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

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

3 October 2019

Matthew Trager

Joan Bruna

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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 Hao Duan Guido Montúfar 25 0 0 16 Jun 2025
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 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 Thomas Chen Patrícia Muñoz Ewald 72 1 0 02 Aug 2024
On the Stability of Gradient Descent for Large Learning Rate Alexandru Cruaciun Debarghya Ghoshdastidar MLT ODL 22 0 0 20 Feb 2024
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 Vahid Shahverdi 112 4 0 29 Jan 2024
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 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 Pierre Bréchet Katerina Papagiannouli Jing An Guido Montúfar 82 4 0 06 Mar 2023
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 Devansh Bisla Jing Wang A. Choromańska 104 37 0 20 Jan 2022
The Geometry of Memoryless Stochastic Policy Optimization in Infinite-Horizon POMDPs Johannes Muller Guido Montúfar 90 8 0 14 Oct 2021
Beyond Linear Algebra Bernd Sturmfels 34 9 0 21 Aug 2021
Convergence of gradient descent for learning linear neural networks Gabin Maxime Nguegnang Holger Rauhut Ulrich Terstiege MLT 61 18 0 04 Aug 2021
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 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 B. Bah Holger Rauhut Ulrich Terstiege Michael Westdickenberg MLT 79 66 0 12 Oct 2019
On the Expressive Power of Deep Polynomial Neural Networks Joe Kileel Matthew Trager Joan Bruna 83 83 0 29 May 2019