One of the key challenges in machine learning is to find interpretable representations of learned functions. The Möbius transform is essential for this purpose, as its coefficients correspond to unique importance scores for sets of input variables. This transform is closely related to widely used game-theoretic notions of importance like the Shapley and Bhanzaf value, but it also captures crucial higher-order interactions.

TL;DR: Get a lifetime license to Windows 11 Pro for just 14.97 and unlock a sleek interface, pro-level security, and AI-powered productivity. Need a new laptop but don't have the budget to buy one? We've found the next best thing: updating your operating system. If you've got an old PC that could use an upgrade, a lifetime license to Microsoft Windows 11 Pro is now just 14.97. But you'll want to act fast because this deal ends June 1 at 11:59 p.m. PT.

TL;DR: Give your productivity a big boost with a lifetime license to Microsoft Office Home & Business for Mac 2021, now 69.97 (reg. There's a reason Microsoft Office is still around in 2025 -- these apps really work. They range from classics like Word and Excel, which have been around since the days of chunky desktop computers, to newer additions like Teams and OneNote. Right now, you can get them forever with this lifetime license to Microsoft Office Home & Business for Mac 2021, on sale for 69.97 (reg. Give your Apple computer an upgrade for under 75 with this Microsoft Office Home & Business for Mac 2021 license.

TL;DR: Never run out of things to watch with this lifetime subscription to BitMar Streaming Content-Finder, now just 14.99 (reg. BitMar is a streaming content finder ready to help you discover free entertainment all over the web -- from movies and shows to songs and more -- and right now, a lifetime subscription to this helpful tool is just 14.99 with code BITMAR5 until June 1. If you're sick of wasting hours hunting down things to watch, it's time to swap to BitMar. It's your very own AI-powered free content finder -- it scours the web to find you millions of free movies, TV shows, videos, music, and more. And unlike all the expensive streaming services you pay for monthly, you pay once for BitMar and enjoy it forever.

At Google I/O 2025, the tech company announced a ton of new AI features, and one of the most interesting is a virtual clothing try-on tool. The Google Shopping "Try it on" feature lets users upload a photo of themselves and then virtually try on clothes, basically the IRL version of the Clueless closet millennials have been dreaming about since 1995. Or, as Mashable Shopping Reporter Haley Henschel put it, "Google's latest shopping feature makes Cher Horowitz's computerized closet a reality." Almost as soon as the feature was released, users started trying to "jailbreak" the tool, which is becoming a fun little tradition for tech writers every time a new AI model or tool is released. On Friday, The Atlantic reported that "Google's new AI shopping tool appears eager to give J.D. Vance breasts."

On May 19, President Donald Trump and First Lady Melania Trump beamed to press and allies as they signed the administration's first major piece of tech regulation, the bipartisan Take It Down Act. It was seen as a win for those who have long been calling on the criminalization of NDII, or the nonconsensual distribution of intimate images, and a federal pathway of redress for victims. Cliff Steinhauer, director of information security and engagement at the National Cybersecurity Alliance, explained it may be a needed kick in the pants to a lethargic legislative arena. "I think it's good that they're going to force social media companies to have a process in place to remove content that people ask to be removed," he said. "This is kind of a start; to build the infrastructure to be able to respond to this type of request, and it's a really thin slice of what the issues with AI are going to be."

What started with Microsoft Build, continued with Google I/O, and ended with Anthropic Code with Claude, plus a big hardware interruption from OpenAI, the week has finally come to a close. AI announcements from the developer conferences jockeyed for news dominance this week, but OpenAI managed to make headlines without an event by announcing that it's going to start making AI devices with iPhone designer Jony Ives We'll get to that, plus all the major AI features from Google and Microsoft and details about Anthropic's new models. Take a look at the AI news of the week, then enjoy a well-deserved weekend. On Thursday, Anthropic introduced the next generation of its Claude models: Opus 4 and Sonnet 4. Claude Opus 4 is the bigger, more powerful model, while Sonnet 4 is smaller and nimbler. Anthropic said both models scored higher than their rivals on agentic AI benchmarks and said they're particularly good for coding and reasoning tasks.

The inversion of diffusion model sampling, which aims to find the corresponding initial noise of a sample, plays a critical role in various tasks. Recently, several heuristic exact inversion samplers have been proposed to address the inexact inversion issue in a training-free manner. However, the theoretical properties of these heuristic samplers remain unknown and they often exhibit mediocre sampling quality. In this paper, we introduce a generic formulation, Bidirectional Explicit Linear Multi-step (BELM) samplers, of the exact inversion samplers, which includes all previously proposed heuristic exact inversion samplers as special cases.

Ukrainian officials have renewed their calls for more sanctions on Russia after Russian forces launched dozens of attack drones and ballistic missiles at Kyiv overnight ahead of a second exchange of soldiers and civilians. Ukraine's military on Saturday said overnight attacks launched from multiple Russian regions used 250 drones and 14 ballistic missiles to hit Kyiv, damaging several apartment buildings and a shopping mall, and injuring at least 15 people. Sites in the Ukrainian regions of Dnipropetrovsk, Odesa and Zaporizhia were also hit, with Ukrainian forces saying six of the ballistic missiles were shot down by its air defences, along with 245 drones, many of which were said to be Iranian-designed. Oleh Syniehubov, head of Kharkiv's regional state administration, said on Saturday morning that four Ukrainians were killed and several others injured over the past 24 hours in the region as a result of multiple Russian attacks. Meanwhile, Russia's Ministry of Defence on Saturday said at least 100 Ukrainian drones attempted to strike Russian targets overnight.

In the literature of studying training dynamics of transformers, several simplifications are commonly adopted such as weight reparameter-ization, attention linearization, special initialization, and lazy regime.