# CoolMomentum: A Method for Stochastic Optimization by Langevin Dynamics with Simulated Annealing Source: [CoolMomentum: A Method for Stochastic Optimization by Langevin Dynamics with Simulated Annealing]() Collection index: [llms.txt]() Data updated: 2025-10-27T06:07:38.365Z Authors: Oleksandr Borysenko, Maksym Byshkin Published: 2020-05-29T14:44:24.000Z ## Abstract Deep learning applications require global optimization of non-convex objective functions, which have multiple local minima. The same problem is often found in physical simulations and may be resolved by the methods of Langevin dynamics with Simulated Annealing, which is a well-established approach for minimization of many-particle potentials. This analogy provides useful insights for non-convex stochastic optimization in machine learning. Here we find that integration of the discretized Langevin equation gives a coordinate updating rule equivalent to the famous Momentum optimization algorithm. As a main result, we show that a gradual decrease of the momentum coefficient from the initial value close to unity until zero is equivalent to application of Simulated Annealing or slow cooling, in physical terms. Making use of this novel approach, we propose CoolMomentum -- a new stochastic optimization method. Applying Coolmomentum to optimization of Resnet-20 on Cifar-10 dataset and Efficientnet-B0 on Imagenet, we demonstrate that it is able to achieve high accuracies. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()