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.

翻译：对比学习中的 InfoNCE 损失函数严重依赖于温度参数，然而其在固定与退火调度下的动力学行为仍未得到充分理解。我们通过在紧致黎曼流形上对 Langevin 动力学下的嵌入演化进行建模，提供了理论分析。在温和的光滑性和能量势垒假设下，我们证明了经典的模拟退火保证可推广至此场景：缓慢的对数反温度调度确保了以概率收敛到一组全局最优表示，而更快的调度则可能陷入次优极小值。我们的结果建立了对比学习与模拟退火之间的联系，为理解和调整温度调度提供了理论基础。