Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the solution operators of partial differential equations (PDEs). These methods can also be used to develop black-box simulators to model system behavior from experimental data, even without a known mathematical model. In this article, we begin by formalizing operator learning as a function-to-function regression problem and review some recent developments in the field. We also discuss PDE-specific operator learning, outlining strategies for incorporating physical and mathematical constraints into architecture design and training processes. Finally, we end by highlighting key future directions such as active data collection and the development of rigorous uncertainty quantification frameworks.

Recent studies have shown that Large Language Models (LLMs) augmented with chain-of-thought (CoT) reasoning demonstrate impressive problem-solving abilities. However, in this work, we identify a recurring issue where these models occasionally generate overly short reasoning, leading to degraded performance on even simple mathematical problems. Specifically, we investigate how reasoning length is embedded in the hidden representations of reasoning models and its impact on accuracy. Our analysis reveals that reasoning length is governed by a linear direction in the representation space, allowing us to induce overly short reasoning by steering the model along this direction. Building on this insight, we introduce ThinkEdit, a simple yet effective weight-editing approach to mitigate the issue of overly short reasoning. We first identify a small subset of attention heads (approximately 2%) that predominantly drive short reasoning behavior. We then edit the output projection weights of these heads to suppress the short reasoning direction. With changes to only 0.1% of the model's parameters, ThinkEdit effectively reduces overly short reasoning and yields notable accuracy gains for short reasoning outputs (+5.44%), along with an overall improvement across multiple math benchmarks (+2.43%). Our findings provide new mechanistic insights into how reasoning length is controlled within LLMs and highlight the potential of fine-grained model interventions to improve reasoning quality. Our code is available at https://github.com/Trustworthy-ML-Lab/ThinkEdit

Existing approaches remain largely constrained by traditional distance metrics, limiting their effectiveness in handling random data. In this work, we introduce the first k-means variant in the literature that operates within a probabilistic metric space, replacing conventional distance measures with a well-defined distance distribution function. This pioneering approach enables more flexible and robust clustering in both deterministic and random datasets, establishing a new foundation for clustering in stochastic environments. By adopting a probabilistic perspective, our method not only introduces a fresh paradigm but also establishes a rigorous theoretical framework that is expected to serve as a key reference for future clustering research involving random data. Extensive experiments on diverse real and synthetic datasets assess our model's effectiveness using widely recognized evaluation metrics, including Silhouette, Davies-Bouldin, Calinski Harabasz, the adjusted Rand index, and distortion. Comparative analyses against established methods such as k-means++, fuzzy c-means, and kernel probabilistic k-means demonstrate the superior performance of our proposed random normed k-means (RNKM) algorithm. Notably, RNKM exhibits a remarkable ability to identify nonlinearly separable structures, making it highly effective in complex clustering scenarios. These findings position RNKM as a groundbreaking advancement in clustering research, offering a powerful alternative to traditional techniques while addressing a long-standing gap in the literature. By bridging probabilistic metrics with clustering, this study provides a foundational reference for future developments and opens new avenues for advanced data analysis in dynamic, data-driven applications.

Tested's Adam Savage paired up with Medtronic to offer his commentary on what can contribute to a longer lifespan, including possible differences between men's and women's health. Former "MythBusters" star Adam Savage is exploring the science of longevity, asking how lifestyle choices, stress and even sleep affect how long we live. Savage, now a YouTube creator and head of the channel Tested, has partnered with health technology company Medtronic to engage in discussions about longevity. While not a researcher himself, he has taken a deep dive into scientific insights from experts and reflected on his own experiences. "Longevity has always been a fascination for me," Savage told Fox News Digital in an exclusive interview.

Gruesome pictures have revealed the shocking impact microplastics could be having on your appearance -- and making you look decrepit and older. Microplastics are now in almost everything we touch, from food and clothing to water, kitchenware and household items - and every American is now thought to have microplastics in their bodies. Now, a UK recycling company has tried to capture the impact these toxins could be having on the skin. In a release, they used AI to estimate how long-term exposure to microplastics at low, medium and high levels could impact a man and a woman's appearance. Mark Hall, a plastic waste expert at the business behind the report, said: 'It's clear to see there are many worrying signs of how this pollution might affect us.

In 2023, M3GAN wowed audiences with campy scares, viral dance moves, and an unforgettable diva doll. Now, in the upcoming sequel M3GAN 2.0, we don't just get one killer AI, we get two! M3GAN 2.0's trailer introduces Amelia (Ivanna Sakhno), a military-grade weapon created using the technology that made -- nay, gifted -- us M3GAN (Amie Donald, voiced by Jenna Davis). As her self-awareness increases, her desire to kill multiplies until she's a threat to all of humanity. Now, she has M3GAN's creator Gemma (Allison Williams) and niece (Violet McGraw) in her sights.

Have I told you the story about Bill Gates and me in those early days of personal computing? To be clear: Bill Gates is older than I am. In 1975, as Bill was leaving Harvard to start Microsoft, I had just skipped my last year of high school and started college. I was the youngest student in engineering school that first year -- the same year Bill and I were using the same computer technology: the Altair 8800 and the Digital Equipment PDP-10. My high school computing experience -- like Bill's -- was formative.

Artificial intelligence has basically taken over and replace traditional web search engines. You've already seen it with AI overviews in Google Search, followed up with OpenAI going the way of SearchGPT. Even alternative search engines like DuckDuckGo are starting to incorporate AI into their platforms, and things aren't slowing down. Well, now we can add another to the pile: Microsoft just released Copilot Search, which is sort of like an AI-infused Bing Search. It takes in data from sources all over the web, then uses Copilot's AI powers to synthesize a summary for you.

This week's Nintendo Direct provided much more info about the Switch 2 but didn't go too deep into the nitty-gritty details of what powers the console. That left NVIDIA, the Mario maker's hardware partner on the console's processor and GPU, to fill in some blanks with a blog post published on Thursday -- including the first confirmation that it uses Deep Learning Super Sampling (DLSS) tech. NVIDIA said the Switch 2's DLSS support helps to give the console "ten times" the graphical performance of the original Switch. The tech lets games render games in a lower resolution, then uses trained AI models and dedicated Tensor Cores to fill in detail. Saying a system has ten times the graphics performance is likely a simplified marketing claim, and its graphical prowess could vary greatly depending on the title.

Instead of shying away from the use of AI in the classroom, many schools are learning just how useful it can be. That is why Anthropic just debuted a new AI chatbot designed to change how students learn. In a post this week, the company announced that it is launching Claude for Education, a specialized version of Claude specifically designed for teachers and students. The chatbot has similarities to the regular version of Claude, but it has a few major differences. A new "learning mode" is the highlight and where Claude for Education is truly different.