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Damien Ferbach

damien.ferbach@mila.quebec
Doctorat - Université de Montréal
Superviseur⋅e principal⋅e
Gauthier Gidel
Google Scholar

Publications

Proving Linear Mode Connectivity of Neural Networks via Optimal Transport
Damien Ferbach
Baptiste Goujaud
Gauthier Gidel
Aymeric Dieuleveut
The energy landscape of high-dimensional non-convex optimization problems is crucial to understanding the effectiveness of modern deep neura… (voir plus)l network architectures. Recent works have experimentally shown that two different solutions found after two runs of a stochastic training are often connected by very simple continuous paths (e.g., linear) modulo a permutation of the weights. In this paper, we provide a framework theoretically explaining this empirical observation. Based on convergence rates in Wasserstein distance of empirical measures, we show that, with high probability, two wide enough two-layer neural networks trained with stochastic gradient descent are linearly connected. Additionally, we express upper and lower bounds on the width of each layer of two deep neural networks with independent neuron weights to be linearly connected. Finally, we empirically demonstrate the validity of our approach by showing how the dimension of the support of the weight distribution of neurons, which dictates Wasserstein convergence rates is correlated with linear mode connectivity.
2024-01-01
AISTATS (publié)
doi.org
arxiv.org
Proving Linear Mode Connectivity of Neural Networks via Optimal Transport
Damien Ferbach
Baptiste Goujaud
Gauthier Gidel
Aymeric Dieuleveut
The energy landscape of high-dimensional non-convex optimization problems is crucial to understanding the effectiveness of modern deep neura… (voir plus)l network architectures. Recent works have experimentally shown that two different solutions found after two runs of a stochastic training are often connected by very simple continuous paths (e.g., linear) modulo a permutation of the weights. In this paper, we provide a framework theoretically explaining this empirical observation. Based on convergence rates in Wasserstein distance of empirical measures, we show that, with high probability, two wide enough two-layer neural networks trained with stochastic gradient descent are linearly connected. Additionally, we express upper and lower bounds on the width of each layer of two deep neural networks with independent neuron weights to be linearly connected. Finally, we empirically demonstrate the validity of our approach by showing how the dimension of the support of the weight distribution of neurons, which dictates Wasserstein convergence rates is correlated with linear mode connectivity.
2023-10-29
ArXiv (prépublication)
doi.org
arxiv.org
A General Framework For Proving The Equivariant Strong Lottery Ticket Hypothesis
Damien Ferbach
Christos Tsirigotis
Gauthier Gidel
Avishek Joey Bose
Joey Bose
The Strong Lottery Ticket Hypothesis (SLTH) stipulates the existence of a subnetwork within a sufficiently overparameterized (dense) neural … (voir plus)network that -- when initialized randomly and without any training -- achieves the accuracy of a fully trained target network. Recent works by Da Cunha et. al 2022; Burkholz 2022 demonstrate that the SLTH can be extended to translation equivariant networks -- i.e. CNNs -- with the same level of overparametrization as needed for the SLTs in dense networks. However, modern neural networks are capable of incorporating more than just translation symmetry, and developing general equivariant architectures such as rotation and permutation has been a powerful design principle. In this paper, we generalize the SLTH to functions that preserve the action of the group
2023-02-01
ICLR.cc/2023/Conference (poster)
doi.org
openreview.net