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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

Science des réseaux

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Optimal routing and design of CO2 based district anergy networks

The progressive loss of brain network fingerprints in Amyotrophic Lateral Sclerosis predicts clinical impairment

Face Reconstruction Fromdeep Facial Embeddings Using A Convolutional Neural Network

Physics-informed neural networks for diffraction tomography

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

Cluster-and-Conquer: When Randomness Meets Graph Locality

True scale-free networks hidden by finite size effects

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Characterization and prediction of clinical pathways of vulnerability to psychosis through graph signal processing

Optimal routing and design of CO2 based district anergy networks

The progressive loss of brain network fingerprints in Amyotrophic Lateral Sclerosis predicts clinical impairment

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

Characterization and prediction of clinical pathways of vulnerability to psychosis through graph signal processing

Face Reconstruction Fromdeep Facial Embeddings Using A Convolutional Neural Network

Cluster-and-Conquer: When Randomness Meets Graph Locality

True scale-free networks hidden by finite size effects

Facilitators First: Building a Tool With Facilitators to Foster a More Collaborative Makerspace Community Through Movement Traces

NICEpath: Finding metabolic pathways in large networks through atom-conserving substrate-product pairs

Physics-informed neural networks for diffraction tomography