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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 informatique

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Frugal Decentralized Learning

Penalized denoising of vehicle trajectories collected by a swarm of drones

A Stepwise Domain Adaptive Segmentation Network With Covariate Shift Alleviation for Remote Sensing Imagery

Direct encapsulation of biomolecules in semi-permeable microcapsules produced with double-emulsions

Understanding Deep Neural Networks using Adversarial Attacks

A multi-scale probabilistic atlas of the human connectome

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

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

A Distributed Luenberger Observer for Linear State Feedback Systems With Quantized and Rate-Limited Communications

Reinforced Attention for Few-Shot Learning and Beyond

Penalized denoising of vehicle trajectories collected by a swarm of drones

Direct encapsulation of biomolecules in semi-permeable microcapsules produced with double-emulsions

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

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

A Distributed Luenberger Observer for Linear State Feedback Systems With Quantized and Rate-Limited Communications

Reinforced Attention for Few-Shot Learning and Beyond

Frugal Decentralized Learning

A Stepwise Domain Adaptive Segmentation Network With Covariate Shift Alleviation for Remote Sensing Imagery

Understanding Deep Neural Networks using Adversarial Attacks

A multi-scale probabilistic atlas of the human connectome