The InfoNCE loss in contrastive learning depends critically on a temperature parameter, yet its dynamics under fixed versus annealed schedules remain poorly understood. We provide a theoretical analysis by modeling embedding evolution under Langevin dynamics on a compact Riemannian manifold. Under mild smoothness and energy-barrier assumptions, we show that classical simulated annealing guarantees extend to this setting: slow logarithmic inverse-temperature schedules ensure convergence in probability to a set of globally optimal representations, while faster schedules risk becoming trapped in suboptimal minima. Our results establish a link between contrastive learning and simulated annealing, providing a principled basis for understanding and tuning temperature schedules.

This supplementary document follows the Datasheets for Datasets template of (8) to document the Global Flood Forecasting (GFF) dataset and its creation. Further resources are provided: in the accompanying publication https://arxiv.org/abs/2409.18591 in the GitHub repository https://github.com/Multihuntr/GFF

We also nuance the idea that learning happens at the edge of chaos by giving evidence that avery desirable feature forneural networks isthehyperbolicity of their Jacobian at initialization.