Fetching the paper…
Reading the bibliography…
Recent work linking deep neural networks and dynamical systems opened up new avenues to analyze deep learning.
The theory of optimal processes. I. The maximum principle
Vladimir G Boltyanskii, Revaz V Gamkrelidze, and Lev S Pontryagin · 1960
Earlier work this paper cites.
Applied optimal control: optimization, estimation and control
Arthur Earl Bryson · 1975
Earlier work this paper cites.
Approximation methods for nonlinear problems with application to two-point boundary value problems
HB Keller · 1975
Earlier work this paper cites.
Optimization of functions on certain subsets of banach spaces
Charles Stegall · 1978
Earlier work this paper cites.
Viscosity solutions of hamilton-Jacobi equations
Michael G Crandall and Pierre-Louis Lions · 1983
Earlier work this paper cites.
Hamilton-Jacobi equations in infinite dimensions I. Uniqueness of viscosity solutions
Michael G Crandall and Pierre-Louis Lions · 1985
Earlier work this paper cites.
Hamilton-Jacobi equations in infinite dimensions. II. Existence of viscosity solutions
Michael G Crandall and Pierre-Louis Lions · 1986
Earlier work this paper cites.
Hamilton-Jacobi equations in infinite dimensions, III
Michael G Crandall and Pierre-Louis Lions · 1986
Earlier work this paper cites.
Remarks on inequalities for large deviation probabilities
IF Pinelis and AI Sakhanenko · 1986
Earlier work this paper cites.
Mathematical theory of optimal processes
Lev S Pontryagin · 1987
Earlier work this paper cites.
A theoretical framework for back-propagation
Yann LeCun · 1988
Earlier work this paper cites.
Topics in propagation of chaos
Alain-Sol Sznitman · 1991
Earlier work this paper cites.
Partial differential equations
Lawrence C. Evans · 1998
Earlier work this paper cites.
The elements of statistical learning
Jerome Friedman, Trevor Hastie, and Robert Tibshirani · 2001
Earlier work this paper cites.
Large population stochastic dynamic games: closed-loop Mckean-Vlasov systems and the Nash certainty equivalence principle
Minyi Huang, Roland P Malhamé, and Peter E Caines · 2006
Earlier work this paper cites.
One-shot learning of object categories
Fei-Fei Li, Rob Fergus, and Pietro Perona · 2006
Earlier work this paper cites.
Mean field games
Jean-Michel Lasry and Pierre-Louis Lions · 2007
Earlier work this paper cites.
Introduction to the mathematical theory of control
Alberto Bressan and Benedetto Piccoli · 2007
Earlier work this paper cites.
Learning deep architectures for AI
Yoshua Bengio · 2009
Earlier work this paper cites.
Notes on mean field games
Pierre Cardaliaguet · 2010
Cited alongside, same era.
A survey on transfer learning
Sinno Jialin Pan and Qiang Yang · 2010
Cited alongside, same era.
The theory of differential equations: classical and qualitative
Walter G Kelley and Allan C Peterson · 2010
Cited alongside, same era.
Mean field games and applications
Olivier Guéant, Jean-Michel Lasry, and Pierre-Louis Lions · 2011
Cited alongside, same era.
A maximum principle for SDEs of mean-field type
Daniel Andersson and Boualem Djehiche · 2011
Cited alongside, same era.
A general stochastic maximum principle for SDEs of mean-field type
Rainer Buckdahn, Boualem Djehiche, and Juan Li · 2011
Cited alongside, same era.
Deep learning
Ian Goodfellow, Yoshua Bengio, and Aaron Courville · 2016
Later among the works it cites.
Deep residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
Later among the works it cites.
A proposal on machine learning via dynamical systems
Weinan E · 2017
Later among the works it cites.
Stable architectures for deep neural networks
Eldad Haber and Lars Ruthotto · 2017
Later among the works it cites.
Reversible architectures for arbitrarily deep residual neural networks
Bo Chang, Lili Meng, Eldad Haber, Lars Ruthotto, David Begert, and Elliot Holtham · 2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Xavier Glorot, Antoine Bordes, and Yoshua Bengio · 2011
Cited alongside, same era.
Cours au collège de france: Théorie des jeuxa champs moyens, 2012
Pierre-Louis Lions · 2012
Cited alongside, same era.
Calculus of variations and optimal control theory: a concise introduction
Daniel Liberzon · 2012
Cited alongside, same era.
Dynamic programming
Richard Bellman · 2013
Cited alongside, same era.
Optimal control: an introduction to the theory and its applications
Michael Athans and Peter L Falb · 2013
Cited alongside, same era.
Mean field games and mean field type control theory
Alain Bensoussan, Jens Frehse, and Phillip Yam · 2013
Cited alongside, same era.
Yiping Lu, Aoxiao Zhong, Quanzheng Li, and Bin Dong · 2017
Later among the works it cites.
Double continuum limit of deep neural networks
Sho Sonoda and Noboru Murata · 2017
Later among the works it cites.
Deep residual learning and PDEs on manifold
Zhen Li and Zuoqiang Shi · 2017
Later among the works it cites.
Dynamic programming for optimal control of stochastic Mckean–Vlasov dynamics
Huyên Pham and Xiaoli Wei · 2017
Later among the works it cites.
Mean-field pontryagin maximum principle
Mattia Bongini, Massimo Fornasier, Francesco Rossi, and Francesco Solombrino · 2017
Later among the works it cites.
Exploring generalization in deep learning
Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, and Nati Srebro · 2017
Later among the works it cites.
Gintare Karolina Dziugaite and Daniel M Roy · 2017
Later among the works it cites.
Maximum principle based algorithms for deep learning
Qianxiao Li, Long Chen, Cheng Tai, and Weinan E · 2018
Closest in time.
An optimal control approach to deep learning and applications to discrete-weight neural networks
Qianxiao Li and Shuji Hao · 2018
Closest in time.
Multi-level residual networks from dynamical systems view
Bo Chang, Lili Meng, Eldad Haber, Frederick Tung, and David Begert · 2018
Closest in time.
Neural ordinary differential equations
Tian Qi Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud · 2018
Closest in time.
Bellman equation and viscosity solutions for mean-field stochastic control problem
Huyên Pham and Xiaoli Wei · 2018
Closest in time.
Stronger generalization bounds for deep nets via a compression approach
Sanjeev Arora, Rong Ge, Behnam Neyshabur, and Yi Zhang · 2018
Closest in time.