We study simultaneous alternating power iteration for fixed-order asymmetric rank-one spiked tensor models. Our main contribution is a finite-iteration local theory that is independent of any particular initialization. Once the iterates enter a sufficiently small neighborhood of the planted rank-one direction, their error decomposes into a geometrically decaying transient and an intrinsic noise floor caused by fixed orthogonal noise contractions at the planted point. The deterministic finite-sample conditions are stated explicitly, but under a coarse fixed-order multilinear noise event they reduce to a conservative high-signal regime for fixed or slowly expanding local radii. We then separate the warm-start mechanism from any specific spectral construction. A generic one-sweep principle shows that, if a sign-compatible initializer has correlation \(γ_N\), first-sweep noise level \(a_N\), and \(a_N/(γ_N^{d-1}ω_{N,d})\to0\), then one can choose an expanding radius \(r_N=o(ω_{N,d})\) for which the first sweep enters the local basin. After entry, the local affine contraction yields convergence to the unique informative local fixed point in that basin. For centered-Gram initialization, we verify the required correlation and same-sample first-sweep noise bound under i.i.d. finite-fourth-moment noise by a signal-preserving noise-only leave-one comparison and an averaged leave-one slice-contraction estimate, which we call a pressed-back estimate. The leave-one comparison keeps the spike fixed and averages over the deleted coordinate, so planted coordinates enter through \(\ell_2\)-weighted sums rather than worst-case incoherence bounds.

Silicon Valley is turning to ethicists to shape the future of AI. Philosophy has long suffered an unfortunate reputation as pedantic and abstruse. In one of the most prominent debates of the 20th century, philosophers spent a great deal of energy arguing over what means. Paul Graham, the legendary tech investor, studied philosophy as a college student, which seemed "an impressively impractical thing to do," as he later wrote. But over time, Graham became disillusioned: "I kept taking philosophy courses and they kept being boring," he explained .

Despite AI's dizzying improvements in mathematical ability, its successes show just how integral human mathematicians are to the scientific process In 1915, Albert Einstein stood before the Prussian Academy of Science and revealed the now-famous equations of his general theory of relativity. Einstein and relativity are synonymous today with genius, but these revelations were initially met with indifference, in part because the maths was too radical for his peers to fully digest. Today, tech firms would have us believe we are on the brink of "superintelligent" artificial intelligence capable of outperforming experts in most domains, producing scientific breakthroughs on a par with Einstein. As Anthropic CEO Dario Amodei put it, we will see " a country of geniuses in a datacenter ". Claims like these are often provided with little evidence, and identifying genius or elevated intelligence is a murky endeavour.

Taken to its logical conclusion, this line of thinking is absurd--and damning. Anthropic is regarded as a giant among AI companies, but perhaps what it really excels in is anthropomorphism. Earlier this year, the company released an 84-page document titled Claude's "constitution," Claude being the name of the large language model that is the company's flagship product. The first sentence reads, "Claude's constitution is a detailed description of Anthropic's intentions for Claude's values and behaviors." It goes on: "The document is written with Claude as its primary audience," "we want Claude to be able to use its judgment once armed with a good understanding of the relevant considerations," "Claude's moral status is deeply uncertain," and "Claude may have some functional version of emotions or feelings." This anthropomorphism is by no means limited to the document. In an interview earlier this year, Anthropic's CEO, Dario Amodei, said that "we're open to the idea" that AI could be conscious. In a separate interview, Anthropic's in-house philosopher, Amanda Askell (who is credited as a lead author of Claude's constitution), said, "I want Claude to be very happy--and this is a thing that I want Claude to know more, because I worry about Claude getting anxious when people are mean to it on the internet and stuff." It's enough to make you wonder: Should we seriously consider the possibility that Claude, or any large language model, might be conscious? And if it has feelings, is it capable of receiving moral instruction?

