A Multinomial Logit (MNL) model is composed of a finite universe of items $[n]=\{1,..., n\}$, each assigned a positive weight. A query specifies an admissible subset -- called a slate -- and the model chooses one item from that slate with probability proportional to its weight. This query model is also known as the Plackett-Luce model or conditional sampling oracle in the literature. Although MNLs have been studied extensively, a basic computational question remains open: given query access to slates, how efficiently can we learn weights so that, for every slate, the induced choice distribution is within total variation distance $\varepsilon$ of the ground truth? This question is central to MNL learning and has direct implications for modern recommender system interfaces. We provide two algorithms for this task, one with adaptive queries and one with non-adaptive queries. Each algorithm outputs an MNL $M'$ that induces, for each slate $S$, a distribution $M'_S$ on $S$ that is within $\varepsilon$ total variation distance of the true distribution. Our adaptive algorithm makes $O\left(\frac{n}{\varepsilon^{3}}\log n\right)$ queries, while our non-adaptive algorithm makes $O\left(\frac{n^{2}}{\varepsilon^{3}}\log n \log\frac{n}{\varepsilon}\right)$ queries. Both algorithms query only slates of size two and run in time proportional to their query complexity. We complement these upper bounds with lower bounds of $Ω\left(\frac{n}{\varepsilon^{2}}\log n\right)$ for adaptive queries and $Ω\left(\frac{n^{2}}{\varepsilon^{2}}\log n\right)$ for non-adaptive queries, thus proving that our adaptive algorithm is optimal in its dependence on the support size $n$, while the non-adaptive one is tight within a $\log n$ factor.

Feature attribution is the dominant paradigm for explaining deep neural networks. However, most existing methods only loosely reflect the model's prediction-making process, thereby merely white-painting the black box. We argue that explanatory alignment is a key aspect of trustworthiness in prediction tasks: explanations must be directly linked to predictions, rather than serving as post-hoc rationalizations. We present model readability as a design principle enabling alignment, and PiNets as a modeling framework to pursue it in a deep learning context. PiNets are pseudo-linear networks that produce instance-wise linear predictions in an arbitrary feature space, making them linearly readable. We illustrate their use on image classification and segmentation tasks, demonstrating how PiNets produce explanations that are faithful across multiple criteria in addition to alignment.

This is high-end recovery gear that's worthy of professional athletes. It's a lot easier to stick to your resolutions when you recover faster. We may earn revenue from the products available on this page and participate in affiliate programs. Recovery gear is not a substitute for sleep, smart training, or eating with fitness in mind, but it can make the day-after soreness far less annoying. Hyperice has discounts right now on Normatec compression systems, Hypervolt percussion massagers, and joint-focused heat therapy that's built for the spots that complain the loudest.

The pivot doesn't look out of place at CES, where Chinese electronics companies are increasingly applying their manufacturing prowess to new industries. If you've never been to Shenzhen, China's electronics capital, the annual CES trade show in Las Vegas is the next best thing. I'm reporting this week from the sprawling event, surrounded by fancy, strange, and often unnecessary gadgets, and despite my sore legs, I've barely scratched the surface. There are at least 900 Chinese tech companies attending CES this year, almost a quarter of the total exhibitors, according to an analysis of the conference's exhibitor directory. I even saw two Chinese humanoid robots at different booths dancing to the same viral Chinese rap song five minutes apart.

Hours after an ICE agent killed the mother of three, Elon Musk's chatbot was undressing her. Grok, created by Elon Musk's xAI, is now central to Twitter. So, increasingly, are its deepfakes. Get your news from a source that's not owned and controlled by oligarchs. Grok, the AI chatbot launched by Elon Musk after his takeover of X, unhesitatingly fulfilled a user's request on Wednesday to generate an image of Renee Nicole Good in a bikini--the woman who was shot and killed by an ICE agent that morning in Minneapolis, as noted by CNN correspondent Hadas Gold and confirmed by the chatbot itself.

You can also have a husbando or even League of Legends G.O.A.T. Faker sometime down the line. Kira is one of Razer's newest AI companions for Project Ava. Last year Razer showed off Project Ava as a digital assistant that lived inside your computer to help adjust settings or provide gaming tips. But now at CES 2026, the company's AI companion platform has gotten a major glow-up while moving into some new digs. Now, in lieu of being constrained entirely to your PC's screen, Razer has given Project Ava a real home in the form of a small tube that can display a 5.5-inch animated hologram of the AI's avatar.

Environment Climate Change Global Warming Why is this infamous iceberg turning blue? Iceberg A-23A is bigger than New York City, but its days are numbered. Breakthroughs, discoveries, and DIY tips sent every weekday. Iceberg A-23A is looking a little blue these days. In late December 2025, NASA and NOAA's Terra satellite spotted the massive iceberg covered with blue meltwater .

Why Are Grok and X Still Available in App Stores? Elon Musk's chatbot has been used to generate thousands of sexualized images of adults and apparent minors. Apple and Google have removed other "nudify" apps--but continue to host X and Grok. Elon Musk's AI chatbot Grok is being used to flood X with thousands of sexualized images of adults and apparent minors wearing minimal clothing. Some of this content appears to not only violate X's own policies, which prohibit sharing illegal content such as child sexual abuse material (CSAM), but may also violate the guidelines of Apple's App Store and the Google Play store.

Even amidst the connectivity nightmare that is CES, I was able to control heaters, tower fans and lights with my voice. Perhaps you like the idea of controlling your home appliances with your voice, but aren't super keen on a data center processing recordings of you. The trade-off for most smart home conveniences is relinquishing at least some of your privacy. Today at CES, I saw a line of voice-controlled home appliances from Emerson Smart that adjust power and setting via voice commands. But commands are recognized on the devices themselves, not carried through Wi-Fi and processed elsewhere.

Engadget's best of CES 2026: All the new tech that caught our eye in Las Vegas This year, over 4,000 exhibitors descended on Las Vegas, Nevada to showcase their wares at CES, and the Engadget team was out in full force . The week started with press conferences from the biggest companies at the show, which were often a flurry of AI buzzwords, vague promises and very little in the way of hard news. More than one company even decided to forgo announcing things during their conferences to make way for more AI chatter, only to publish press releases later quietly admitting that, yes, actually, they did make some consumer technology. It's appropriate, I guess, that as we're beginning to feel the knock-on cost effects of the AI industry's insatiable appetite for compute resources -- higher utility bills and device prices -- companies would rather use their flashy conferences to reinforce AI's supposedly must-have attributes rather than actually inform the public about their new products. We're by no means AI luddites at Engadget, but it's fair to say that our team is more excited by tangible products that enrich our lives than iterative improvements to large language models. So, away from all of the bombast of NVIDIA's marathon keynote and Lenovo's somehow simultaneously gaudy and dull Sphere show, it's been a pleasure to evaluate the crowd of weird new gadgets, appliances, toys and robots vying for our attention.