Datasets may contain observations with multiple labels. If the labels are not mutually exclusive, and if the labels vary greatly in frequency, obtaining a sample that includes sufficient observations with scarcer labels to make inferences about those labels, and which deviates from the population frequencies in a known manner, creates challenges. In this paper, we consider a multivariate Bernoulli distribution as our underlying distribution of a multi-label problem. We present a novel sampling algorithm that takes label dependencies into account. It uses observed label frequencies to estimate multivariate Bernoulli distribution parameters and calculate weights for each label combination. This approach ensures the weighted sampling acquires target distribution characteristics while accounting for label dependencies. We applied this approach to a sample of research articles from Web of Science labeled with 64 biomedical topic categories. We aimed to preserve category frequency order, reduce frequency differences between most and least common categories, and account for category dependencies. This approach produced a more balanced sub-sample, enhancing the representation of minority categories.

Verifying uniform conditions over continuous spaces through random sampling is fundamental in machine learning and control theory, yet classical coverage analyses often yield conservative bounds, particularly at small failure probabilities. We study uniform random sampling on the $d$-dimensional unit hypercube and analyze the number of uncovered subcubes after discretization. By applying a concentration inequality to the uncovered-count statistic, we derive a sample complexity bound with a logarithmic dependence on the failure probability ($δ$), i.e., $M =O( \tilde{C}\ln(\frac{2\tilde{C}}δ))$, which contrasts sharply with the classical linear $1/δ$ dependence. Under standard Lipschitz and uniformity assumptions, we present a self-contained derivation and compare our result with classical coupon-collector rates. Numerical studies across dimensions, precision levels, and confidence targets indicate that our bound tracks practical coverage requirements more tightly and scales favorably as $δ\to 0$. Our findings offer a sharper theoretical tool for algorithms that rely on grid-based coverage guarantees, enabling more efficient sampling, especially in high-confidence regimes.

For four decades statistical physics has been providing a framework to analyse neural networks. A long-standing question remained on its capacity to tackle deep learning models capturing rich feature learning effects, thus going beyond the narrow networks or kernel methods analysed until now. We positively answer through the study of the supervised learning of a multi-layer perceptron. Importantly, (i) its width scales as the input dimension, making it more prone to feature learning than ultra wide networks, and more expressive than narrow ones or ones with fixed embedding layers; and (ii) we focus on the challenging interpolation regime where the number of trainable parameters and data are comparable, which forces the model to adapt to the task. We consider the matched teacher-student setting. Therefore, we provide the fundamental limits of learning random deep neural network targets and identify the sufficient statistics describing what is learnt by an optimally trained network as the data budget increases. A rich phenomenology emerges with various learning transitions. With enough data, optimal performance is attained through the model's "specialisation" towards the target, but it can be hard to reach for training algorithms which get attracted by sub-optimal solutions predicted by the theory. Specialisation occurs inhomogeneously across layers, propagating from shallow towards deep ones, but also across neurons in each layer. Furthermore, deeper targets are harder to learn. Despite its simplicity, the Bayes-optimal setting provides insights on how the depth, non-linearity and finite (proportional) width influence neural networks in the feature learning regime that are potentially relevant in much more general settings.

June Squibb sparkles opposite Cynthia Nixon in a futuristic drama, and Michelle Williams loses her way in Eugene O'Neill's Pulitzer Prize winner. Appropriately enough, Jordan Harrison's déjà-vu-inducing "Marjorie Prime" has been here before. The Off Broadway theatre Playwrights Horizons produced the poignant sci-fi play about hyperrealistic re-creations of the dead--so-called Primes, which are used as a supportive technology for the bereaved--in Anne Kauffman's spirited, delicately comic production, back in 2015. Lois Smith, then eighty-five years old, played Marjorie, a woman struggling with dementia. It's the early twenty-sixties, and so Marjorie is attended by a holographic Prime of her husband, Walter, who tells her stories from her own life.

In the same month that Grok opted for a second Holocaust over vaporizing Elon Musk's brain, the AI chatbot is on the fritz again. Following the Bondi Beach shooting in Australia during a festival to mark the start of Hanukkah, Grok is responding to user requests with inaccurate or completely unrelated info, as first spotted by . Grok's confusion seems to be most apparent with a viral video that shows a 43-year-old bystander, identified as Ahmed al Ahmed, wrestling a gun away from an attacker during the incident, which has left at least 16 dead, according to the latest news reports . Grok's responses show it repeatedly misidentifying the individual who stopped one of the gunmen. In other cases, Grok responds to the same image about the Bondi Beach shooting with irrelevant details about allegations of targeted civilian shootings in Palestine.

Kindle's in-book AI assistant can answer all your questions without spoilers But the catch is authors and publishers can't opt out of having this feature in their works. If you're several chapters into a novel and forgot who a character was, Amazon is hoping its new Kindle feature will jog your memory without ever having to put the e-reader down. This feature, called Ask this Book, was announced during Amazon's hardware event in September, but is finally available for US users on the Kindle iOS app. According to Amazon, the feature can currently be found on thousands of English best-selling Kindle titles and only reveals information up to your current reading position for spoiler-free responses. To use it, you can highlight a passage in any book you've bought or borrowed and ask it questions about plot, characters or other crucial details, and the AI assistant will offer immediate, contextual, spoiler-free information.

'Hero' who wrestled gun from Bondi shooter named as Ahmed al Ahmed A hero bystander who was filmed wrestling a gun from one of the Bondi Beach attackers has been named as 43-year-old Ahmed al Ahmed. Video verified by the BBC showed Mr Ahmed run at the gunman and seize his weapon, before turning the gun round on him, forcing his retreat. Mr Ahmed, a fruit shop owner and father of two, remains in hospital, where he has undergone surgery for bullet wounds to his arm and hand, his family told 7News Australia. Eleven people were killed in the shooting on Sunday night, as more than 1,000 people attended an event to celebrate Hanukkah. The attack has since been declared by police as a terrorist incident targeting the Jewish community.

This material may not be published, broadcast, rewritten, or redistributed. Quotes displayed in real-time or delayed by at least 15 minutes. Market data provided by Factset . Powered and implemented by FactSet Digital Solutions . Mutual Fund and ETF data provided by Refinitiv Lipper .

Australian police say a shooting at Bondi Beach, which killed 12 people - including one gunman - targeted the Jewish community on the first day of Hanukkah. Twenty-nine people were injured, with a second gunman in critical condition. Drone footage appears to show a gunman firing from a bridge in a nearby carpark. In the wake of a recent fatal shark attack, the BBC is off the coast in Sydney to learn how authorities are trying to protect people. The BBC's Katy Watson was in the courtroom as Erin Patterson was sentenced to life.

Researchers theorize that they might be imitating snakes. Breakthroughs, discoveries, and DIY tips sent every weekday. A caterpillar-looking bug hangs out on a stem, minding its own business. Suddenly, forceps emerge, moving towards the creature. As soon as they touch the chunky insect, it hisses and whips its body side-to-side.