Tropical Geometry of Deep Neural Networks

18 May 2018

Papers citing "Tropical Geometry of Deep Neural Networks"

27 / 27 papers shown

Title
On the Depth of Monotone ReLU Neural Networks and ICNNs Egor Bakaev Florestan Brunck Christoph Hertrich Daniel Reichman Amir Yehudayoff 26 1 0 09 May 2025
Learnable polynomial, trigonometric, and tropical activations Ismail Khalfaoui-Hassani Stefan Kesselheim 64 0 0 03 Feb 2025
An Invitation to Neuroalgebraic Geometry Giovanni Luca Marchetti Vahid Shahverdi Stefano Mereta Matthew Trager Kathlén Kohn 119 2 0 31 Jan 2025
Neural Networks and (Virtual) Extended Formulations Christoph Hertrich Georg Loho 78 3 0 05 Nov 2024
On the Geometry of Deep Learning Randall Balestriero Ahmed Imtiaz Humayun Richard G. Baraniuk AI4CE 47 1 0 09 Aug 2024
Tight Certified Robustness via Min-Max Representations of ReLU Neural Networks Brendon G. Anderson Samuel Pfrommer Somayeh Sojoudi OOD 34 1 0 07 Oct 2023
Synthesizing Programmatic Policies with Actor-Critic Algorithms and ReLU Networks S. Orfanos Levi H. S. Lelis 21 6 0 04 Aug 2023
When Deep Learning Meets Polyhedral Theory: A Survey Joey Huchette Gonzalo Muñoz Thiago Serra Calvin Tsay AI4CE 94 32 0 29 Apr 2023
The Power of Typed Affine Decision Structures: A Case Study Gerrit Nolte Maximilian Schlüter Alnis Murtovi Bernhard Steffen AAML 20 3 0 28 Apr 2023
LEURN: Learning Explainable Univariate Rules with Neural Networks Çağlar Aytekin FAtt 29 0 0 27 Mar 2023
Abstract Visual Reasoning: An Algebraic Approach for Solving Raven's Progressive Matrices Jingyi Xu Tushar Vaidya Y. Blankenship Saket Chandra Zhangsheng Lai Kai Fong Ernest Chong 41 8 0 21 Mar 2023
Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopes Christian Haase Christoph Hertrich Georg Loho 34 22 0 24 Feb 2023
Predicting the cardinality and maximum degree of a reduced Gröbner basis S. Jamshidi Eric Kang Sonja Petrović 19 0 0 10 Feb 2023
Neural Networks are Decision Trees Çağlar Aytekin FAtt 32 24 0 11 Oct 2022
The tropical geometry of causal inference for extremes N. Tran CML 27 4 0 20 Jul 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
$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
An enriched category theory of language: from syntax to semantics T. Bradley John Terilla Yiannis Vlassopoulos 29 26 0 15 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
Advances in the training, pruning and enforcement of shape constraints of Morphological Neural Networks using Tropical Algebra Nikolaos Dimitriadis Petros Maragos 13 9 0 15 Nov 2020
Sparse Approximate Solutions to Max-Plus Equations with Application to Multivariate Convex Regression Nikos Tsilivis Anastasios Tsiamis Petros Maragos 29 3 0 06 Nov 2020
On the Decision Boundaries of Neural Networks: A Tropical Geometry Perspective Motasem Alfarra Adel Bibi Hasan Hammoud M. Gaafar Guohao Li 16 26 0 20 Feb 2020
A Universal Approximation Result for Difference of log-sum-exp Neural Networks G. Calafiore S. Gaubert Member C. Possieri 17 44 0 21 May 2019
Empirical Bounds on Linear Regions of Deep Rectifier Networks Thiago Serra Srikumar Ramalingam 8 42 0 08 Oct 2018
On the Spectral Bias of Neural Networks Nasim Rahaman A. Baratin Devansh Arpit Felix Dräxler Min Lin Fred Hamprecht Yoshua Bengio Aaron Courville 57 1,394 0 22 Jun 2018
Log-sum-exp neural networks and posynomial models for convex and log-log-convex data M. Akian S. Gaubert Jérémie Guillaud 11 25 0 20 Jun 2018
Benefits of depth in neural networks Matus Telgarsky 153 602 0 14 Feb 2016