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arXiv · 2603.12552

Asymptotic and Finite-Time Guarantees for Langevin-Based Temperature Annealing in InfoNCE

Faris Chaudhry
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Abstract

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.

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Faris Chaudhry. 2026-03-13. Asymptotic and Finite-Time Guarantees for Langevin-Based Temperature Annealing in InfoNCE. https://arxiv.org/abs/2603.12552

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