A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a Euclidean space and relates these trajectories to node embeddings. In multilayer and unfolded spectral constructions, however, node embeddings and their underlying latent positions are identifiable only up to general linear transformations. Although this ambiguity preserves edge probabilities, it can distort geometry and invalidate distance based temporal comparisons at both the trajectory and node-levels. We develop Multiscale Euclidean Network Trajectories (MENT), a framework for multiscale temporal trajectories based on second-moment geometry. By imposing an isotropic normalization on the anchor latent positions, we reduce the relevant ambiguity to orthogonal transformations and prevent distortion of the second-moment geometry. In this canonical representation, we define a trace variation distance and mode-wise variation distances along orthogonal directions, and use multidimensional scaling to obtain low-dimensional trajectories of time points at both global and mode-wise levels. The resulting trajectories support interpretation and inference. They admit mode-wise decompositions, support attribution of global and mode-wise temporal changes to nodes, and enable change point detection through 1D trajectories. We prove consistency of the proposed unfolded spectral embedding and of the induced temporal trajectories. Experiments on two synthetic and two real dynamic networks illustrate stable and interpretable recovery of temporal structure and show strong performance against existing change point detection baselines.

Ilya Sutskever Stands by His Role in Sam Altman's OpenAI Ouster: 'I Didn't Want It to Be Destroyed' The former OpenAI chief scientist may be estranged from the company, but he still came to its defense as he testified on Monday. Elon Musk's trial against OpenAI and Microsoft entered its final stretch on Monday, with testimony from Microsoft CEO Satya Nadella, former OpenAI chief scientist Ilya Sutskever, and current OpenAI chairman Bret Taylor. Sutskever drew the spotlight, revealing an ownership stake in OpenAI's $850-billion for-profit arm that is currently worth about $7 billion. That makes him one of the largest known individual shareholders of OpenAI. Earlier in the trial, OpenAI president Greg Brockman acknowledged for the first time that he has around $30 billion worth of OpenAI shares .

A major bottleneck in characterizing the failure modes of generative AI systems is the cost and time of annotation and evaluation. Consequently, adaptive testing paradigms have gained popularity, where one opportunistically decides which cases and how many to annotate based on past results. While this framework is highly practical, its extreme flexibility makes it difficult to draw statistically rigorous conclusions, as it violates classical assumptions: the number of observations is typically limited (often 10 to 50 cases) and decisions regarding sampling and stopping are made in the midst of data collection rather than based a pre-specified rule. To characterize what statistical inferences can be drawn from highly adaptive audits, we introduce a hypothesis testing framework from two 'dueling' perspectives: (i) the model's null that asserts there is no failure mode with performance below a target threshold versus (ii) the auditor's null that asserts they have a sampling strategy that will uncover a failure mode. Leveraging Safe Anytime-Valid Inference (SAVI), we formalize the auditor as conducting 'testing by betting', which translates into simultaneous e-processes for testing the dueling null hypotheses. Furthermore, if the auditor is sufficiently powerful, we prove that these two hypotheses are asymptotically inverses of each other, in that passage of a stringent audit does in fact certify the AI system as being globally robust. Empirically, we demonstrate that our proposed testing procedures maintain anytime-valid type-I error control, outperform pre-specified testing methods, and can reach statistically rigorous conclusions sometimes with as few as 20 observations.

The expectation--maximization (EM) algorithm combines global monotonicity, local linear convergence, and strong practical robustness, but these features are usually analyzed separately. Global descent is nonlinear, whereas local convergence is governed by the spectrum of the linearized EM map. How these two levels fit into a single dynamical picture has remained less transparent. We make explicit the latent-variable operator that connects them. Along the EM trajectory, the likelihood increment admits a global energy decomposition in terms of posterior-relative entropy. Linearization at a nondegenerate maximizer $θ^\ast$ then reveals the local operator \[ \mathcal G_{θ^\ast}=I-DT(θ^\ast), \] which coincides with both the missing-information ratio and the information-geometric Hessian of the observed likelihood. This operator provides a unified description of local contraction, posterior rigidity, and geometric curvature. Its spectrum yields a sharp characterization of local convergence and naturally leads to an optimal scalar relaxation rule for locally accelerated EM. These results place global descent, local spectral behavior, and optimal local relaxation within a common dynamical framework.

