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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 35 / No. 9: AAAI-21 Technical Tracks 9

A Recipe for Global Convergence Guarantee in Deep Neural Networks

February 1, 2023

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Authors

Kenji Kawaguchi

Harvard University


Qingyun Sun

Stanford University


DOI:

10.1609/aaai.v35i9.16984


Abstract:

Existing global convergence guarantees of (stochastic) gradient descent do not apply to practical deep networks in the practical regime of deep learning beyond the neural tangent kernel (NTK) regime. This paper proposes an algorithm, which is ensured to have global convergence guarantees in the practical regime beyond the NTK regime, under a verifiable condition called the expressivity condition. The expressivity condition is defined to be both data-dependent and architecture-dependent, which is the key property that makes our results applicable for practical settings beyond the NTK regime. On the one hand, the expressivity condition is theoretically proven to hold data-independently for fully-connected deep neural networks with narrow hidden layers and a single wide layer. On the other hand, the expressivity condition is numerically shown to hold data-dependently for deep (convolutional) ResNet with batch normalization with various standard image datasets. We also show that the the proposed algorithm has generalization performances comparable with those of the heuristic algorithm, with the same hyper-parameters and total number of iterations. Therefore, the proposed algorithm can be viewed as a step towards providing theoretical guarantees for deep learning in the practical regime.

Topics: AAAI

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Kenji Kawaguchi||Qingyun Sun A Recipe for Global Convergence Guarantee in Deep Neural Networks Proceedings of the AAAI Conference on Artificial Intelligence (2021) 8074-8082.

Kenji Kawaguchi||Qingyun Sun A Recipe for Global Convergence Guarantee in Deep Neural Networks AAAI 2021, 8074-8082.

Kenji Kawaguchi||Qingyun Sun (2021). A Recipe for Global Convergence Guarantee in Deep Neural Networks. Proceedings of the AAAI Conference on Artificial Intelligence, 8074-8082.

Kenji Kawaguchi||Qingyun Sun. A Recipe for Global Convergence Guarantee in Deep Neural Networks. Proceedings of the AAAI Conference on Artificial Intelligence 2021 p.8074-8082.

Kenji Kawaguchi||Qingyun Sun. 2021. A Recipe for Global Convergence Guarantee in Deep Neural Networks. "Proceedings of the AAAI Conference on Artificial Intelligence". 8074-8082.

Kenji Kawaguchi||Qingyun Sun. (2021) "A Recipe for Global Convergence Guarantee in Deep Neural Networks", Proceedings of the AAAI Conference on Artificial Intelligence, p.8074-8082

Kenji Kawaguchi||Qingyun Sun, "A Recipe for Global Convergence Guarantee in Deep Neural Networks", AAAI, p.8074-8082, 2021.

Kenji Kawaguchi||Qingyun Sun. "A Recipe for Global Convergence Guarantee in Deep Neural Networks". Proceedings of the AAAI Conference on Artificial Intelligence, 2021, p.8074-8082.

Kenji Kawaguchi||Qingyun Sun. "A Recipe for Global Convergence Guarantee in Deep Neural Networks". Proceedings of the AAAI Conference on Artificial Intelligence, (2021): 8074-8082.

Kenji Kawaguchi||Qingyun Sun. A Recipe for Global Convergence Guarantee in Deep Neural Networks. AAAI[Internet]. 2021[cited 2023]; 8074-8082.


ISSN: 2374-3468


Published by AAAI Press, Palo Alto, California USA
Copyright 2022, Association for the Advancement of
Artificial Intelligence 1900 Embarcadero Road, Suite
101, Palo Alto, California 94303 All Rights Reserved

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