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

Faris Chaudhry

cs.LGMar 13, 2026

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

Authors: Faris Chaudhry

Organizations: Imperial College London, United Kingdom

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.

Contrastive Learning

Contrastive learning trains representations by bringing related examples together and separating unrelated ones for recognition, retrieval, and transfer.

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Similarity search generalisation in contrastive learning with InfoNCE loss

Nick Whiteley

School of Mathematics, University of Bristol, U.K.

Neural Network Generalization Contrastive Learning Statistical Learning Theory

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Similarity search is a primary application of embedding models trained by contrastive learning. For one of the most popular contrastive learning loss functions, InfoNCE, we show that the population risk with

k

negative samples is

O(1/k)

close to an expected cross-entropy which quantifies deviation between i) a softmax similarity search over unseen data using the learned embedding function, and ii) an idealised softmax search over the same data but using similarity implicitly represented in the positive sample generator. This complements existing interpretations of InfoNCE in the

k\to\infty

limit which are phrased in terms of mutual information, and alignment versus uniformity in embeddings. To quantify generalisation performance, we introduce a new continuity bound for the InfoNCE loss, obtained via Gâteaux differentiation. The bound preserves the structure of averaging over negative samples present in the loss function and features an ``inverse temperature'' parameter which can be tuned to account for the algorithmic temperature. For embedding functions which are Lipschitz in a parameter, this yields a simple demonstration that the averaging effect of

k

negative samples in the InfoNCE loss carries over to stabilisation of the generalisation error as

k

grows.

Abstract

Contrastive Learning

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