For such neural networks, we prove a non-constant lower bound of that are compatible with certain polyhedral complexes, more precisely with the the best known lower bound in general is still 2. We focus on neural networks linear functions on R .

Although Multimodal Large Language Models (MLLMs) have demonstrated remarkable achievements in recent years, they remain vulnerable to adversarial examples that result in harmful responses. Existing attacks typically focus on optimizing adversarial perturbations for a certain multimodal image-prompt pair or fixed training dataset, which often leads to overfitting. Consequently, these perturbations fail to remain malicious once transferred to attack unseen image-prompt pairs, suffering from significant resource costs to cover the diverse multimodal inputs in complicated real-world scenarios. To alleviate this issue, this paper proposes a novel adversarial attack on MLLMs based on distribution approximation theory, which models the potential image-prompt input distribution and adds the same distribution-fitting adversarial perturbation on multimodal input pairs to achieve effective cross-image/prompt transfer attacks. Specifically, we exploit the Laplace approximation to model the Gaussian distribution of the image and prompt inputs for the MLLM, deriving an estimate of the mean and covariance parameters. By sampling from this approximated distribution with Monte Carlo mechanism, we efficiently optimize and fit a single input-agnostic perturbation over diverse image-prompt pairs, yielding strong universality and transferability. Extensive experiments are conducted to verify the strong adversarial capabilities of our proposed attack against prevalent MLLMs spanning a spectrum of images/prompts.

Devices that monitor seniors for safety are appealing to worried loved ones and underresourced home care agencies. It was January of 2026 in North Seattle, and my 86-year-old father was struggling to move around his house. "I'm stumbling around here," my 86-year-old father told a guest in his home this past January. "Oooh, ooh, careful," the guest replied. "Yeah, I almost fell down."

LLMs typically respond quickly, but their SVG outputs tend to be short and structurally simplistic.

No one can say for sure what's going on in the president's head. His 25 greatest obsessions can get us a little closer. This is the year the first baby boomers--those born in 1946--turn 80, and that cohort includes Donald Trump. We have all recently lived through what it means to have an 80-year-old commander in chief, but at a political moment that's simultaneously more horrific, erratic, and just plain befuddling than anything this country has seen in ages, we wanted to understand the brain of 80-year-old president. Plenty of people are trying to discern whether his recent rants and raves are due to a more serious cognitive decline--we understand the instinct; we've done it too --but we went a different (if related) route. The more we dug into Trump's many fixations, the more we realized that this man still thinks he lives in the 1980s. We also discovered--without too much surprise--that he often seems to fundamentally misunderstand the works he treasures most deeply. These items might not replace a brain map, but they do create a certain holistic view of what animates and splinters Trump's mind. Sometimes, they just help explain his worldview. Other times, they seem to have had real influence on policy and the America that Trump is trying to create. Welcome to Trump Brain, the 25 things that define who the president is--and what he wants. Please enable javascript to fully experience this interactive. When millions of people took to the streets in October to protest Trump's authoritarianism, the president responded by dunking on his critics online. Specifically, he posted an A.I.-generated video of a fighter jet, piloted by himself in a literal crown, dropping human excrement onto the crowds. It was perhaps Trump's most juvenile use of A.I. slop yet--the kind of low-quality, feverish content made possible by artificial intelligence. Trump undoubtedly is the perfect president for the A.I. slop era. In some ways, this is because he's the ideal audience for it: Like many older internet users delighted by the technology, Trump seems to enjoy mindless, cartoonish, childish content. One of the videos he shared depicted him playing soccer with Cristiano Ronaldo in the Oval Office.

So Claude and I tried to make a database for tracking the petty grievances of the masses. The dog that ushered me into the technological future was "low and thick." That's all my mother registered before it T-boned her in a city park earlier this year: dense, heavy, and traveling fast enough to fracture her right tibia. Let's discuss what this set in motion in my life: Having successfully learned nothing about coding for two and a half decades, I would soon be attempting my very first software development project. If you've ever had a low and thick dog break your mom's shin bone, you know the stream of lesser indignities that follows.

Daron Acemoglu is more cautious than most about predictions of a jobs apocalypse. A few months before he was awarded the Nobel Prize in economics in 2024, Daron Acemoglu published a paper that earned him few fans in Silicon Valley. Contrary to what Big Tech CEOs had been promising--an overhaul of all white-collar work--Acemoglu estimated that AI would give only a small boost to US productivity and would not obviate the need for human work. It's okay at automating certain tasks, he wrote, but some jobs will be perfectly fine. Two years later, Acemoglu's measured take has not caught on. Chatter about an AI jobs apocalypse pops up everywhere from Senator Bernie Sanders's rallies to conversations I overhear in line at the grocery store.

For screenwriters like me--and job seekers all over--AI gig work is the new waiting tables. In eight months, I've done 20 of these soul-crushing contracts for five different platforms. My name on the platform is ri611. I work as an AI trainer. I assess whether a chatbot's tone is natural or flat, affected or annoying. I identify patterns in pictures of furniture; search the internet for group photos of strangers whom I'll eliminate from the portrait, one by one. I trawl through bizarre videos so I can annotate and time-stamp the barking of a dog, the moment a stranger walks past a window, the precise millisecond a balloon pops. I generate anime sex scenes and decapitate young women, coax LLMs into giving me recipes for bombs made of household items, and generate invites to a reprise of January 6 at the White House, all as part of a red team whose purpose is to test safety precautions and probe weaknesses. I work for companies with names like Mercor and Outlier and Task-ify and Turing and Handshake and Micro1. In my "other" career, I am a Hollywood writer and showrunner. I create prime-time TV, usually featuring a middle-class white lady having the worst day of her life, with some salt-of-the-earth police interference to raise the stakes. You can find my shows on Paramount and Hulu and the BBC.

Tech advances not only made IVF safer and more effective; they fundamentally changed the way we think about our reproduction. Technology is changing the way we make babies. The pioneering work of the scientists who invented IVF led to the birth of the first "test tube baby" in 1978. We've come a long, long way since then. This week, I've been working on a piece about the cutting edge of IVF technologies and what's coming next. Think AI and robots and, potentially, gene-edited embryos.