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Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek, Arthur Jacot

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

Réseau de télécommunications

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DeepNC: Deep Generative Network Completion

Investigating cognitive ability using action-based models of structural brain networks

Optimal routing and design of CO2 based district anergy networks

Fair Incentivization of Bandwidth Sharing in Decentralized Storage Networks

Face Reconstruction Fromdeep Facial Embeddings Using A Convolutional Neural Network

Physics-informed neural networks for diffraction tomography

LENA: Communication-Efficient Distributed Learning with Self-Triggered Gradient Uploads

The Impact of Collaborative Scheduling and Routing for Interconnected Logistics: A European Case Study

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Railway timetable rescheduling with capacity constraint

Optimal routing and design of CO2 based district anergy networks

LENA: Communication-Efficient Distributed Learning with Self-Triggered Gradient Uploads

DeepNC: Deep Generative Network Completion

Investigating cognitive ability using action-based models of structural brain networks

Fair Incentivization of Bandwidth Sharing in Decentralized Storage Networks

Railway timetable rescheduling with capacity constraint

The Impact of Collaborative Scheduling and Routing for Interconnected Logistics: A European Case Study

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Face Reconstruction Fromdeep Facial Embeddings Using A Convolutional Neural Network

Physics-informed neural networks for diffraction tomography