A key strength of diffusion models lies in their flexibility, since their outputs can be controlled at sampling time through guidance. However, beyond simple cases such as conditional sampling, the target distribution is often left implicit, defined only through a sampling rule or a heuristic energy function. To address this, we propose Jeffrey guidance, a principled framework that extends diffusion-model control to applications beyond what standard guidance can express. It leverages Jeffrey's rule of conditioning to update marginal distributions towards a prescribed target, preserving the conditional structure and minimally perturbing the joint distribution. We first demonstrate Jeffrey guidance by targeting a prescribed embedding distribution. With Inception embeddings as the target, this leads to substantial reductions in FID on both CIFAR-10 and FFHQ. We further apply Jeffrey guidance to fairness on CelebA-HQ, updating an unconditional diffusion model to enforce independence between attributes.

Forecasting the evolution of complex dynamical systems remains a fundamentally challenging task, primarily due to pronounced nonlinear interactions, high-dimensional state spaces, and the concomitant requirement for rigorous and reliable uncertainty quantification. Contemporary reduced-order modelling (ROM) frameworks frequently exhibit inherent trade-offs among predictive accuracy, numerical stability, and interpretability, and thus often fail to achieve an optimal balance among these competing objectives. To address these limitations, we propose a framework for forecasting complex dynamical systems via a kernel autonomous ordinary differential equation approach based on Gaussian Processes and Quadratic Order Model Reduction. Our base method, the Gaussian Process Ordinary Differential Equations model, allows accurate short-term forecasting with uncertainty quantification, and it provably converges to the real autonomous equation in the smooth case. We integrate it with quadratic order reduced-order modelling and sphere projection for learning the latent dynamics efficiently while preserving stability. Numerical experiments demonstrate that our full model outperforms ROM forecasting methods such as Extended Dynamic Mode Decomposition, Bagging Optimised Dynamic Mode Decomposition and Linear and Nonlinear Disambiguation Optimisation in terms of accuracy or computational costs. These results demonstrate the potential of the framework as a robust and stable tool for forecasting complex dynamical systems with rigorous uncertainty quantification.

Today on, we take an early look at the SpaceX IPO and why you might find yourself among the investors without even realizing it. This week on, our hosts discuss SpaceX officially going public and who will benefit the most from it, as well as Apple's WWDC and the brand-new release of Siri AI. They also get into how Meta removed a face-recognition feature after a WIRED report exposed it--and later in the show: an investigation into how New York Knicks' owner James Dolan created an extensive surveillance system inside all of his Madison Square Garden properties. Write to us at [email protected] . You can always listen to this week's podcast through the audio player on this page, but if you want to subscribe for free to get every episode, here's how: If you're on an iPhone or iPad, open the app called Podcasts, or just tap this link . Before we start, two quick things. If you've been enjoying listening to the show, would appreciate it if you took a second to rate it in your app of choice. It really helps us reach more people. Second, if you have any questions related to tech, privacy, or politics that you would like me, Zoë, and Leah to take on, now is the time to submit them to [email protected] . It doesn't matter how big or how small, we want to hear from you and get you answers. I'm a little tired, but it's because I got to see Lionel Messi play soccer last night and score a goal on a penalty kick. It was a friendly of Argentina versus Iceland. You'll never guess who won. Is that an obvious thing? It's far from their first attempt, but it's going to stick this time. We're also taking an early look at the SpaceX IPO this week, which is slated to become the world's largest IPO of all time. We'll get into who is slated to benefit the most. Elon Musk, who is already the world's richest man, but on track to become even richer and why you might find yourself among the investors without even realizing it. And in case you missed it, WIRED reporters recently uncovered that Meta had silently embedded code that would power a face-recognition system for its smart classes in the Meta AI app on millions of people's phones.

Crowding the gates of a major health care conference, protesters called for Palantir to be booted out of the UK's National Health Service over privacy concerns and political grievances. Protesters wearing hospital gowns and wielding signs gathered outside a UK health care conference on Thursday to object to a deal between the country's National Health Service and American software company Palantir . At 8 am local time, the group, around 80 people in total, crowded the entryway to the NHS ConfedExpo in Manchester. They wanted to appeal to NHS leadership to terminate a contract worth up to $440 million over concerns around national security, data privacy, and the company's political affiliations . The contract, which includes access to Palantir's data analytics and artificial intelligence services, is intended to run until 2031 but includes a break clause that permits the government to withdraw the agreement next February.

