastic processes (62M45)
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Uses Software
Cites Work
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- Machine learning strategies for systems with invariance properties
- Heterogeneous credit portfolios and the dynamics of the aggregate losses
- Large portfolio losses: A dynamic contagion model
- Approximation and estimation bounds for artificial neural networks
- McKean-Vlasov limit for interacting random processes in random media.
- A stochastic McKean-Vlasov equation for absorbing diffusions on the half-line
- Multilayer feedforward networks are universal approximators
- Large deviations and mean-field theory for asymmetric random recurrent neural networks
- Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
- Default clustering in large portfolios: typical events
- DGM: a deep learning algorithm for solving partial differential equations
- Mean-field Langevin dynamics and energy landscape of neural networks
- Mean field analysis of neural networks: a central limit theorem
- Particle systems with a singular mean-field self-excitation. Application to neuronal networks
- Mean-Field Limit of a Stochastic Particle System Smoothly Interacting Through Threshold Hitting-Times and Applications to Neural Networks with Dendritic Component
- The Variational Formulation of the Fokker--Planck Equation
- A mean field view of the landscape of two-layer neural networks
- LARGE PORTFOLIO ASYMPTOTICS FOR LOSS FROM DEFAULT
- Universal features of price formation in financial markets: perspectives from deep learning
- Systemic Risk in Interbanking Networks
- Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
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