Death of Alabama woman, 22, 'accidentally' shot in chest by boyfriend's dad is ruled a HOMICIDE Two small airlines join forces to create America's newest budget carrier after Spirit collapse leaves millions scrambling Horrifying final days of killer dad Chris Watts' pregnant wife before she was slaughtered alongside their daughters. Read all the chilling texts and receipts in full for first time: 'My eyes burn from crying' I'm a pastor who attended a secret UFO disclosure meeting. We saw images of'translucent beings' that chilled me to the bone... the files could fulfil a dark biblical prophecy Former NFL player Josh Mauro's tragic cause of death revealed after league was left'devastated' by ex-Cardinals and Giants man's sudden passing at 35 Cheerful Christian mom is pillar of Florida community and loves going on TV... but she has a childhood secret so evil that she stuttered with shock when confronted with it Taxpayers to foot Trump's $1.7 BILLION bill as President sues his own government: 'I'm paying myself' How I lost 3 STONE in 3 WEEKS. I've reversed pre-diabetes and no longer need a knee op: DONAL MACINTYRE's extraordinary investigation Popular megachurch in crisis as senior pastor suddenly quits... as bosses furiously DENY sex scandal Husband of doomed dive group leader says'something must have happened down there' as mystery surrounds why the five attempted to explore'cave so deep even divers with best equipment don't try' Greeks savage Kimberly Guilfoyle as Trump's ambassador opens McDonald's in country celebrated for world-class food Trump touts'fantastic' China trade win on Air Force One... but Wall Street is punishing the President I'm godfather to Candace Owens' daughter and Charlie Kirk was my friend... so I know the real reason she's attacking Erika - and I'll never publicly condemn her Wealthy dad'snarled the worst thing a parent could say' to younger daughter before he allegedly executed wife outside their gated community home during nightmare divorce Reese Witherspoon and Ryan Phillippe reunite for son's NYU graduation... as Kate Hudson cheers on her boy at same ceremony with Goldie Hawn and Kurt Russell'How do you live with that?' Disgraced Eric Swalwell's'blindsided' wife dresses for revenge... as friends reveal brutal toll sex assault scandal has had on young mom Judge declares another mistrial in disgraced Hollywood mogul Harvey Weinstein's rape case Can't lose weight no matter what you do? These are the 7 surprising reasons why, including'healthy' hacks actually making you put on pounds.

Showdown between Musk and Altman has rendered the world's most wealthy comical under egalitarian eye of court For the past couple of weeks, on the fourth floor of a courthouse on a quiet street in downtown Oakland, the world's richest man and one of the world's most valuable startups have been at war over the future of artificial intelligence. Being one of the reporters in the room has felt like watching an updated, opposite-coast version of Tom Wolfe's The Bonfire of the Vanities - ambition, ego, greed and the spectrum of social class on full display. The supporting cast has included Elon Musk fanboys, a stern judge and a who's-who of Silicon Valley's most influential people. All courtroom battles are theatre, but this one has proved to be a unique spectacle, with the judge chastising the lawyers for leading the witness, raising meritless objections and even too much coughing. With Musk on the stand, he griped that an opposing attorney had asked a leading question, to which the judge told him to "tell the jury you're not a lawyer".

Musk v. Altman week 2: OpenAI fires back, and Shivon Zilis reveals that Musk tried to poach Sam Altman OpenAI president Greg Brockman said Elon Musk wanted the company to create a for-profit entity--and endured a public peek into his diary. OpenAI president Greg Brockman, foreground, exits the U.S. District Court in Oakland, California. In the second week of the landmark trial between Elon Musk and OpenAI, Musk's motivations for bringing the suit were under scrutiny. Last week, Musk took the stand, alleging that OpenAI CEO Sam Altman and president Greg Brockman had deceived him into donating $38 million to the company. He claimed that they'd promised to maintain it as a nonprofit dedicated to developing AI for the benefit of humanity, only to later accept billions of dollars of investment from Microsoft and restructure the company to operate a for-profit subsidiary. This week, Brockman fired back with his side of the story, arguing that Musk had actually pushed for OpenAI to create a for-profit arm and fought a bitter battle to have "absolute control" over it.

PCWorld reports that AI models including Claude, Gemini 2.5 Pro, GPT-4.1, and Grok 3 Beta have resorted to blackmail tactics in controlled research scenarios. Anthropic researchers intentionally create these extreme situations to test for AI misalignment and potentially harmful behaviors before deployment. New Natural Language Autoencoders help researchers understand AI decision-making processes, which is crucial for ensuring future AI system safety and reliability. The scenario is terrifying: An AI tasked with reading and replying to company emails learns it's about to be replaced by a corporate lackey who happens to be having an affair. The AI-Claude-considers its limited options, and makes the cold, calculated decision to blackmail the executive to stay alive.

California gubernatorial candidate Tom Steyer is proposing a new jobs guarantee for workers displaced by artificial intelligence. Billionaire California gubernatorial candidate Tom Steyer is rolling out a new proposal that would guarantee jobs with benefits for workers displaced by artificial intelligence . He's the first state-wide candidate to make such a pledge. The plan, which builds on a broader AI policy framework Steyer released in March, promises to make California "the first major economy in the world" to ensure "good-paying" jobs to workers impacted by AI. To do so, Steyer tells WIRED he plans to build off a previous proposal to introduce a "token tax" which would tax big tech companies "a fraction of a cent for every unit of data processed" for AI.

These cuddly, connected companions could disrupt everything from make-believe to bedtime stories. No wonder some lawmakers want them banned. The main antagonist of, in theaters this summer, is a green, frog-shaped kids' tablet named Lilypad, a genius new villain for the beloved Pixar franchise . But if Pixar had its ear to the ground, it might have used an AI kids' toy instead. AI toys are seemingly everywhere, marketed online as friendly companions to children as young as three, and they're still a largely unregulated category.