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BrachistoneLR: A Brachistochrone-Inspired Learning-Rate Schedule and a Controlled Benchmark of Scheduling Policies

arXiv · AI, language, vision and robotics · article · Sep 8, 2026 · UTC

The learning-rate schedule is a consequential choice in training deep networks, yet the policies in common use are heuristic, and published comparisons are hard to read, because architecture, dataset, and budget tend to vary alongside the schedule. We study BrachistoneLR, a schedule built by mapping the vertical coordinate of the brachistochrone, the curve of fastest descent under gravity, onto the range between a peak and a floor rate. Expanding the definition shows it to be cosine annealing with the half-period set to E - 1 instead of E, the configuration a standard implementation gives when

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