OpenAI is in the midst of overhauling ChatGPT . The goal is to transform the chatbot's simple interface into a personalized AI agent that can handle tasks in every facet of your personal and professional life. The company has taken to calling this new product, privately and publicly, a "super app." The all-in-one platform represents one of the biggest bets OpenAI has ever made, and one engineering leader now holds enormous sway over whether it pays off: Thibault Sottiaux. Last month, Sottiaux was appointed OpenAI's head of core products, overseeing both ChatGPT and Codex, as well as combining them into the future super app.

Elon Musk's SpaceX valued at nearly $1.8tn ahead of record share sale SpaceX has raised $75bn (£56bn) from financial firms ahead of it becoming a publicly traded company on Friday, in what is expected to be the highest-value stock listing in history. In a filing with the US Securities and Exchange Commission, the space exploration and artificial intelligence (AI) company said it had sold $75bn in shares priced at $135 each. The share price matches the estimate SpaceX gave last week, leaving the firm's expected initial stock market value to be nearly $1.8tn. At that value, chief executive Elon Musk - already the richest man in the world - is set to become the world's first trillionaire. Once shares start trading, their value could rise or fall depending on how many shares are made available for sale, and how strong the demand is for those shares.

Activists raised a 40-foot-tall inflatable Elon Musk in Manhattan to draw attention to the risk he allegedly poses to investors. It was surrounded by black banners with statements alleging "Grok makes AI child porn" and "SpaceX owns Grok," referring to the Musk-owned AI chatbot whose image-generation tool was used to create a flood of sexualized images of minors earlier this year. Masked attendants stood nearby, handing out flyers with additional information, but they would not speak with the media. The demonstration was helmed by Safe AI Now (SAIN), which describes itself as "a coalition of faith leaders, family advocates, child development experts, online safety organizations, educators, legal professionals, technologists, and concerned citizens," ahead of SpaceX's initial public offering on Friday. The location was strategically chosen--right in front of the Nasdaq and the offices of JP Morgan, one of the banks participating in the IPO .

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Elon Musk delivers a speech during the World Economic Forum Annual Meeting in Davos, Switzerland, on 22 January 2026. Elon Musk delivers a speech during the World Economic Forum Annual Meeting in Davos, Switzerland, on 22 January 2026. Musk's xAI fired engineer for raising concerns about Grok chatbot, lawsuit claims A former engineer at Elon Musk's xAI who now heads a thinktank focused on AI safety filed a lawsuit claiming he was fired from the SpaceX subsidiary for raising concerns about the risks artificial intelligence poses to humanity. Devin Kim claims in the lawsuit filed in California state court on Tuesday that his efforts to place guardrails on the development of the chatbot Grok made him a target for company leadership. The lawsuit comes ahead of SpaceX's planned initial public offering, the largest ever, on Friday.

Summer Game Fest just wrapped up its sixth year and, like a beautifully cel-shaded version of The Blob, the show just keeps on growing. The official Summer Game Fest 2026 showcase took place on June 5, but the surrounding buffet of new game reveals, release date announcements, review opportunities and developer spotlights actually ran from June 1 all the way to June 9. That's more than an entire week of near-constant video game news and trailers to consume, and here we've gathered absolutely all of it in one tidy but lengthy package. First up, a collection of Engadget's previews and reporting from Summer Game Fest Play Days in Los Angeles, which ran from June 6-8: Control Resonant's take on New York feels like the Backrooms Silent Hill Townfall brings atmospheric horror to '90s Scotland with incredible attention to detail Saw: Genesis looks the most fun when you're the murderous mastermind Alien: Isolation 2 keeps the classic horror game's uncompromising approach to raising tension Spyro: A Realm Beyond sees the '90s purple dragon make a big comeback Be like Carl from Summer House and get in the MIX with another high-energy stream filled with great-looking upcoming indie games, gathered by the folks at the Media Indie Exchange. The MIX hosts a smattering of annual online indie showcases, and alongside in-person events, they've been spreading the good gaming word for the past 10 years.