THEORY
RESEARCH
Fluctuation-dissipation relations for stochastic gradient descent
May 03, 2019
Abstract
The notion of the stationary equilibrium ensemble has played a central role in statistical mechanics. In machine learning as well, training serves as generalized equilibration that drives the probability distribution of model parameters toward stationarity. Here, we derive stationary fluctuation-dissipation relations that link measurable quantities and hyperparameters in the stochastic gradient descent algorithm. These relations hold exactly for any stationary state and can in particular be used to adaptively set training schedule. We can further use the relations to efficiently extract information pertaining to a loss-function landscape such as the magnitudes of its Hessian and anharmonicity. Our claims are empirically verified.
Related Publications
February 11, 2026
RESEARCH
COMPUTER VISION
UniT: Unified Multimodal Chain-of-Thought Test-time Scaling
Leon Liangyu Chen, Haoyu Ma, Zhipeng Fan, Ziqi Huang, Animesh Sinha, Xiaoliang Dai, Jialiang Wang, Zecheng He, Jianwei Yang, Chunyuan Li, Junzhe Sun, Chu Wang, Serena Yeung-Levy, Felix Juefei-Xu
February 11, 2026
December 18, 2025
RESEARCH
COMPUTER VISION
Pixel Seal: Adversarial-only training for invisible image and video watermarking
Tomáš Souček, Pierre Fernandez, Hady Elsahar, Sylvestre Rebuffi, Valeriu Lacatusu, Tuan Tran, Tom Sander, Alexandre Mourachko
December 18, 2025
November 19, 2025
RESEARCH
COMPUTER VISION
SAM 3: Segment Anything with Concepts
Nicolas Carion, Laura Gustafson, Yuan-Ting Hu, Shoubhik Debnath, Ronghang Hu, Didac Suris Coll-Vinent, Chaitanya Ryali, Kalyan Vasudev Alwala, Haitham Khedr, Andrew Huang, Jie Lei, Tengyu Ma, Baishan Guo, Arpit Kalla, Markus Marks, Joseph Greer, Meng Wang, Peize Sun, Roman Rädle, Triantafyllos Afouras, Effrosyni Mavroudi, Katherine Xu, Tsung-Han Wu, Yu Zhou, Liliane Momeni, Rishi Hazra, Shuangrui Ding, Sagar Vaze, Francois Porcher, Feng Li, Siyuan Li, Aishwarya Kamath, Ho Kei Cheng, Piotr Dollar, Nikhila Ravi, Kate Saenko, Pengchuan Zhang, Christoph Feichtenhofer
November 19, 2025
November 18, 2025
RESEARCH
CORE MACHINE LEARNING
Souper-Model: How Simple Arithmetic Unlocks State-of-the-Art LLM Performance
Shalini Maiti *, Amar Budhiraja *, Bhavul Gauri, Gaurav Chaurasia, Anton Protopopov, Alexis Audran-Reiss, Michael Slater, Despoina Magka, Tatiana Shavrina, Roberta Raileanu, Yoram Bachrach, * Equal authorship
November 18, 2025
Help Us Pioneer The Future of AI
We share our open source frameworks, tools, libraries, and models for everything from research exploration to large-scale production deployment.
Our approach
Latest news
Foundational models
Meta © 2026