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The expressivity of neural networks as a function of their depth, width and type of activation units has been an important question in deep learning theory.
Coexistence of the cycles of a continuous mapping of the line into itself
OM Sharkovsky · 1964
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On cycles and structure of continuous mapping
OM Sharkovsky · 1965
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Period three implies chaos
Tien-Yien Li and James A Yorke · 1975
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Almost optimal lower bounds for small depth circuits
John Hastad · 1986
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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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Combinatorial dynamics and entropy in dimension one
Lluís Alsedà, Jaume Llibre, and Michał Misiurewicz · 2000
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Lower bounds on the complexity of approximating continuous functions by sigmoidal neural networks
Michael Schmitt · 2000
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On the number of linear regions of deep neural networks
Guido F Montufar, Razvan Pascanu, Kyunghyun Cho, and Yoshua Bengio · 2014
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Representation benefits of deep feedforward networks
Matus Telgarsky · 2015
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Understanding deep neural networks with rectified linear units
Raman Arora, Amitabh Basu, Poorya Mianjy, and Anirbit Mukherjee · 2016
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The power of depth for feedforward neural networks
Ronen Eldan and Ohad Shamir · 2016
Cited alongside, same era.
Benefits of depth in neural networks
Matus Telgarsky · 2016
Later among the works it cites.
On the expressive power of deep neural networks
Maithra Raghu, Ben Poole, Jon Kleinberg, Surya Ganguli, and Jascha Sohl Dickstein · 2017
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Deep relu networks have surprisingly few activation patterns
Boris Hanin and David Rolnick · 2019
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On the expressive power of deep polynomial neural networks
Joe Kileel, Matthew Trager, and Joan Bruna · 2019
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Is deeper better only when shallow is good?
Eran Malach and Shai Shalev-Shwartz · 2019
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Super-linear gate and super-quadratic wire lower bounds for depth-two and depth-three threshold circuits
Daniel M Kane and Ryan Williams · 2016
Cited alongside, same era.
Exponential expressivity in deep neural networks through transient chaos
Ben Poole, Subhaneil Lahiri, Maithra Raghu, Jascha Sohl-Dickstein, and Surya Ganguli · 2016
Cited alongside, same era.
Depth-width trade-offs for relu networks via sharkovsky’s theorem
Vaggos Chatziafratis, Sai Ganesh Nagarajan, Ioannis Panageas, and Xiao Wang · 2020
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