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A long standing open problem in the theory of neural networks is the development of quantitative methods to estimate and compare the capabilities of different architectures.
A logical calculus of the ideas immanent in nervous activity
W. McCulloch and W. Pitts · 1943
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The perceptron: A probabilistic model for information storage and organization in the brain
F. Rosenblatt · 1958
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Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition
Thomas M Cover · 1965
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Lower bounds of the number of threshold functions and a maximum weight
Saburo Muroga · 1965
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Partitions of n-space by hyperplanes
RO Winder · 1966
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A back-propagation programmed network that simulates response properties of a subset of posterior parietal neurons
David Zipser and Richard A Andersen · 1988
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Oscillations and synchronizations in neural networks: an exploration of the labeling hypothesis
P. Baldi and A. F. Atiya · 1989
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What size net gives valid generalization?
Eric B Baum and David Haussler · 1989
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Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell Stinchcombe, and Halbert White · 1989
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Asymptotics of the logarithm of the number of threshold functions of the algebra of logic
Yu A Zuev · 1989
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Combinatorial-probability and geometric methods in threshold logic
Yu A Zuev · 1991
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On the probability that a random ± \pm 1-matrix is singular
Jeff Kahn, János Komlós, and Endre Szemerédi · 1995
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Emergence of simple-cell receptive field properties by learning a sparse code for natural images
Bruno A Olshausen and David J Field · 1996
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Almost linear vc dimension bounds for piecewise polynomial networks
Peter L Bartlett, Vitaly Maiorov, and Ron Meir · 1999
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Discrete mathematics of neural networks: selected topics
Martin Anthony · 2001
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Autoencoders, Unsupervised Learning, and Deep Architectures
Using goal-driven deep learning models to understand sensory cortex
Daniel LK Yamins and James J DiCarlo · 2016
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Understanding deep learning requires rethinking generalization
Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2016
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Nearly-tight vc-dimension and pseudodimension bounds for piecewise linear neural networks
Peter L Bartlett, Nick Harvey, Chris Liaw, and Abbas Mehrabian · 2017
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Event-Driven Random Back-Propagation: Enabling Neuromorphic Deep Learning Machines
Emre O. Neftci, Somnath Paul, Charles Augustine, and Georgios Detorakis · 2017
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Mastering the game of go without human knowledge
David Silver, Julian Schrittwieser, Karen Simonyan, Ioannis Antonoglou, Aja Huang, Arthur Guez, Thomas Hubert, Lucas Baker, Matthew Lai, Adrian Bolton, et al · 2017
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High-dimensional probability. An introduction with applications in data science
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Zhanxing Zhu, Jingfeng Wu, Bing Yu, Lei Wu, and Jinwen Ma · 2018
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