Flatter, faster: scaling momentum for optimal speedup of SGD

• URL: http://arxiv.org/abs/2210.16400v2
• Date: Tue, 13 Jun 2023 04:47:46 GMT
• Title: Flatter, faster: scaling momentum for optimal speedup of SGD
• Authors: Aditya Cowsik, Tankut Can and Paolo Glorioso
• Abstract summary: We study training dynamics arising from interplay between gradient descent (SGD) and label noise and momentum in the training of neural networks. We find that scaling the momentum hyper parameter $1-NISTbeta$ with the learning rate to the power of $2/3$ maximally accelerates training, without sacrificing generalization.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Commonly used optimization algorithms often show a trade-off between good generalization and fast training times. For instance, stochastic gradient descent (SGD) tends to have good generalization; however, adaptive gradient methods have superior training times. Momentum can help accelerate training with SGD, but so far there has been no principled way to select the momentum hyperparameter. Here we study training dynamics arising from the interplay between SGD with label noise and momentum in the training of overparametrized neural networks. We find that scaling the momentum hyperparameter $1-\beta$ with the learning rate to the power of $2/3$ maximally accelerates training, without sacrificing generalization. To analytically derive this result we develop an architecture-independent framework, where the main assumption is the existence of a degenerate manifold of global minimizers, as is natural in overparametrized models. Training dynamics display the emergence of two characteristic timescales that are well-separated for generic values of the hyperparameters. The maximum acceleration of training is reached when these two timescales meet, which in turn determines the scaling limit we propose. We confirm our scaling rule for synthetic regression problems (matrix sensing and teacher-student paradigm) and classification for realistic datasets (ResNet-18 on CIFAR10, 6-layer MLP on FashionMNIST), suggesting the robustness of our scaling rule to variations in architectures and datasets.

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