LLM training data mixture optimization breaks when training pools shift — every prior proxy experiment becomes stale.
Last month, OpenAI announced that its latest version of ChatGPT had solved a major math problem, one that had stumped experts ...
Place any number of dots on a two-dimensional plane—say, a piece of paper—and measure the distance between each pair. If you rearrange the dots, how many pairs could be positioned exactly the same ...
A famed physicist’s scribbles reveal the answer to a quintessential dilemma: When dining out, is it better to stick with an old favorite, or try something new? Nobel Prize–winning physicist Richard ...
Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary ...
OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdős in 1946. If this sounds ...
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Mixture problem
Learn how to solve equations from word problems. A word problem is a real-world simulation of a mathematics principle. We can solve equations from a word problem by first understanding what the ...
Elizabeth Guevara is a personal finance reporter who explains the world of business and economics and how it impacts your finances. She joined Investopedia in 2024. Investopedia / Photo Composite by ...
David Cutler is in the spotlight for his work on a tasty-sounding mathematics problem. In January, the New York Times featured a research paper authored by Cutler and Neil Sloane, the founder of The ...
The NBA plans to address tanking, but there are problems with the league's seven potential solutions
Last week, the NBA fined the Utah Jazz $500,000 for "conduct detrimental to the league" and the Indiana Pacers $100,000 for violating the league's Player Participation Policy after both teams altered ...
One idle evening last October, Mehtaab Sawhney took up an old pastime. He began perusing the website erdosproblems.com, an updated record of the 1,179 conjectures left behind by the eccentric and ...
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