Function-Space Learning Rates

• URL: http://arxiv.org/abs/2502.17405v1
• Date: Mon, 24 Feb 2025 18:31:58 GMT
• Title: Function-Space Learning Rates
• Authors: Edward Milsom, Ben Anson, Laurence Aitchison,
• Abstract summary: We develop efficient methods to measure and set function-space learning rates in arbitrary neural networks.<n>We demonstrate two key applications: (1) analysing the dynamics of standard neural network optimisers in function space, rather than parameter space.
• Score: 23.09717258810923
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider layerwise function-space learning rates, which measure the magnitude of the change in a neural network's output function in response to an update to a parameter tensor. This contrasts with traditional learning rates, which describe the magnitude of changes in parameter space. We develop efficient methods to measure and set function-space learning rates in arbitrary neural networks, requiring only minimal computational overhead through a few additional backward passes that can be performed at the start of, or periodically during, training. We demonstrate two key applications: (1) analysing the dynamics of standard neural network optimisers in function space, rather than parameter space, and (2) introducing FLeRM (Function-space Learning Rate Matching), a novel approach to hyperparameter transfer across model scales. FLeRM records function-space learning rates while training a small, cheap base model, then automatically adjusts parameter-space layerwise learning rates when training larger models to maintain consistent function-space updates. FLeRM gives hyperparameter transfer across model width, depth, initialisation scale, and LoRA rank in various architectures including MLPs with residual connections and transformers with different layer normalisation schemes.

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