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Positive-Negative Momentum: Manipulating Stochastic Gradient Noise to Improve Generalization
Zeke Xie · Li Yuan · Zhanxing Zhu · Masashi Sugiyama

Tue Jul 20 07:20 AM -- 07:25 AM (PDT) @

It is well-known that stochastic gradient noise (SGN) acts as implicit regularization for deep learning and is essentially important for both optimization and generalization of deep networks. Some works attempted to artificially simulate SGN by injecting random noise to improve deep learning. However, it turned out that the injected simple random noise cannot work as well as SGN, which is anisotropic and parameter-dependent. For simulating SGN at low computational costs and without changing the learning rate or batch size, we propose the Positive-Negative Momentum (PNM) approach that is a powerful alternative to conventional Momentum in classic optimizers. The introduced PNM method maintains two approximate independent momentum terms. Then, we can control the magnitude of SGN explicitly by adjusting the momentum difference. We theoretically prove the convergence guarantee and the generalization advantage of PNM over Stochastic Gradient Descent (SGD). By incorporating PNM into the two conventional optimizers, SGD with Momentum and Adam, our extensive experiments empirically verified the significant advantage of the PNM-based variants over the corresponding conventional Momentum-based optimizers. Code: \url{https://github.com/zeke-xie/Positive-Negative-Momentum}.

Author Information

Zeke Xie (The University of Tokyo/RIKEN)

He obtained Ph.D. in machine learning and M.E. both from The University of Tokyo. He was fortunately supervised by Prof. Masashi Sugiyama and Prof. Issei Sato. He was also affiliated with RIKEN AIP during the Ph.D. study. Before that, he obtained Bachelor of Science from University of Science and Technology of China. His research interests generally lies in machine learning, especially including Deep Learning Theory, Imperfect Information Learning, and AI + Science.

Li Yuan (National Univerisity of Singapore)
Zhanxing Zhu (Peking University)
Masashi Sugiyama (RIKEN / The University of Tokyo)

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