Positive-Negative Momentum: Manipulating Stochastic Gradient Noise to Improve Generalization

TL;DR

This paper introduces Positive-Negative Momentum (PNM), a novel optimizer component that manipulates stochastic gradient noise to enhance deep learning generalization, with theoretical guarantees and empirical improvements over traditional methods.

Contribution

PNM is a new method that explicitly controls stochastic gradient noise by maintaining two momentum terms, improving generalization without increasing computational costs.

Findings

PNM outperforms traditional momentum in deep learning tasks.

Theoretical proof of convergence and generalization benefits.

Empirical results show significant accuracy improvements.

Abstract

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.