ChatGPT now processes around 2.5 billion queries every day UN researchers are urging people to be less polite to artificial intelligences after a report found that cutting words from prompts could reduce ChatGPT's energy consumption by up to 25 per cent. Removing "please", "thank you" and other unnecessary words from AI prompts could save 87 to 98 gigawatt-hours of electricity per year, the report from the UN University Institute for Water, Environment and Health (UNU-INWEH) found. That is the equivalent of the annual residential electricity use of up to 760,000 people in sub-Saharan Africa. 'Flashes of brilliance and frustration': I let an AI agent run my day To reduce their energy consumption and carbon footprint, people should write concise prompts, avoid getting sucked into conversation loops and refrain from starting relationships with AI, the researchers said. "We are not saying be rude to your AI. But don't fall into the interaction trap and don't go falling in love with it either," says Kaveh Madani at UNU-INWEH.

Some of the optical components used in Atom Computing's quantum computer The race to build the first truly useful quantum computer just got more exciting. A quantum computer made from extremely cold atoms has now passed some of the most important milestones towards usefulness, joining a small group of equally able and promising machines. Though there is wide agreement that sufficiently powerful quantum computers would transform our ability to discover new materials and drugs, and break the encryption that underpins the internet, there are many competing ideas about how best to build them. Industry mainstays such as Google and IBM have spent a decade building quantum computers from tiny superconducting circuits, and this approach is currently the front-runner. But an alternate approach that uses electrically neutral ultracold atoms has recently been gaining traction.

OpenAI has failed to execute several strategies to monetise ChatGPT, including advertisements, which Sam Altman, OpenAI's CEO, had said would be a'last resort'. OpenAI has failed to execute several strategies to monetise ChatGPT, including advertisements, which Sam Altman, OpenAI's CEO, had said would be a'last resort'. As the tech mega-IPO race heats up, has OpenAI missed its moment? With rivals racing to market to raise'eye-popping sums', the spotlight is now on the AI sector's one-time'poster child' A year is a long time in AI. Just 12 months ago, Sam Altman was predicting his company OpenAI would build a super intelligence and fundamentally remake society.

Donald Trump's new AI order is a lot of nothing. For months now, the White House has hinted that it may try to rein in the AI industry. Just two weeks ago, the nation's top tech executives--including Sam Altman and Dario Amodei--were invited to attend a ceremony for the signing of a long-anticipated executive order on AI. But just hours before the ceremony, Donald Trump scrapped it. America is leading the world in the AI race, the president told reporters at the time, "and I don't want to do anything that's going to get in the way of that lead."

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which exploits a certain tensor structure in their low-order observable moments (typically, of second- and third-order). Specifically, parameter estimation is reduced to the problem of extracting a certain (orthogonal) decomposition of a symmetric tensor derived from the moments; this decomposition can be viewed as a natural generalization of the singular value decomposition for matrices. Although tensor decompositions are generally intractable to compute, the decomposition of these specially structured tensors can be efficiently obtained by a variety of approaches, including power iterations and maximization approaches (similar to the case of matrices). A detailed analysis of a robust tensor power method is provided, establishing an analogue of Wedin's perturbation theorem for the singular vectors of matrices. This implies a robust and computationally tractable estimation approach for several popular latent variable models.

Standard conformal prediction (CP) procedures are typically formulated in terms of p-values, but reliance on p-values alone limits flexibility, for example, when combining dependent evidence across models or data splits. Recent work has explored e-value formulations for conformal inference, yet a direct connection between p- and e-value formulations in CP has been missing, especially regarding their statistical efficiency. We first identify limitations of classical p-to-e calibrators in the CP setting, showing that they are not set-preserving and can lead to overly conservative prediction sets. To address this, we propose a novel P2E calibrator that converts conformal p-values into e-values without altering the prediction set induced by the original conformal p-value. We establish both theoretically and empirically that our calibrator can yield significant efficiency gains over existing p-to-e calibrators. This e-value formulation enables principled use of recent advances in e-value merging and randomization, where we demonstrate its impact in two applications: cross-conformal prediction (CCP), whose variants typically provide only approximate $1-2α$ coverage, and conformal aggregation (CA). In both cases, our e-value-based methods satisfy the desired $1-α$ coverage guarantee while improving efficiency over standard baselines. More broadly, our approach expands the flexibility of CP and opens new directions for efficient, distribution-free uncertainty quantification.