The incredible offer appeared to loyalty card holders of the European electronics chain on November 8. After 11 days the company began contacting buyers, calling it a clear mistake. Italian electronics retailer MediaWorld has scrambled to fix a world-historic iPad pricing error. On November 8, an offer for loyalty card holders appeared on the website of MediaWorld, a European electronics retailer. No catch, no strings attached.

The 1,500-year-old site was hidden beneath the dark, damp ice. Breakthroughs, discoveries, and DIY tips sent every weekday. In the fall of 2024, a hiker named Helge Titland was trekking through Aurlandsfjellet, a mountainous region and plateau in Norway and got a little more than just some time with nature. Titland found some strange wooden stakes peaking out of melting snow. He wisely reported it to local archaeologists, but snow returned before the team could investigate.

Many online platforms act as intermediaries between a seller and a set of buyers. Examples of such settings include online retailers (such as Ebay) selling items on behalf of sellers to buyers, or advertising exchanges (such as AdX) selling pageviews on behalf of publishers to advertisers. In such settings, revenue sharing is a central part of running such a marketplace for the intermediary, and fixed-percentage revenue sharing schemes are often used to split the revenue among the platform and the sellers. In particular, such revenue sharing schemes require the platform to (i) take at most a constant fraction \alpha of the revenue from auctions and (ii) pay the seller at least the seller declared opportunity cost c for each item sold. A straightforward way to satisfy the constraints is to set a reserve price at c / (1 - \alpha) for each item, but it is not the optimal solution on maximizing the profit of the intermediary.

The cornerstone of modern math wouldn't be possible without the Hindu-Arabic numerical system. Breakthroughs, discoveries, and DIY tips sent every weekday. Most people know about Pi Day (3/14), but there are even rarer days on the calendar like Pythagorean Triple Square Day (9/16/25). The poetry of mathematics manifests everywhere in nature, but few numerical patterns are more common than the Fibonacci Sequence . First described in 1202 by mathematician Italian Leonardo Bonacci (Fibonacci is a shortening of or "son of Bonacci"), the concept involves adding 1 and 1 together, then doing the same for every successive pair of numbers.

Online kernel learning (OKL) is a flexible framework to approach prediction problems, since the large approximation space provided by reproducing kernel Hilbert spaces can contain an accurate function for the problem. Nonetheless, optimizing over this space is computationally expensive. Not only first order methods accumulate $\O(\sqrt{T})$ more loss than the optimal function, but the curse of kernelization results in a $\O(t)$ per step complexity. Second-order methods get closer to the optimum much faster, suffering only $\O(\log(T))$ regret, but second-order updates are even more expensive, with a $\O(t^2)$ per-step cost. Existing approximate OKL methods try to reduce this complexity either by limiting the Support Vectors (SV) introduced in the predictor, or by avoiding the kernelization process altogether using embedding.

We propose Sketched Online Newton (SON), an online second order learning algorithm that enjoys substantially improved regret guarantees for ill-conditioned data. SON is an enhanced version of the Online Newton Step, which, via sketching techniques enjoys a running time linear in the dimension and sketch size. We further develop sparse forms of the sketching methods (such as Oja's rule), making the computation linear in the sparsity of features. Together, the algorithm eliminates all computational obstacles in previous second order online learning approaches.

Related work Although first-order OKL methods cannot achieve logarithmic regret, many approximation methods have been proposed to make them scale to large datasets.

In real-world task-oriented dialogue (TOD) settings, agents are required to strictly adhere to complex instructions while conducting multi-turn conversations with customers. These instructions are typically presented in natural language format and include general guidelines and step-by-step procedures with complex constraints. Existing TOD benchmarks often oversimplify the complex nature of these instructions by reducing them to simple schemas composed of intents, slots, and API call configurations. To address this gap and systematically benchmark LLMs' instruction-following capabilities, we propose TOD-ProcBench, a challenging benchmark featuring complex process instructions with intricate, fine-grained constraints that evaluates various LLMs' abilities to understand and follow instructions in multi-turn TODs. Our benchmark dataset comprises instruction documents derived from the high-quality ABCD dataset with corresponding conversations under human quality control. We formulate fine-grained constraints and action procedures as multi-level condition-action instruction statements. We design three tasks to comprehensively benchmark LLMs' complex instruction-following capabilities in multi-turn TODs. Task 1 evaluates how LLMs retrieve the most relevant statement from a complex instruction and predict the corresponding next action. In Task 2, we synthesize instruction-violating responses by injecting inconsistencies and manipulating the original instructions, and then we analyze how effectively LLMs can identify instruction-violating responses. Task 3 investigates LLMs' abilities in conditional generation of instruction-following responses based on the original complex instructions. Additionally, we conduct studies on the impact of multilingual settings and different instruction text formats on compliance performance. We release our benchmark under the Llama 3.3 Community License Agreement.

We may earn revenue from the products available on this page and participate in affiliate programs. The turkey hasn't even hit the table yet, but Amazon's Black Friday Week sale is already in full swing. There are literally thousands of products on sale right now, which can make it seem impossible to sift through. Luckily, it's our job to sit around trying to find the best possible bargains. We'll be updating this post throughout the week with the best overall Amazon deals, so keep checking back until you've spent all of your holiday budget.

Gear Home Smart Home Bird Buddy's best smart feeders are only $229 during Amazon's Black Friday sale, and some models are even less If you've been waiting to try a smart bird feeder that lets you see new avian pals up close, it's the best time of the year to get almost half off. Your backyard paparazzi career starts now. We may earn revenue from the products available on this page and participate in affiliate programs. The Bird Buddy smart feeder has turned a lot of readers into accidental birders over the years. This editor-approved source of avian infotainment was PopSci's most-clicked Black Friday deal in 2023, then sold out again during Prime Day in 2024.