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Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sums

16 April 2021

Papers citing "Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sums"

27 / 27 papers shown

Title
Neural Networks and (Virtual) Extended Formulations Christoph Hertrich Georg Loho 115 3 0 05 Nov 2024
When Deep Learning Meets Polyhedral Theory: A Survey Joey Huchette Gonzalo Muñoz Thiago Serra Calvin Tsay AI4CE 154 37 0 29 Apr 2023
Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks Cristian Bodnar Fabrizio Frasca Yu Guang Wang N. Otter Guido Montúfar Pietro Lio M. Bronstein 109 257 0 04 Mar 2021
Tight Bounds on the Smallest Eigenvalue of the Neural Tangent Kernel for Deep ReLU Networks Quynh N. Nguyen Marco Mondelli Guido Montúfar 76 83 0 21 Dec 2020
On the Number of Linear Regions of Convolutional Neural Networks Huan Xiong Lei Huang Mengyang Yu Li Liu Fan Zhu Ling Shao MLT 61 68 0 01 Jun 2020
Empirical Studies on the Properties of Linear Regions in Deep Neural Networks Xiao Zhang Dongrui Wu 50 38 0 04 Jan 2020
Deep ReLU Networks Have Surprisingly Few Activation Patterns Boris Hanin David Rolnick 90 228 0 03 Jun 2019
The Geometry of Deep Networks: Power Diagram Subdivision Randall Balestriero Romain Cosentino B. Aazhang Richard Baraniuk AI4CE 57 64 0 21 May 2019
A Sober Look at Neural Network Initializations Ingo Steinwart 36 9 0 27 Mar 2019
Complexity of Linear Regions in Deep Networks Boris Hanin David Rolnick 49 234 0 25 Jan 2019
Empirical Bounds on Linear Regions of Deep Rectifier Networks Thiago Serra Srikumar Ramalingam 65 42 0 08 Oct 2018
A Framework for the construction of upper bounds on the number of affine linear regions of ReLU feed-forward neural networks Peter Hinz Sara van de Geer 61 23 0 05 Jun 2018
A Tropical Approach to Neural Networks with Piecewise Linear Activations Vasileios Charisopoulos Petros Maragos 60 40 0 22 May 2018
Tropical Geometry of Deep Neural Networks Liwen Zhang Gregory Naitzat Lek-Heng Lim 87 140 0 18 May 2018
How to Start Training: The Effect of Initialization and Architecture Boris Hanin David Rolnick 91 256 0 05 Mar 2018
Bounding and Counting Linear Regions of Deep Neural Networks Thiago Serra Christian Tjandraatmadja Srikumar Ramalingam MLT 67 251 0 06 Nov 2017
Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks Peter L. Bartlett Nick Harvey Christopher Liaw Abbas Mehrabian 213 434 0 08 Mar 2017
Understanding Deep Neural Networks with Rectified Linear Units R. Arora A. Basu Poorya Mianjy Anirbit Mukherjee PINN 164 643 0 04 Nov 2016
Error bounds for approximations with deep ReLU networks Dmitry Yarotsky 198 1,236 0 03 Oct 2016
On the Expressive Power of Deep Neural Networks M. Raghu Ben Poole Jon M. Kleinberg Surya Ganguli Jascha Narain Sohl-Dickstein 84 791 0 16 Jun 2016
Benefits of depth in neural networks Matus Telgarsky 380 609 0 14 Feb 2016
The Power of Depth for Feedforward Neural Networks Ronen Eldan Ohad Shamir 228 732 0 12 Dec 2015
Representation Benefits of Deep Feedforward Networks Matus Telgarsky 86 242 0 27 Sep 2015
Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification Kaiming He Xinming Zhang Shaoqing Ren Jian Sun VLM 350 18,654 0 06 Feb 2015
On the Number of Linear Regions of Deep Neural Networks Guido Montúfar Razvan Pascanu Kyunghyun Cho Yoshua Bengio 96 1,256 0 08 Feb 2014
On the number of response regions of deep feed forward networks with piece-wise linear activations Razvan Pascanu Guido Montúfar Yoshua Bengio FAtt 124 257 0 20 Dec 2013
Maxout Networks Ian Goodfellow David Warde-Farley M. Berk Mirza Aaron Courville Yoshua Bengio OOD 264 2,179 0 18 Feb 2013