Dimension-adapted Momentum Outscales SGD

• URL: http://arxiv.org/abs/2505.16098v1
• Date: Thu, 22 May 2025 00:58:50 GMT
• Title: Dimension-adapted Momentum Outscales SGD
• Authors: Damien Ferbach, Katie Everett, Gauthier Gidel, Elliot Paquette, Courtney Paquette,
• Abstract summary: We investigate scaling laws for momentum algorithms with small batch on the power law random model.<n>When trained with a momentum algorithm, our analysis reveals four distinct loss curve determined by varying data-target complexities.<n>While traditional gradient descent with momentum (SGDM) yields identical scaling law exponents to SGD, dimension-adapted Nesterov acceleration (DANA) improves these exponents.
• Score: 22.487084876365213
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate scaling laws for stochastic momentum algorithms with small batch on the power law random features model, parameterized by data complexity, target complexity, and model size. When trained with a stochastic momentum algorithm, our analysis reveals four distinct loss curve shapes determined by varying data-target complexities. While traditional stochastic gradient descent with momentum (SGD-M) yields identical scaling law exponents to SGD, dimension-adapted Nesterov acceleration (DANA) improves these exponents by scaling momentum hyperparameters based on model size and data complexity. This outscaling phenomenon, which also improves compute-optimal scaling behavior, is achieved by DANA across a broad range of data and target complexities, while traditional methods fall short. Extensive experiments on high-dimensional synthetic quadratics validate our theoretical predictions and large-scale text experiments with LSTMs show DANA's improved loss exponents over SGD hold in a practical setting.

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