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Pure and Spurious Critical Points: a Geometric Study of Linear Networks
v1v2 (latest)

Pure and Spurious Critical Points: a Geometric Study of Linear Networks

3 October 2019
Matthew Trager
Kathlén Kohn
Joan Bruna
ArXiv (abs)PDFHTML

Papers citing "Pure and Spurious Critical Points: a Geometric Study of Linear Networks"

19 / 19 papers shown
Title
Understanding Learning Invariance in Deep Linear Networks
Understanding Learning Invariance in Deep Linear Networks
Hao Duan
Guido Montúfar
25
0
0
16 Jun 2025
Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders
Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders
Jonghyun Ham
Maximilian Fleissner
Debarghya Ghoshdastidar
AI4CE
33
0
0
30 May 2025
Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry
Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry
Giovanni Luca Marchetti
Vahid Shahverdi
Stefano Mereta
Matthew Trager
Kathlén Kohn
153
2
0
31 Jan 2025
Gradient flow in parameter space is equivalent to linear interpolation in output space
Gradient flow in parameter space is equivalent to linear interpolation in output space
Thomas Chen
Patrícia Muñoz Ewald
72
1
0
02 Aug 2024
On the Stability of Gradient Descent for Large Learning Rate
On the Stability of Gradient Descent for Large Learning Rate
Alexandru Cruaciun
Debarghya Ghoshdastidar
MLTODL
22
0
0
20 Feb 2024
Neural Rank Collapse: Weight Decay and Small Within-Class Variability
  Yield Low-Rank Bias
Neural Rank Collapse: Weight Decay and Small Within-Class Variability Yield Low-Rank Bias
Emanuele Zangrando
Piero Deidda
Simone Brugiapaglia
Nicola Guglielmi
Francesco Tudisco
83
8
0
06 Feb 2024
Algebraic Complexity and Neurovariety of Linear Convolutional Networks
Algebraic Complexity and Neurovariety of Linear Convolutional Networks
Vahid Shahverdi
112
4
0
29 Jan 2024
Geometry of Linear Neural Networks: Equivariance and Invariance under Permutation Groups
Geometry of Linear Neural Networks: Equivariance and Invariance under Permutation Groups
Kathlén Kohn
Anna-Laura Sattelberger
Vahid Shahverdi
97
4
0
24 Sep 2023
Function Space and Critical Points of Linear Convolutional Networks
Function Space and Critical Points of Linear Convolutional Networks
Kathlén Kohn
Guido Montúfar
Vahid Shahverdi
Matthew Trager
85
14
0
12 Apr 2023
Critical Points and Convergence Analysis of Generative Deep Linear
  Networks Trained with Bures-Wasserstein Loss
Critical Points and Convergence Analysis of Generative Deep Linear Networks Trained with Bures-Wasserstein Loss
Pierre Bréchet
Katerina Papagiannouli
Jing An
Guido Montúfar
82
4
0
06 Mar 2023
Functional dimension of feedforward ReLU neural networks
Functional dimension of feedforward ReLU neural networks
J. E. Grigsby
Kathryn A. Lindsey
R. Meyerhoff
Chen-Chun Wu
60
12
0
08 Sep 2022
Low-Pass Filtering SGD for Recovering Flat Optima in the Deep Learning
  Optimization Landscape
Low-Pass Filtering SGD for Recovering Flat Optima in the Deep Learning Optimization Landscape
Devansh Bisla
Jing Wang
A. Choromańska
104
37
0
20 Jan 2022
The Geometry of Memoryless Stochastic Policy Optimization in
  Infinite-Horizon POMDPs
The Geometry of Memoryless Stochastic Policy Optimization in Infinite-Horizon POMDPs
Johannes Muller
Guido Montúfar
90
8
0
14 Oct 2021
Beyond Linear Algebra
Beyond Linear Algebra
Bernd Sturmfels
34
9
0
21 Aug 2021
Convergence of gradient descent for learning linear neural networks
Convergence of gradient descent for learning linear neural networks
Gabin Maxime Nguegnang
Holger Rauhut
Ulrich Terstiege
MLT
63
18
0
04 Aug 2021
Geometry of Linear Convolutional Networks
Geometry of Linear Convolutional Networks
Kathlén Kohn
Thomas Merkh
Guido Montúfar
Matthew Trager
115
20
0
03 Aug 2021
The loss landscape of deep linear neural networks: a second-order
  analysis
The loss landscape of deep linear neural networks: a second-order analysis
El Mehdi Achour
Franccois Malgouyres
Sébastien Gerchinovitz
ODL
65
10
0
28 Jul 2021
Learning deep linear neural networks: Riemannian gradient flows and
  convergence to global minimizers
Learning deep linear neural networks: Riemannian gradient flows and convergence to global minimizers
B. Bah
Holger Rauhut
Ulrich Terstiege
Michael Westdickenberg
MLT
79
66
0
12 Oct 2019
On the Expressive Power of Deep Polynomial Neural Networks
On the Expressive Power of Deep Polynomial Neural Networks
Joe Kileel
Matthew Trager
Joan Bruna
83
83
0
29 May 2019
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