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.

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The technology helped them while harvesting the vast majority of their community's food. Apache, Navajo, and Shoshoni (pictured above) are only a few of the Indigenous tribes that utilized cradleboards. Breakthroughs, discoveries, and DIY tips sent every weekday. Indigenous women were technological trailblazers. But while lived experiences and communal histories have long supported this, they routinely fail to receive the credit they deserve .

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Breakthroughs, discoveries, and DIY tips sent every weekday. Nearly one in three U.S. households harbor a cold-hearted killer. Some even have a well-known proclivity for torture. And while the popular pets are best known for downing birds and cornering mice, they are also adept at hunting all manner of bugs. Host a cat in your home long enough and you'll likely become accustomed to regular deliveries of amputated insect legs, wings, or the occasional whole carcass.

In 2024, superstorm Gannon generated auroras-and wreaked havoc on this radiation-blocking layer. Breakthroughs, discoveries, and DIY tips sent every weekday. Last year, the most violent geomagnetic storm to strike Earth in over two decades did more than disrupt GPS systems and internet connections. According to a study published today in the journal, superstorm Gannon also squeezed the planet's protective layer of ionized particles to one-fifth its normal size. Geomagnetic storms aren't rare occurrences, but most of them remain relatively benign.

After defying multiple mass extinctions on Earth, the hardy plant passes an intergalactic test. Breakthroughs, discoveries, and DIY tips sent every weekday. While it may appear humble, Earth's moss is built darn tough. It thrives in extreme environments -from the bitter cold, low-oxygen air of the Himalayas, down to the parched sands of Death Valley. Some species even make their home among the lava fields of active volcanoes .