Asymptotic and Finite-Time Guarantees for Langevin-Based Temperature Annealing in InfoNCE
arXiv:2603.12552v1 Announce Type: new 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.
arXiv:2603.12552v1 Announce Type: new 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.
Executive Summary
This article provides a theoretical analysis of the InfoNCE loss in contrastive learning under Langevin dynamics on a compact Riemannian manifold. The authors demonstrate that slow logarithmic inverse-temperature schedules ensure convergence to globally optimal representations, while faster schedules risk becoming trapped in suboptimal minima. This work establishes a link between contrastive learning and simulated annealing, offering a principled basis for understanding and tuning temperature schedules. The findings have significant implications for the development of effective temperature annealing strategies in contrastive learning, with potential applications in a range of machine learning and optimization tasks.
Key Points
- ▸ The article provides a theoretical analysis of InfoNCE loss under Langevin dynamics
- ▸ Slow logarithmic inverse-temperature schedules ensure convergence to globally optimal representations
- ▸ Faster schedules risk becoming trapped in suboptimal minima
Merits
Strength in Theoretical Foundation
The article builds on a solid theoretical framework, providing a principled basis for understanding temperature schedules in contrastive learning.
Significance for Contrastive Learning
The findings have significant implications for the development of effective temperature annealing strategies in contrastive learning.
Methodological Innovation
The use of Langevin dynamics on a compact Riemannian manifold offers a novel approach to analyzing temperature schedules in contrastive learning.
Demerits
Limitation to Specific Settings
The analysis is limited to compact Riemannian manifolds and may not generalize to more complex or higher-dimensional spaces.
Assumptions on Smoothness and Energy Barriers
The analysis relies on mild smoothness and energy-barrier assumptions, which may not hold in all practical settings.
Expert Commentary
The article provides a significant contribution to the theoretical understanding of temperature schedules in contrastive learning. The use of Langevin dynamics on a compact Riemannian manifold offers a novel approach to analyzing temperature schedules, and the findings have significant implications for the development of effective temperature annealing strategies. However, the analysis is limited to specific settings and relies on mild smoothness and energy-barrier assumptions, which may not hold in all practical settings. Nevertheless, the work provides a principled basis for understanding and tuning temperature schedules, and its implications can inform the development of more efficient and effective algorithms for contrastive learning.
Recommendations
- ✓ Future work should aim to generalize the analysis to more complex and higher-dimensional spaces, and to investigate the robustness of the findings under different smoothness and energy-barrier assumptions.
- ✓ The results of the article can be used to inform the development of more effective temperature annealing strategies in contrastive learning, leading to improved performance in machine learning tasks.
