Log In Sign Up

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

by   Zeke Xie, et al.

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: <>.


On the Hyperparameters in Stochastic Gradient Descent with Momentum

Following the same routine as [SSJ20], we continue to present the theore...

Calibrating the Learning Rate for Adaptive Gradient Methods to Improve Generalization Performance

Although adaptive gradient methods (AGMs) have fast speed in training de...

Towards understanding how momentum improves generalization in deep learning

Stochastic gradient descent (SGD) with momentum is widely used for train...

Spherical Perspective on Learning with Batch Norm

Batch Normalization (BN) is a prominent deep learning technique. In spit...

Asynchrony begets Momentum, with an Application to Deep Learning

Asynchronous methods are widely used in deep learning, but have limited ...

Code Repositories


The official PyTorch Implementations of Positive-Negative Momentum Optimizers.

view repo