Anthropic has usurped OpenAI as the world's most valuable artificial intelligence startup, soaring to a $965bn valuation ahead of expected public listings by the rival firms. Anthropic, the maker of the Claude family of chatbots, said on Thursday that it had raised $65bn from private investors after a fundraising round led by Altimeter Capital, Greenoaks, Dragoneer and Sequoia Capital. "This funding will help us serve the historic demand we are experiencing, stay at the research frontier, and bring Claude to more of the places where work happens," Anthropic's Chief Financial Officer Krishna Rao said in a statement. Altimeter Capital CEO Brad Gerstner hailed the adoption of Claude among the "world's most demanding organisations" as evidence of Anthropic's command in the field. "This momentum positions Anthropic to lead the next phase of AI innovation and capture the enormous opportunity ahead," Gerstner said.

Random sampling is a fundamental tool in modern machine learning and numerical linear algebra for reducing the computational cost of large-scale matrix problems. Existing analyses, however, rely primarily on subspace embedding guarantees, which do not precisely characterize the statistical bias of nonlinear random oblique projections induced by sampling, which arises ubiquitously in subsampled least squares and fast low-rank approximation methods. Because (pseudo)inversion is nonlinear, these random oblique projections can be systematically biased even when the underlying sketch is unbiased, thereby introducing hidden bias into downstream least squares and low-rank approximation solutions. In this work, we develop a unified non-asymptotic theory for random oblique projections in high dimensions. We show that standard random sampling schemes generally induce a systematic statistical bias overlooked by classical subspace embedding-style analyses, and we propose a principled debiasing framework to correct it. We illustrate the power of the theory through two canonical applications. For subsampled least squares, we obtain sharp bias--variance characterizations, reveal previously unrecognized statistical suboptimality in widely used sampling schemes, and identify when debiasing yields provable improvements. For fast CUR decomposition, we develop a debiased approach with improved approximation accuracy. Numerical experiments further validate our theoretical findings.

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The boss of Standard Chartered has apologised after describing employees whose jobs are vulnerable to being replaced by Artificial Intelligence (AI) as lower value human capital. Discussing how automation was likely to lead to thousands of job cuts at the bank at a recent conference, Bill Winters said it wasn't about cost cutting but replacing, in some cases, lower value, human capital, with the financial capital and the investment capital that we're putting in. He later sought to contextualise the remarks via LinkedIn and said he was sorry for his wording, which had caused upset to some colleagues. He said he was committed to helping staff cope with the accelerating pace of change. The rise of AI tools has led to predictions of huge job losses, particularly for tech workers and graduates.

Don't forget the bear spray. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Breakthroughs, discoveries, and DIY tips sent six days a week. The park, spread across 2.2 million acres and three states, includes half of Earth's active geysers, the Grand Canyon of the Yellowstone River, and stunning wildlife. Ahead of the 2026 summer tourist season, Yellowstone National Park recommends following these 10 steps for making the most out of your visit.

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We study the dynamic joint assortment selection and positioning problem, where the attraction of each product depends on both its intrinsic appeal and its display position under a Multinomial Logit (MNL) choice framework. Our study ranges from the multiplicative position effects model, in which each product's attraction is scaled by a position-specific factor, to a general position effects model assigning independent attraction parameters to every product--position pair to capture heterogeneous synergies. For both models, we design round-based learning algorithms that update decisions after every single feedback, and establish the first regret-optimal characterization. Besides, our round-based algorithms provide the prompt operations needed by modern platforms. For the multiplicative model, we develop a cross-position pairwise maximum likelihood estimator with a clipping mechanism, and prove that our algorithm P2MLE-UCB attains a regret of $\tilde{O}(\sqrt{NT})$, matching the lower bound and closing the $\sqrt{K}$ gap left by prior epoch-based analyses. For the general model, we establish a minimax lower bound and propose GP2-UCB with a matching upper bound. Moreover, we design an efficient subroutine for the per-round joint assortment and positioning optimization based on Dinkelbach's method and maximum-weight bipartite matching. Numerical experiments on synthetic data and the Expedia dataset show that our algorithms consistently outperform state-of-the-art benchmarks.

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