arXiv:2605.22644v1 Announce Type: new Abstract: Stochastic Gradient Descent (SGD) is commonly modeled as a Langevin process, assuming that minibatch noise acts as Brownian motion. However, this approximation relies on a continuous-time limit and a sqrt(eta) noise scaling that does not match the discrete SGD update at finite learning rate. In this work, we propose an alternative formulation of SGD as deterministic dynamics in a fluctuating loss landscape induced by minibatch sampling. Starting directly from the discrete update, we derive a master equation for the parameter distribution and obta
This research provides a fundamental re-evaluation of how core AI optimization algorithms are understood, coming at a time of rapid AI expansion and increasing demand for robust and predictable models.
A deeper theoretical understanding of SGD can lead to more efficient, stable, and powerful AI models, impacting research, development, and deployment across the entire AI landscape.
The fundamental theoretical framework for understanding and optimizing deep learning models is being refined, potentially leading to new algorithmic design principles beyond traditional assumptions.
- · AI researchers
- · Deep learning practitioners
- · AI model developers
- · Machine learning hardware optimizers
- · Those relying solely on existing heuristic approaches
- · AI development lagging in theoretical advancements
Improved understanding and theoretical guarantees for Stochastic Gradient Descent (SGD) in AI model training.
Development of new, more efficient, and robust optimization algorithms for deep learning based on this refined theoretical understanding.
Acceleration of AI research and deployment due to more predictable and performant models, potentially lowering computational costs and increasing model capabilities.
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Read at arXiv cs.LG