Fetching the paper…
Reading the bibliography…
We algorithmically determine the regions and facets of all dimensions of the canonical polyhedral complex, the universal object into which a ReLU network decomposes its input space.
J. Elisenda Grigsby and Kathryn Lindsey · 2008
Earlier work this paper cites.
Rectified linear units improve restricted boltzmann machines
Vinod Nair and Geoffrey E. Hinton · 2010
Earlier work this paper cites.
On the number of linear regions of deep neural networks
Guido F Montufar, Razvan Pascanu, Kyunghyun Cho, and Yoshua Bengio · 2014
Earlier work this paper cites.
On the complexity of neural network classifiers: A comparison between shallow and deep architectures
Monica Bianchini and Franco Scarselli · 2014
Earlier work this paper cites.
Elementary applied topology
Robert Ghrist · 2014
Earlier work this paper cites.
Topics in Hyperplane Arrangements
Marcelo Aguiar and Swapneel Mahajan · 2017
Earlier work this paper cites.
Piecewise Linear Morse Theory
Romain Grunert · 2017
Earlier work this paper cites.
Bounding and counting linear regions of deep neural networks
Thiago Serra, Christian Tjandraatmadja, and Srikumar Ramalingam · 2018
Earlier work this paper cites.
On characterizing the capacity of neural networks using algebraic topology
William H. Guss and Ruslan Salakhutdinov · 2018
Cited alongside, same era.
Tropical geometry of deep neural networks
Liwen Zhang, Gregory Naitzat, and Lek-Heng Lim · 2018
Cited alongside, same era.
SageMath, the Sage Mathematics Software System (Version 9.0)
The Sage Developers · 2018
Cited alongside, same era.
Empirical study of the topology and geometry of deep networks
Alhussein Fawzi, Seyed-Mohsen Moosavi-Dezfooli, Pascal Frossard, and Stefano Soatto · 2018
Cited alongside, same era.
Deep relu networks have surprisingly few activation patterns
Boris Hanin and David Rolnick · 2019
Cited alongside, same era.
Analysis of Combinatorial Neural Codes: An Algebraic Approach
Carina Curto, Alan Veliz-Cuba, and Nora Youngs · 2019
Later among the works it cites.
Pytorch: An imperative style, high-performance deep learning library
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala · 2019
Later among the works it cites.
Hyperplane neural codes and the polar complex
Vladimir Itskov, Alexander Kunin, and Zvi Rosen · 2020
Later among the works it cites.
Empirical studies on the properties of linear regions in deep neural networks
Xiao Zhang and Dongrui Wu · 2020
Later among the works it cites.
On the decision boundaries of deep neural networks: A tropical geometry perspective
Motasem Alfarra, Adel Bibi, Hasan Hammoud, Mohamed Gaafar, and Bernard Ghanem · 2020
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Boris Hanin and David Rolnick · 2019
Cited alongside, same era.
The geometry of deep networks: Power diagram subdivision
Randall Balestriero, Romain Cosentino, Behnaam Aazhang, and Richard Baraniuk · 2019
Cited alongside, same era.
Finding the homology of decision boundaries with active learning
Weizhi Li, Gautam Dasarathy, Karthikeyan Natesan Ramamurthy, and Visar Berisha · 2020
Later among the works it cites.
Local and global topological complexity measures of relu neural network functions, 2022
J. Elisenda Grigsby, Kathryn Lindsey, and Marissa Masden · 2022
Closest in time.