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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

Frontière (topologie)

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A Shape Derivative Approach to Domain Simplification

From SU(2)5 to SU(2)3 Wess-Zumino-Witten transitions in a frustrated spin-52 chain

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

Induction of a chromatin boundary in vivo upon insertion of a tad border

A unifying framework for form-finding and topology-finding of tensegrity structures

Global bifurcation at isolated singular points of the Hadamard derivative

Entanglement Entropy from Nonequilibrium Work

Robust Fano resonance in a topological mechanical beam

Instability of Thin Concrete Walls with a Single Layer of Reinforcement under Cyclic Loading: Numerical Simulation and Improved Equivalent Boundary Element Model for Assessment

Environmental impact minimization of reticular structures made of reused and new elements through Life Cycle Assessment and Mixed-Integer Linear Programming

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

Entanglement Entropy from Nonequilibrium Work

A unifying framework for form-finding and topology-finding of tensegrity structures

Induction of a chromatin boundary in vivo upon insertion of a tad border

Global bifurcation at isolated singular points of the Hadamard derivative

Robust Fano resonance in a topological mechanical beam

Instability of Thin Concrete Walls with a Single Layer of Reinforcement under Cyclic Loading: Numerical Simulation and Improved Equivalent Boundary Element Model for Assessment

Environmental impact minimization of reticular structures made of reused and new elements through Life Cycle Assessment and Mixed-Integer Linear Programming

A Shape Derivative Approach to Domain Simplification

From SU(2)5 to SU(2)3 Wess-Zumino-Witten transitions in a frustrated spin-52 chain