Computing the polar decomposition and the related matrix sign function has been a well-studied problem in numerical analysis for decades. Recently, it has emerged as an important subroutine within the Muon algorithm for training deep neural networks. However, the requirements of this application differ sharply from classical settings: deep learning demands GPU-friendly algorithms that prioritize high throughput over high precision. We introduce Polar Express, a new method for computing the polar decomposition. Like Newton-Schulz and other classical polynomial methods, our approach uses only matrix-matrix multiplications, making it very efficient on GPUs. Inspired by earlier work of Chen & Chow and Nakatsukasa & Freund, Polar Express adapts the update rule at each iteration by solving a minimax optimization problem. We prove that this strategy minimizes error in a worst-case sense, allowing Polar Express to converge as rapidly as possible both in the early iterations and asymptotically. We also address finite-precision issues, making it practical to use in bfloat16. When integrated into the Muon training framework, our method leads to consistent improvements in validation loss when training a GPT-2 model on one billion tokens from the FineWeb dataset, outperforming recent alternatives across a range of learning rates.

Tom Hanks and wife Rita Wilson walked the Pre-Grammy GALA red carpet discussing what they believe is the success to a great relationship, after being married for 34 years. Tom Hanks is warning fans about a potential AI-generated scam. The "Forrest Gump" actor says his name and likeness are being used without his consent in a dental promotion, and that users should "beware." I have nothing to do with it," he wrote, signing his name in a post on Instagram. Tom Hanks condemned a dental promotion using his name and likeness to promote their plan. A representative for Hanks did not immediately return Fox News Digital's request for comment. It is unclear where the image originated. Hanks recently gave his own two cents on artificial intelligence – noting that its use in the industry is nothing new but has "always been" lingering. "The first time we did a movie that had a huge amount of our own data locked in a computer, literally what we looked like, was a movie called'The Polar Express,'" Hanks said on "The Adam Buxton Podcast" about his 2004 animated film that used the technology. Film preparation for "The Polar Express" included motion capture. "And we saw this coming.

Tom Hanks and wife Rita Wilson walked the Pre-Grammy GALA red carpet and discussed what they believe is the success to a great relationship after being married for 34 years. Hollywood heavy-hitter Tom Hanks is weighing in on the use of artificial intelligence in films, especially as he grows older and his name and likeness are still coveted. The "A Man Called Otto" actor gave his opinion on AI – noting that its use in the industry is nothing new and has rather "always been" lingering. "The first time we did a movie that had a huge amount of our own data locked in a computer, literally what we looked like, was a movie called'The Polar Express,'" Hanks said on "The Adam Buxton Podcast" about his 2004 animated film. "And we saw this coming. We saw that there was going to be this ability to take 0s and 1s inside a computer and turn it into a face and a character. Now, that is only grown a billion-fold since then, and we see it everywhere. And I can tell you that there is discussions going on in all of the guilds, all of the agencies and all of legal firms in order to come up with the legal ramifications of my face and my voice – and everybody else's – being our intellectual property," he added.

Two-time Oscar-winner Tom Hanks could live forever on the big screen with the help of artificial intelligence. Hanks, 66, claims to have predicted the rise of AI in the film industry 20 years ago and believes it will recreate him in films long after he is dead. He said the powers of AI came to him when making the 2004 computer-animated movie The Polar Express when he was reimagined as a digital train conductor. 'What is a bonafide possibility right now is - if I wanted to - I could get together and pitch a series of seven movies that would star me in them in which I would be 32 years old from now until kingdom come,' Hanks said, speaking with British comedian Adam Buxton. 'I can tell you that there's discussions going on in all of the guilds, all of the agencies, and all of the legal firms in order to come up with the legal ramifications of my face and my voice and everybody else's being our intellectual property,' Hanks said.