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In this paper, we prove a conjecture published in 1989 and also partially address an open problem announced at the Conference on Learning Theory (COLT) 2015.
Some NP-complete problems in quadratic and nonlinear programming
Murty, Katta G, & Kabadi, Santosh N. 1987 · 1987
Earlier work this paper cites.
Linear learning: Landscapes and algorithms
Baldi, Pierre. 1989 · 1989
Earlier work this paper cites.
Neural networks and principal component analysis: Learning from examples without local minima
Baldi, Pierre, & Hornik, Kurt. 1989 · 1989
Earlier work this paper cites.
Training a 3-node neural network is NP-complete
Blum, Avrim L, & Rivest, Ronald L. 1992 · 1992
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The Schur complement and its applications
Zhang, Fuzhen. 2006 · 2006
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Variational analysis
Rockafellar, R Tyrrell, & Wets, Roger J-B. 2009 · 2009
Cited alongside, same era.
Complex-valued autoencoders
Baldi, Pierre, & Lu, Zhiqin. 2012 · 2012
Cited alongside, same era.
Identifying and attacking the saddle point problem in high-dimensional non-convex optimization
Dauphin, Yann N, Pascanu, Razvan, Gulcehre, Caglar, Cho, Kyunghyun, Ganguli, Surya, & Bengio, Yoshua. 2014 · 2014
Cited alongside, same era.
On the computational efficiency of training neural networks
Livni, Roi, Shalev-Shwartz, Shai, & Shamir, Ohad. 2014 · 2014
Cited alongside, same era.
The Loss Surfaces of Multilayer Networks
Choromanska, Anna, Henaff, MIkael, Mathieu, Michael, Ben Arous, Gerard, & LeCun, Yann. 2015a
Cited in the paper.
Open Problem: The landscape of the loss surfaces of multilayer networks
Choromanska, Anna, LeCun, Yann, & Arous, Gérard Ben. 2015b
Cited in the paper.
Exact solutions to the nonlinear dynamics of learning in deep linear neural networks
Saxe, Andrew M, McClelland, James L, & Ganguli, Surya. 2014 · 2014
Later among the works it cites.
Escaping From Saddle Points—Online Stochastic Gradient for Tensor Decomposition
Ge, Rong, Huang, Furong, Jin, Chi, & Yuan, Yang. 2015 · 2015
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Deep Learning
Goodfellow, Ian, Bengio, Yoshua, & Courville, Aaron. 2016 · 2016
Closest in time.
Learning Real and Boolean Functions: When Is Deep Better Than Shallow
Mhaskar, Hrushikesh, Liao, Qianli, & Poggio, Tomaso. 2016 · 2016
Closest in time.
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