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Curious about using AI to help with work tasks but aren't sure where to start? Let 1min.AI serve as your one-stop shop. This handy platform combines several popular AI models -- including ChatGPT, Gemini, and Midjourney -- into one app, letting you test out their unique features without hopping between services. Right now, a lifetime subscription to the 1min.AI Advanced Business Plan can be yours for just 79.97 (reg. Once it's done, just give it a human once-over, and it will be good to go.

The movement for corporate city states cannot believe its good luck. For years, it has been pushing the extreme notion that wealthy, tax-averse people should up and start their own high-tech fiefdoms, whether new countries on artificial islands in international waters ("seasteading") or pro-business "freedom cities" such as Próspera, a glorified gated community combined with a wild west med spa on a Honduran island. Yet despite backing from the heavy-hitter venture capitalists Peter Thiel and Marc Andreessen, their extreme libertarian dreams kept bogging down: it turns out most self-respecting rich people don't actually want to live on floating oil rigs, even if it means lower taxes, and while Próspera might be nice for a holiday and some body "upgrades", its extra-national status is currently being challenged in court. Now, all of a sudden, this once-fringe network of corporate secessionists finds itself knocking on open doors at the dead center of global power. The first sign that fortunes were shifting came in 2023, when a campaigning Donald Trump, seemingly out of nowhere, promised to hold a contest that would lead to the creation of 10 "freedom cities" on federal lands. The trial balloon barely registered at the time, lost in the daily deluge of outrageous claims. Since the new administration took office, however, would-be country starters have been on a lobbying blitz, determined to turn Trump's pledge into reality. "The energy in DC is absolutely electric," Trey Goff, the chief of staff of Próspera, recently enthused after a trip to Capitol Hill.

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Ready for a robot that not only looks human but also acts and reacts like one, expressing emotions like shyness, excitement or friendliness? Disney Research, the innovation powerhouse behind The Walt Disney Company, has turned this into reality. Its latest creation is an autonomous humanoid robot that can mimic human emotions and behaviors in real time. Think of it as a real-life WALL-E, but with even more personality. This groundbreaking robot uses advanced artificial intelligence to replicate natural gestures and deliberate actions with striking accuracy.

The interior of Jeff Bridges's garage, in Santa Barbara, California, has the ramshackle ease of an extravagant dorm room: a tiger-print rug, a potter's wheel, guitars, a rogue toothbrush, taped-up printouts of ideas he finds provocative or perhaps grounding ("Enlightenment is a communal experience"), and piles of books, from Richard Powers's "Bewilderment" to "Who Cares?! A black-and-white portrait of Captain Beefheart, incongruously dressed in a jacket and tie, hangs on a wall near an electric piano. When I arrived, on a recent afternoon, I did not take note of a lava lamp, but its presence didn't feel out of the question. Bridges was wearing rubber slides and a periwinkle-blue cardigan. He excitedly spread out a large furry blanket on a recliner and invited me to sit down: "Your throne, man!" he said. Earlier this month, Bridges released "Slow Magic, 1977-1978," a series of songs he recorded when he was in his late twenties, an emergent movie star, and involved in a regular Wednesday-night jam session with a coterie of musicians and oddballs from the west side of Los Angeles (the jams were organized by Steve Baim, who attended University High School with Bridges; they took place in various beach houses and, occasionally, at the Village, the recording studio where, around the same time, Fleetwood Mac was making "Tusk"). "Slow Magic" is great and also bonkers. On "Kong," Bridges recounts a story line he pitched for a potential "King Kong" sequel (in 1976, Bridges starred as the long-haired primatologist Jack Prescott in a "Kong" remake produced by Dino De Laurentiis); the track features animated narration from the actor Burgess Meredith, and its lyrics are centered on the revelation that Kong is actually a robot. "It's a sad story, but he was just a monkey machine!" Bridges wails in a tottering falsetto. On "Obnoxious," a weirdly tender song about feeling sad and having a stomachache ("I went to the bathroom / And threw up"), there are echoes of Frank Zappa and the Band. What I like most about the record is how social it feels: friends in a room, being dumb, intermittently (even inadvertently) doing something miraculous. "When recording technology kept improving, I said, 'Oh, I don't need anybody!

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The original version of this story appeared in Quanta Magazine. Large language models work well because they're so large. The latest models from OpenAI, Meta, and DeepSeek use hundreds of billions of "parameters"--the adjustable knobs that determine connections among data and get tweaked during the training process. With more parameters, the models are better able to identify patterns and connections, which in turn makes them more powerful and accurate. But this power comes at a cost.

This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase information remains inaccessible. Leveraging the inherent sparsity of many real-world signals, we introduce a novel sparse quasi-Bayesian approach and provide the first theoretical guarantees for such an approach. Specifically, we employ a scaled Student distribution as a continuous shrinkage prior to enforce sparsity and analyze the method using the PAC-Bayesian inequality framework. Our results establish that the proposed Bayesian estimator achieves minimax-optimal convergence rates under sub-exponential noise, matching those of state-of-the-art frequentist methods. To ensure computational feasibility, we develop an efficient Langevin Monte Carlo sampling algorithm. Through numerical experiments, we demonstrate that our method performs comparably to existing frequentist techniques, highlighting its potential as a principled alternative for sparse phase retrieval in noisy settings.

Discovering constants of motion is meaningful in helping understand the dynamical systems, but inevitably needs proficient mathematical skills and keen analytical capabilities. With the prevalence of deep learning, methods employing neural networks, such as Constant Of Motion nETwork (COMET), are promising in handling this scientific problem. Although the COMET method can produce better predictions on dynamics by exploiting the discovered constants of motion, there is still plenty of room to sharpen it. In this paper, we propose a novel neural network architecture, built using the singular-value-decomposition (SVD) technique, and a two-phase training algorithm to improve the performance of COMET. Extensive experiments show that our approach not only retains the advantages of COMET, such as applying to non-Hamiltonian systems and indicating the number of constants of motion, but also can be more lightweight and noise-robust than COMET.