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An inertial Newton algorithm for deep learning
Castera C., Bolte J., Févotte C., and Pauwels E. (2019) · 1905
Earlier work this paper cites.
A stochastic approximation method
Robbins H. and Monro, S. (1951) · 1951
Earlier work this paper cites.
Fonctionnelles sous-différentiables, Séminaire Jean Leray
Moreau J.-J. (1963) · 1963
Earlier work this paper cites.
Convex functions and dual extremum problems
Rockafellar R. T. (1963) · 1963
Earlier work this paper cites.
On the maximal monotonicity of subdifferential mappings
Rockafellar R. (1970) · 1970
Earlier work this paper cites.
Analysis of recursive stochastic algorithms
Ljung L. (1977) · 1977
Earlier work this paper cites.
Compiling fast partial derivatives of functions given by algorithms (No. COO-2383-0063; UILU-ENG-80-1702; UIUCDCS-R-80-1002)
Speelpenning, B. (1980) · 1980
Earlier work this paper cites.
Nonsmooth analysis: differential calculus of nondifferentiable mappings
Ioffe A. D. (1981) · 1981
Earlier work this paper cites.
Optimization and nonsmooth analysis
Clarke F. H. (1983) · 1983
Earlier work this paper cites.
Differential inclusions: set-valued maps and viability theory (Vol. 264). Springer
Aubin, J. P., and Cellina, A. (1984) · 1984
Earlier work this paper cites.
Learning representations by back-propagating errors
Rumelhart E., Hinton E., and Williams J. (1986) · 1986
Earlier work this paper cites.
Tangentially continuous directional derivatives in nonsmooth analysis
Correa R. and Jofre, A. (1989) · 1989
Earlier work this paper cites.
Comptes rendus de l’Académie des Sciences, 308, 241-244
Valadier, M. (1989). Entraînement unilatéral, lignes de descente, fonctions lipschitziennes non pathologiques · 1989
Earlier work this paper cites.
Integration of subdifferentials of lower semicontinuous functions on Banach spaces
Thibault, L. and Zagrodny, D. (1995) · 1995
Earlier work this paper cites.
Pathological Lipschitz functions in ℝ n \mathbb{R}^{n}
Wang X. (1995) · 1995
Earlier work this paper cites.
Geometric categories and o-minimal structures
van den Dries L. and Miller C. (1996) · 1996
Earlier work this paper cites.
Essentially smooth Lipschitz functions
Borwein J. M. and Moors W. B. (1997) · 1997
Earlier work this paper cites.
A chain rule for essentially smooth Lipschitz functions
Borwein J. M. and Moors, W. B. (1998) · 1998
Earlier work this paper cites.
On gradients of functions definable in o-minimal structures
Kurdyka, K. (1998) · 1998
Earlier work this paper cites.
Variational analysis
Rockafellar, R. T., and Wets, R. J. B. (1998) · 1998
Cited alongside, same era.
Dynamics of stochastic approximation algorithms
Benaïm, M. (1999) · 1999
Cited alongside, same era.
RAAG notes, Institut de Recherche Mathématique de Rennes, 81 pages, November 1999
Coste M., An introduction to o-minimal geometry · 1999
Cited alongside, same era.
The heavy ball with friction method, I. The continuous dynamical system: global exploration of the local minima of a real-valued function by asymptotic analysis of a dissipative dynamical system
Attouch H., Goudou X. and Redont P. (2000) · 2000
Cited alongside, same era.
Proof of the gradient conjecture of R. Thom
Kurdyka, K., Mostowski, T. and Parusinski, A. (2000) · 2000
Cited alongside, same era.
Generalized subdifferentials: a Baire categorical approach
Borwein, J., Moors, W. and Wang, X. (2001) · 2001
Deep sparse rectifier neural networks
Glorot X., Bordes A. and Bengio Y. (2011) · 2011
Later among the works it cites.
Non-asymptotic analysis of stochastic approximation algorithms for machine learning
Moulines E. and Bach, F. (2011) · 2011
Later among the works it cites.
