In practical instances of nonconvex matrix factorization, the rank of the true solution $r^{\star}$ is often unknown, so the rank $r$ of the model can be overspecified as $r>r^{\star}$. This over-parameterized regime of matrix factorization significantly slows down the convergence of local search algorithms, from a linear rate with $r=r^{\star}$ to a sublinear rate when $r>r^{\star}$. We propose an inexpensive preconditioner for the matrix sensing variant of nonconvex matrix factorization that restores the convergence rate of gradient descent back to linear, even in the over-parameterized case, while also making it agnostic to possible ill-conditioning in the ground truth. Classical gradient descent in a neighborhood of the solution slows down due to the need for the model matrix factor to become singular. Our key result is that this singularity can be corrected by $\ell_{2}$ regularization with a specific range of values for the damping parameter. In fact, a good damping parameter can be inexpensively estimated from the current iterate. The resulting algorithm, which we call preconditioned gradient descent or PrecGD, is stable under noise, and converges linearly to an information theoretically optimal error bound. Our numerical experiments find that PrecGD works equally well in restoring the linear convergence of other variants of nonconvex matrix factorization in the over-parameterized regime.

The start of any season of Doctor Who is important, doubly so when there's a new co-star to introduce. "The Robot Revolution" has to get us to fall in love with Belinda Chandra (Varada Sethu), ensnare new fans and keep existing ones hooked. Especially since it's the second of two series that Disney paid for, meaning it's got to do well enough to keep the money flowing. It's an awkward teenage date, with Alan clearly trying to win the heart of his beau by buying her one of those star adoption certificates. In 2025, Belinda is now a nurse at a busy London hospital where, in the background, the Doctor is searching for her.

Netflix has started testing a new search feature powered by OpenAI that can help customers find movies and shows to watch, according to Bloomberg. The streaming service has reportedly given select users in Australia and New Zealand the option to use the tool. It will allow users to search for terms other than a specific show's title, an actor's name or the genre they want to watch. Bloomberg says it will give them a way to search for content using more specific terms, like their mood. Presumably, that means the service can surface dramatic shows for a search query that says "sad," and seeing as it's powered by generative AI, users will most likely be able to use natural language in their search terms.

On April 14, Waymo will start testing its robotaxi technology outside the US for the first time. Waymo is taking it slow and will not be operating them without a driver behind the wheel yet, however. Drivers from Tokyo taxi company Nihon Kotsu Co. will be driving the cars around Chiyoda, Minato, Shinjuku and four other wards in the Japanese capital. The cameras and radars equipped on the I-PACE vehicles will collect data on Tokyo's roads, which are typically narrower than roads in the US. They'll provide the company with information on local infrastructure, road conditions and the driving patterns of locals.

This photo posted by DOGE on Feb. 11, 2025, shows shelving and cardboard boxes which DODGE says workers at the underground mine facility use to store federal worker retirement papers. The White House announces that it will implement AI technology to improve efficiency in federal records keeping. HISTORIC EFFICIENCY: Fox News Digital has learned that the U.S. Office of Personnel Management (OPM) will post an updated Privacy Impact Assessment (PIA) at the close of business Wednesday that paves the way for artificial intelligence to improve government efficiency and enhance the federal record-keeping process. NOT IN KANSAS ANYMORE: The use of artifical intelligence to reimagine the classic film "The Wizard of Oz" will likely see mixed reactions from fans, experts told Fox News Digital. BAD-FAITH TACTICS: OpenAI escalated its legal battle with Elon Musk by countersuing the Tesla and xAI CEO, claiming in a lawsuit he "has tried every tool available to harm" the company.

The Israeli spyware maker NSO Group has been on the US Department of Commerce "blacklist" since 2021 over its business of selling targeted hacking tools. But a WIRED investigation has found that the company now appears to be working to stage a comeback in Trump's America, hiring a lobbying firm with the ties to the administration to make its case. As the White House continues its massive gutting of the United States federal government, remote and hybrid workers have been forced back to the office in a poorly coordinated effort that has left critical employees without necessary resources--even reliable Wi-Fi. And Elon Musk's so-called Department of Government Efficiency (DOGE) held a "hackathon" in Washington, DC, this week to work on developing a "mega API" that could act as a bridge between software systems for accessing and sharing IRS data more easily. Meanwhile, new research this week indicates that misconfigured sexual fantasy-focused AI chatbots are leaking users' chats on the open internet--revealing explicit prompts and conversations that in some cases include descriptions of child sexual abuse.

FlashBot Arm is designed to interact more like a human. As you navigate through your daily routine, whether it's grabbing a meal at a restaurant, visiting a healthcare center or checking into a hotel, you might soon encounter a new kind of robot at these places. It's called the FlashBot Arm, and Pudu Robotics is behind it. This semi-humanoid robot combines advanced manipulation capabilities with intelligent delivery features, making it a significant innovation in the service robotics sector. Unlike traditional robots, the FlashBot Arm is designed to interact with its environment in a more human-like way.

By pretty much every objective measure, HBO's adaptation of the hit postapocalyptic video game The Last of Us has been a roaring success. Never before has a video game narrative been molded into Emmy nominations and such warm reception among respectable critics, industry darlings, and people who have no idea what the term "one-shotting" means. You'd think that the devotees who first fell in love with the game back when it was originally released in 2013 would be toasting the cultural ascendance of their favorite medium--and especially how the story's complicated morality has impacted those who've never picked up a controller. And yet, for as long as the show has been on television, its most dogmatic fans have been caught up in a controversy of much inferior consequence: Specifically, they're furious that Bella Ramsey doesn't look much like Ellie. On the most basic level, this observation is correct.

With the second season of The Last of Us returning to our screens, it might be comforting to think that the show is purely fictional. But believe it or not, the show's haunting zombies aren't that far from reality. Real-life'zombie-making' fungi burrow into their host's flesh and manipulate their minds to turn them into hyperactive super spreaders. As it stands, these mind-warping parasites only affect certain insects. However, the stages of infection are eerily similar to those seen in the hit HBO show.

Doctor Who's second season on Disney kicked off Saturday with "The Robot Revolution." The season arc revolves around new companion Belinda Chandra (Varada Sethu) -- latest in a long tradition of reluctant (or "kidnapped") companions aboard the TARDIS. But that's just the surface level of an episode that contains a surprising number of homages for all its shiny newness, and a real-life story behind the scenes that changed Belinda's very name. The International Star Registry is one of many real-life companies claiming to give you naming rights for objects in space. Given that its services have been used to name stars for Queen Elizabeth II, King Charles III, and Princess Diana, this American company may be more well-known in the UK now.