Bounding and Counting Linear Regions of Deep Neural Networks

6 November 2017

Thiago Serra

Christian Tjandraatmadja

Srikumar Ramalingam

MLT

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Papers citing "Bounding and Counting Linear Regions of Deep Neural Networks"

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Towards Rigorous Understanding of Neural Networks via Semantics-preserving Transformations Maximilian Schlüter Gerrit Nolte Alnis Murtovi Bernhard Steffen 29 6 0 19 Jan 2023
Getting Away with More Network Pruning: From Sparsity to Geometry and Linear Regions Junyang Cai Khai-Nguyen Nguyen Nishant Shrestha Aidan Good Ruisen Tu Xin Yu Shandian Zhe Thiago Serra MLT 40 7 0 19 Jan 2023
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Non-Linear Coordination Graphs Yipeng Kang Tonghan Wang Xiao-Ren Wu Qianlan Yang Chongjie Zhang 37 9 0 26 Oct 2022
Improved Bounds on Neural Complexity for Representing Piecewise Linear Functions Kuan-Lin Chen H. Garudadri Bhaskar D. Rao 11 19 0 13 Oct 2022
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On the Number of Regions of Piecewise Linear Neural Networks Alexis Goujon Arian Etemadi M. Unser 44 13 0 17 Jun 2022
Lower and Upper Bounds for Numbers of Linear Regions of Graph Convolutional Networks Hao Chen Yu Wang Huan Xiong GNN 16 6 0 01 Jun 2022
On the Feasibility and Generality of Patch-based Adversarial Attacks on Semantic Segmentation Problems Soma Kontár A. Horváth AAML 35 1 0 21 May 2022
$Training Fully Connected Neural Networks is $\exists\mathbb{R}$-Complete$ Training Fully Connected Neural Networks is $\exists\mathbb{R}$ -Complete Daniel Bertschinger Christoph Hertrich Paul Jungeblut Tillmann Miltzow Simon Weber OffRL 61 30 0 04 Apr 2022
The Combinatorial Brain Surgeon: Pruning Weights That Cancel One Another in Neural Networks Xin Yu Thiago Serra Srikumar Ramalingam Shandian Zhe 44 48 0 09 Mar 2022
Training Thinner and Deeper Neural Networks: Jumpstart Regularization Carles Roger Riera Molina Camilo Rey Thiago Serra Eloi Puertas O. Pujol 27 4 0 30 Jan 2022
A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis T. Lew Lucas Janson Riccardo Bonalli Marco Pavone 32 18 0 10 Dec 2021
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Convergence of Deep ReLU Networks Yuesheng Xu Haizhang Zhang 37 27 0 27 Jul 2021
Multifidelity Modeling for Physics-Informed Neural Networks (PINNs) Michael Penwarden Shandian Zhe A. Narayan Robert M. Kirby 29 43 0 25 Jun 2021
Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sums Guido Montúfar Yue Ren Leon Zhang 20 39 0 16 Apr 2021
Fast Jacobian-Vector Product for Deep Networks Randall Balestriero Richard Baraniuk 31 4 0 01 Apr 2021
Tight Bounds on the Smallest Eigenvalue of the Neural Tangent Kernel for Deep ReLU Networks Quynh N. Nguyen Marco Mondelli Guido Montúfar 25 81 0 21 Dec 2020
Certified Monotonic Neural Networks Xingchao Liu Xing Han Na Zhang Qiang Liu 24 79 0 20 Nov 2020
On the Number of Linear Functions Composing Deep Neural Network: Towards a Refined Definition of Neural Networks Complexity Yuuki Takai Akiyoshi Sannai Matthieu Cordonnier 80 4 0 23 Oct 2020
Continual Learning in Low-rank Orthogonal Subspaces Arslan Chaudhry Naeemullah Khan P. Dokania Philip Torr CLL 33 115 0 22 Oct 2020
Influence Functions in Deep Learning Are Fragile S. Basu Phillip E. Pope S. Feizi TDI 37 219 0 25 Jun 2020
The Depth-to-Width Interplay in Self-Attention Yoav Levine Noam Wies Or Sharir Hofit Bata Amnon Shashua 30 45 0 22 Jun 2020
In Proximity of ReLU DNN, PWA Function, and Explicit MPC Saman Fahandezh-Saadi Masayoshi Tomizuka 18 4 0 09 Jun 2020
Provably Good Solutions to the Knapsack Problem via Neural Networks of Bounded Size Christoph Hertrich M. Skutella 50 21 0 28 May 2020
Approximation in shift-invariant spaces with deep ReLU neural networks Yunfei Yang Zhen Li Yang Wang 34 14 0 25 May 2020
An Outer-approximation Guided Optimization Approach for Constrained Neural Network Inverse Problems Myun-Seok Cheon 8 5 0 24 Feb 2020
Empirical Studies on the Properties of Linear Regions in Deep Neural Networks Xiao Zhang Dongrui Wu 21 38 0 04 Jan 2020
Lossless Compression of Deep Neural Networks Thiago Serra Abhinav Kumar Srikumar Ramalingam 24 56 0 01 Jan 2020
Is Deeper Better only when Shallow is Good? Eran Malach Shai Shalev-Shwartz 28 45 0 08 Mar 2019