We solve a regularized weighted low-rank approximation problem by a stochastic gradient descent on a manifold. To guarantee the convergence of our stochastic gradient descent, we establish a convergence theorem on manifolds for retraction-based stochastic gradient descents admitting confinements. On sample data from the Netflix Prize training dataset, our algorithm outperforms the existing stochastic gradient descent on Euclidean spaces. We also compare the accelerated line search on this manifold to the existing accelerated line search on Euclidean spaces.

Fox News Flash top headlines are here. Check out what's clicking on Foxnews.com. Why did humans start speaking? Scientists suggest genetics played a big role – and they say the evolution of this singular ability was key to our survival. A new study links a particular gene to the ancient origins of spoken language, proposing that a protein variant found only in humans may have helped us communicate in a novel way.

It's been nearly four years since Spotify first announced that lossless audio streaming was on tap, and here we are, still waiting. Now there's another burst of chatter about the long-delayed feature, with Bloomberg reporting that Spotify HiFi is still in the pipeline--for those willing to pay extra. According to Bloomberg, lossless Spotify streaming will come in a new add-on called Music Pro, which will offer other benefits including AI-powered music remixing tools as well as discounted concert tickets. And yes, Spotify Music Pro will cost extra--possibly as much as 5.99 on top of your current Spotify Premium subscription, Bloomberg reports. That means individual Spotify Premium subscribers could be paying roughly 18 a month for lossless music streaming privileges.

Spotify is rolling out a Music Pro tier later this year that will give users access to higher-quality audio and remixing tools, according to Bloomberg. The tier will reportedly cost users 6 per month on top of their 12 Premium subscription, but they'll be priced differently across regions and will be cheaper in less-developed markets. Many long-time Spotify subscribers, however, will probably say that they'll believe it when they see it. The service teased a high-fidelity streaming option way back in 2017 and had confirmed that it was working to provide users with access to lossless audio in 2021. Several reports about the feature's availability had come out over the years after the company's confirmation. In 2024, Bloomberg also reported that HiFi streaming is expected to arrive before the year ended as a 5 add-on.

Infamous for his expletive-laden viral rants at livestreamed awards shows, Fares is a refreshingly firy and unpredictable voice in an all too corporate industry. As he puts it, "It doesn't matter where I work or what I do, I will always say what I want. People say to me that that's refreshing – but isn't it weird that you cannot say what you think in interviews? Do we live in a fucking communist country? Obviously, you have got to respect certain boundaries, but to not even be able to express what you think personally about stuff? Yet while gamers know him as a grinning chaos merchant and passionate ambassador of co-op gameplay, in Fares' adopted homeland of Sweden, he is best known as an award-winning film director. Jalla! was a domestic box office success, while his 2005 drama Zozo was a more introspective work about his childhood experience of fleeing the Lebanese civil war. Twenty years, five feature films and three video games later, Zozo was just one of many cathartic endeavours for Fares. "I've always been a storyteller," he says. "When I was young, I'd draw my own comics.

SHOPPING – Contains affiliated content. Products featured in this Shopping Finder article are selected by our shopping writers. If you make a purchase using links on this page, Dailymail.co.uk will earn an affiliate commission. The day Apple fans have been waiting for is nearly here. After many months of rumours, the tech giant is finally due to unveil a slew of new products on Wednesday.

Oscar Wilde said, "The difference between literature and journalism is that journalism is unreadable, and literature is not read." Unfortunately, The digitally archived journalism of Oscar Wilde's 19th century often has no or poor quality Optical Character Recognition (OCR), reducing the accessibility of these archives and making them unreadable both figuratively and literally. This paper helps address the issue by performing OCR on "The Nineteenth Century Serials Edition" (NCSE), an 84k-page collection of 19th-century English newspapers and periodicals, using Pixtral 12B, a pre-trained image-to-text language model. The OCR capability of Pixtral was compared to 4 other OCR approaches, achieving a median character error rate of 1%, 5x lower than the next best model. The resulting NCSE v2.0 dataset features improved article identification, high-quality OCR, and text classified into four types and seventeen topics. The dataset contains 1.4 million entries, and 321 million words. Example use cases demonstrate analysis of topic similarity, readability, and event tracking. NCSE v2.0 is freely available to encourage historical and sociological research. As a result, 21st-century readers can now share Oscar Wilde's disappointment with 19th-century journalistic standards, reading the unreadable from the comfort of their own computers.

