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Sharp Minima Can Generalize For Deep Nets
Laurent Dinh · Razvan Pascanu · Samy Bengio · Yoshua Bengio

Sun Aug 06 06:06 PM -- 06:24 PM (PDT) @ C4.8

Despite their overwhelming capacity to overfit, deep learning architectures tend to generalize relatively well to unseen data, allowing them to be deployed in practice. However, explaining why this is the case is still an open area of research. One standing hypothesis that is gaining popularity, e.g. \citet{hochreiter1997flat, keskar2016large}, is that the flatness of minima of the loss function found by stochastic gradient based methods results in good generalization. This paper argues that most notions of flatness are problematic for deep models and can not be directly applied to explain generalization. Specifically, when focusing on deep networks with rectifier units, we can exploit the particular geometry of parameter space induced by the inherent symmetries that these architectures exhibit to build equivalent models corresponding to arbitrarily sharper minima. Or, depending on the definition of flatness, it is the same for any given minimum. Furthermore, if we allow to reparametrize a function, the geometry of its parameters can change drastically without affecting its generalization properties.

Author Information

Laurent Dinh (University of Montreal)
Razvan Pascanu (DeepMind)
Samy Bengio (Google Brain)
Yoshua Bengio (U. Montreal)

Yoshua Bengio is recognized as one of the world’s leading experts in artificial intelligence and a pioneer in deep learning. Since 1993, he has been a professor in the Department of Computer Science and Operational Research at the Université de Montréal. He is the founder and scientific director of Mila, the Quebec Institute of Artificial Intelligence, the world’s largest university-based research group in deep learning. He is a member of the NeurIPS board and co-founder and general chair for the ICLR conference, as well as program director of the CIFAR program on Learning in Machines and Brains and is Fellow of the same institution. In 2018, Yoshua Bengio ranked as the computer scientist with the most new citations, worldwide, thanks to his many publications. In 2019, he received the ACM A.M. Turing Award, “the Nobel Prize of Computing”, jointly with Geoffrey Hinton and Yann LeCun for conceptual and engineering breakthroughs that have made deep neural networks a critical component of computing. In 2020 he was nominated Fellow of the Royal Society of London.

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