Why Larger Learning Rates and Smaller Batches Improve Generalization: RBC Borealis Explains
SimonPrinceAI · x · 2026-08-14
RBC Borealis released the latest article in its series on ODEs and SDEs in machine learning, analyzing the underlying mechanisms of optimization algorithms from a mathematical perspective.
- Theoretical Model: The article treats gradient descent (GD) with infinitesimal step sizes as an ODE, and stochastic gradient descent (SGD) as an SDE. Analyzing the SDE model reveals the trade-off between batch size and step size during optimization, and how the final expected loss relates to the width of the minimum at convergence.
- Practical Application: In the practical case of finite step sizes, the deviation from the infinitesimal limit manifests as an additive regularization term (known as implicit regularization).
- Core Conclusion: This implicit regularization effect mathematically explains why larger learning rates and smaller batches lead to better generalization in neural networks.
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