On stable piecewise linearization and generalized algorithmic differentiation
Griewank A. (2013) · 2013
Later among the works it cites.
Bolte J., Sabach S., and Teboulle M. (2014). Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Mathematical Programming, 146(1-2), 459-494
2014
Later among the works it cites.
Measure theory and fine properties of functions
Evans, L. C. and Gariepy, R. F. (2015) · 2015
Later among the works it cites.
Deep learning
Le Cun Y., Bengio Y., and Hinton, G. (2015) · 2015
alphaXiv searches the wider corpus for related work and actual follow-ups.
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Cited alongside, same era.
Automatic differentiation of algorithms: from simulation to optimization
Corliss G., Faure C., Griewank A., Hascoet L. and Naumann U. (Editors) (2002) · 2002
Cited alongside, same era.
Stochastic approximation and recursive algorithms and applications (Vol. 35)
Kushner H. and Yin, G. G. (2003) · 2003
Cited alongside, same era.
Infinite Dimensional Analysis (3rd edition)
Aliprantis C.D., and Border K.C. (2005) · 2005
Cited alongside, same era.
Stochastic approximations and differential inclusions
Benaïm, M., Hofbauer, J., and Sorin, S. (2005) · 2005
Cited alongside, same era.
Integrability of subdifferentials of directionally Lipschitz functions
Thibault, L. and Zlateva, N. (2005) · 2005
Cited alongside, same era.
Variational analysis and generalized differentiation I: Basic theory
Mordukhovich B. S. (2006) · 2006
Cited alongside, same era.
Later among the works it cites.
Tensorflow: A system for large-scale machine learning
Abadi M., Barham P., Chen J., Chen Z., Davis A., Dean J., Devin M., Ghemawat S., Irving G., Isard M., Kudlur M., Levenberg J., Monga R., Moore S., Murray D., Steiner B., Tucker P., Vasudevan V., Warden P., Wicke M., Yu Y. and Zheng X. (2016) · 2016
Later among the works it cites.
On Lipschitz optimization based on gray-box piecewise linearization
Griewank A., Walther A., Fiege S. and Bosse T. (2016) · 2016
Later among the works it cites.
Ioffe, A. D. (2017). Variational analysis of regular mappings. Springer Monographs in Mathematics. Springer, Cham
2017
Later among the works it cites.
Automatic differentiation in Pytorch
Paszke A., Gross S., Chintala S., Chanan G., Yang E., DeVito Z., Lin Z., Desmaison A., Antiga L. and Lerer A. (2017) · 2017
Later among the works it cites.
Opérateurs monotones aléatoires et application à l’optimisation stochastique
Adil, S. (2018) · 2018
Later among the works it cites.
Convergence and Dynamical Behavior of the Adam Algorithm for Non Convex Stochastic Optimization
Barakat, A., and Bianchi, P. (2018) · 2018
Later among the works it cites.
Automatic differentiation in machine learning: a survey
Baydin A., Pearlmutter B., Radul A. and Siskind J. (2018) · 2018
Later among the works it cites.
Optimization methods for large-scale machine learning
Bottou L., Curtis F. E. and Nocedal J. (2018) · 2018
Later among the works it cites.
Chizat, L., and Bach, F. (2018). On the global convergence of gradient descent for over-parameterized models using optimal transport. In Advances in neural information processing systems, 3036-3046
2018
Later among the works it cites.
Provably correct automatic sub-differentiation for qualified programs
Kakade, S. M. and Lee, J. D. (2018) · 2018
Later among the works it cites.
Analysis of nonsmooth stochastic approximation: the differential inclusion approach
Majewski, S., Miasojedow, B. and Moulines, E. (2018) · 2018
Later among the works it cites.
Constant step stochastic approximations involving differential inclusions: Stability, long-run convergence and applications
Bianchi, P., Hachem, W., and Salim, A. (2019) · 2019
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Stochastic subgradient method converges on tame functions, 20(1), 119-154
Davis, D., Drusvyatskiy, D., Kakade, S., and Lee, J. D. (2020) · 2020
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