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."

We ask: when do Bayesian model averaging (BMA) weights over decision trees carry sufficient epistemic information to justify committed exploitation of the averaging distribution? We answer this question in closed form for Bayesian decision trees (BDTs) with Dirichlet-Multinomial leaf models and a Catalan-exponential tree-size prior (Schetinin&Jakaite, 2025), establishing a complete non-asymptotic theory of rational commitment thresholds.

In a nutshell, the outcomes ought to be indistinguishable from random draws from the predictive distributions. In this paper, we review, extend, and bridge notions of calibration that have been proposed for classification and regression tasks. Particular emphasis is given to hierarchical relations between the various notions, as they apply to general real-valued data, continuous outcomes, count data, nominal classes, and binary outcomes. To highlight a number of contributions, we introduce the notion of modal calibration for nominal outcomes, we distinguish full, partial, and average calibration in this setting, and we show that double probability integral transform (PIT) calibration is logically independent of previously proposed concepts of calibration for discrete outcomes. Furthermore, we generalize extant results on concepts of calibration that are expressed in terms of properties or functionals of the predictive distributions, such as means, quantiles, or event probabilities. Throughout the paper, we illustrate the concepts and their hierarchical relations in worked examples, and we provide algorithmic tools that support the construction of instructive examples and counterexamples. Keywords: Auto-calibration, confidence calibration, diagnostic evaluation of probabilistic predictions, distributional properties, probability integral transform (PIT), reliability.

This paper investigates non-stationary online learning using the metric of interval regret, which requires an online algorithm to perform well over every time interval. We propose the first online learning algorithm that achieves an interval regret bound scaling with gradient variation, a fundamental measure of the cumulative change in online function gradients, which relates to various problem-dependent quantities and is closely connected to stochastic optimization and other problems. Our method employs a simple and efficient two-layer online ensemble structure that achieves strong theoretical guarantees. Specifically, it enjoys a regret bound that simultaneously adapts to various problem-dependent quantities while also preserving the minimax-optimal rate in the worst case. Moreover, recognizing the challenge of hyperparameter tuning, we introduce a Lipschitz- and smoothness-agnostic variant that automatically adapts to these potentially unknown constants. This is primarily enabled by a novel Lipschitz-adaptive meta algorithm, which may be of independent interest. Beyond interval regret, our method also yields broader implications: it provides versatile bounds for interval dynamic regret, a stronger measure that competes with changing comparators over any interval, and yields the first piecewise characterization for stochastic extended adversarial optimization. Theoretical findings are validated by experiments.

Large Language Models remain plagued by hallucinations. Recent work has sought to tame their prevalence using statistical techniques based on conformal prediction, with both theoretical and empirical success. However, these methods operate in a post-hoc fashion, treating the sampling procedure itself as atomic and then surgically altering samples to remove hallucinated claims. This disconnect between filtering and generation can result in samples that are incoherent, inconsistent, or simply unlikely under the model itself. Moreover, post-hoc surgery is unable to shift probability mass towards more useful and helpful responses. To address these issues, we propose to instead sample from approximations to an LLM posterior, where the conditioning event corresponds to a calibrated, high-scoring region. We develop a calibration procedure tailored to the setting of conditional sequential generation that effectively identifies this region and achieves target risk control. Empirically, we apply our method to case studies focused on open-ended biography generation and mathematical problem solving; compared to prior work, we obtain the same statistical guarantees, with higher downstream utility.