How AI settled the complexity of the oldest SGD algorithm

Michał Dereziński; Xiaoyu Dong

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arXiv · 2606.29593

How AI settled the complexity of the oldest SGD algorithm

Michał Dereziński·Xiaoyu Dong

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Abstract

In 1937, Stefan Kaczmarz proposed a simple algorithm for solving systems of linear equations. This algorithm turned out to be the earliest known example of stochastic gradient descent, a ubiquitous computing paradigm that drives the training of modern AI models such as ChatGPT and Gemini. Now, those AI models have joined forces to discover the worst-case complexity of the Kaczmarz algorithm. This paper tells the story of how it happened.

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Michał Dereziński, Xiaoyu Dong. 2026-06-28. How AI settled the complexity of the oldest SGD algorithm. https://arxiv.org/abs/2606.29593

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