arXiv:2606.29593v1 Announce Type: new 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.
The accelerating capabilities of advanced AI models have reached a point where they can contribute to fundamental algorithmic discovery, even for long-standing problems.
This development signals a new era where AI itself is a tool for fundamental scientific and algorithmic breakthroughs, potentially accelerating progress across many fields.
The role of AI shifts from primarily applying existing algorithms to actively discovering and optimizing them, potentially disrupting traditional research methodologies.
- · AI research labs
- · Machine learning developers
- · Scientific research institutions
- · High-performance computing sector
AI models become indispensable tools for optimizing foundational algorithms across diverse scientific and engineering disciplines.
This acceleration of algorithmic discovery could lead to unexpected breakthroughs in fields currently bottlenecks by computational complexity.
The reliance on AI for fundamental research might raise questions about causality, interpretability, and the nature of discovery itself.
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Read at arXiv cs.LG