AI systems often exhibit political bias, influencing users' opinions and decision-making. While political neutrality-defined as the absence of bias-is often seen as an ideal solution for fairness and safety, this position paper argues that true political neutrality is neither feasible nor universally desirable due to its subjective nature and the biases inherent in AI training data, algorithms, and user interactions. However, inspired by Joseph Raz's philosophical insight that "neutrality [...] can be a matter of degree" (Raz, 1986), we argue that striving for some neutrality remains essential for promoting balanced AI interactions and mitigating user manipulation. Therefore, we use the term "approximation" of political neutrality to shift the focus from unattainable absolutes to achievable, practical proxies. We propose eight techniques for approximating neutrality across three levels of conceptualizing AI, examining their trade-offs and implementation strategies. In addition, we explore two concrete applications of these approximations to illustrate their practicality. Finally, we assess our framework on current large language models (LLMs) at the output level, providing a demonstration of how it can be evaluated. This work seeks to advance nuanced discussions of political neutrality in AI and promote the development of responsible, aligned language models.

Abstract--Large language models (LLMs) face the challenge of hallucinations - outputs that seem coherent but are actually incorrect. A particularly damaging type is fact-conflicting hallucination (FCH), where generated content contradicts established facts. Addressing FCH presents three main challenges: 1) Automatically constructing and maintaining large-scale benchmark datasets is difficult and resource-intensive; 2) Generating complex and efficient test cases that the LLM has not been trained on - especially those involving intricate temporal features - is challenging, yet crucial for eliciting hallucinations; and 3) Validating the reasoning behind LLM outputs is inherently difficult, particularly with complex logical relationships, as it requires transparency in the model's decision-making process. LLMs are tested using these cases through template-based prompts, which require them to generate both answers and reasoning steps. T o validate the reasoning, we propose two semantic-aware oracles that compare the semantic structure of LLM outputs to the ground truths. Key insights reveal that LLMs struggle with out-of-distribution knowledge and logical reasoning. These findings highlight the importance of continued efforts to detect and mitigate hallucinations in LLMs. Large Language Models (LLMs) have revolutionized language processing, demonstrating impressive text generation and comprehension capabilities with diverse applications. However, despite their growing use, LLMs face significant security and privacy challenges [1], [2], [3], [4], [5], which affect their overall effectiveness and reliability . A critical issue is the phenomenon of hallucination, where LLMs generate outputs that are coherent but factually incorrect or irrelevant. This tendency to produce misleading information compromises the safety and usability of LLM-based systems. This paper focuses on fact-conflicting hallucina tion (FCH), the most prominent form of hallucination in LLMs. FCH occurs when LLMs generate content that directly contradicts established facts. For instance, as illustrated in Figure 1, an LLM incorrectly asserts that " Haruki Murakami won the Nobel Prize in Literature in 2016 ", whereas the fact is that "Haruki Murakami has not won the Nobel Prize, though he has received numerous other literary awards ". Such inaccuracies can significantly lead to user confusion and undermine the trust and reliability that are crucial for LLM applications. N. Li, K. Wang, and H. Wang are with Huazhong University of Science and T echnology, China. Song is with the National University of Singapore, Singapore. Li is with the University of New South Wales, Australia.

The ability to generate SPARQL queries from natural language questions is crucial for ensuring efficient and accurate retrieval of structured data from knowledge graphs (KG). While large language models (LLMs) have been widely adopted for SPARQL query generation, they are often susceptible to hallucinations and out-of-distribution errors when producing KG elements like Uniform Resource Identifiers (URIs) based on internal parametric knowledge. This often results in content that appears plausible but is factually incorrect, posing significant challenges for their use in real-world information retrieval (IR) applications. This has led to increased research aimed at detecting and mitigating such errors. In this paper, we introduce PGMR (Post-Generation Memory Retrieval), a modular framework that incorporates a non-parametric memory module to retrieve KG elements and enhance LLM-based SPARQL query generation. Our experimental results indicate that PGMR consistently delivers strong performance across diverse datasets, data distributions, and LLMs. Notably, PGMR significantly mitigates URI hallucinations, nearly eliminating the problem in several scenarios.