Score-based generative models are trained in high-dimensional ambient spaces, yet many data distributions are supported on low-dimensional nonlinear structures. We prove that, for compact $d$-dimensional smooth manifolds $\mathcal{M} \subset [0,1]^D$ with $d > 2$ and $β$-Hölder densities strictly positive on $\mathcal{M}$, a variance-preserving SGM estimator attains the intrinsic Wasserstein--1 sample exponent $\tilde{\mathcal{O}}(D^{\mathcal{O}_β(d)}n^{-(β+1)/(d+2β)})$, up to logarithmic factors and explicit geometry and density factors. The full nonasymptotic bound explicitly isolates the finite-order geometry envelope, Hölder radius, density lower bound, ambient dependence, and finite-order correction terms. The analysis separates score approximation into a large-noise tangent-cell regime and a small-noise projection-centered, de-Gaussianized Laplace regime. The key technical ingredient is a ReLU implementation of nearest-projection coordinates via finite intrinsic anchors and Gauss--Newton iterations, rather than approximating the manifold projection as a black-box high-dimensional smooth map. Consequently, for families with polynomially controlled geometry and density lower bounds, the constructed score-network parameters have polynomial ambient dependence.

Science Space Deep Space Fastest comet ever recorded spewed 70 Olympic pools' worth of water daily More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. A new study of the interstellar comet 3I/ATLAS led by the University of Michigan shows that its water has a remarkably high content of deuterium. This form of hydrogen is comparatively less abundant in our solar system, enabling researchers to glean new insights about other planetary processes at work in our galaxy. Breakthroughs, discoveries, and DIY tips sent six days a week. Astronomers knew 3I/ATLAS wasn't a local comet not long after first spotting it in July 2025 .

An artist's impression of 3I/ATLAS is shown as it passes near the Sun, illuminating one side of the comet. On the side of the comet closer to the sun, the methanol gas is shown in blue, with icy dust grains still present in the gas. On the dark side of the comet, the hydrogen cyanide is shown in orange. Breakthroughs, discoveries, and DIY tips sent six days a week. The comet 3I/ATLAS is well on its way back into deep space, but the famous cosmic visitor continues to fascinate astronomers.

Listed order was determined by a coin toss.

The interstellar space rock shows off the illuminating effects of its brush with the sun. Breakthroughs, discoveries, and DIY tips sent six days a week. After months of unprecedented observations, astronomers are bidding goodbye to the beloved comet 3I/ATLAS . First spotted in July 2025, the frigid, dusty space rock is only the third known interstellar object to pass through the solar system, offering researchers the rare opportunity to examine a visitor from deep space. Among other discoveries, scientists have since confirmed that the interstellar comet is the fastest ever recorded as well as covered in ice volcanoes --and definitely not extraterrestrial tourists .

We demonstrate the effectiveness of our method on both simulated 2D images andreal3Dbrain magnetic resonance (MR) images.

From surveys of the pre-Sputnik skies to analysis of interstellar visitors, scientists are rethinking how and where to look for physical traces of alien technology. Science fiction is awash in the material remnants of extraterrestrial civilizations, which surface in everything from the classic books of Arthur C. Clarke to game franchises like and . The discovery of the first interstellar objects in the solar system within the past decade has sparked speculation that they could be alien artifacts or spaceships, though the scientific consensus remains that all three of these visitors have natural explanations. That said, scientists have been anticipating the possibility of encountering alien artifacts since the dawn of the space age. "In the history of technosignatures, the possibility that there could be artifacts in the solar system has been around for a long time," says Adam Frank, a professor of astrophysics at the University of Rochester.

The new Atlas will be deployed at Hyundai and Google DeepMind first. Boston Dynamics' Atlas is finally entering production. After years of testing this humanoid robot (and forcing it to dance), the robotics company announced at CES 2026 that the final version of the machine is being built now. The first companies to receive deployments will be Hyundai, Boston Dynamics' majority shareholder, and Google DeepMind, the firm's new AI partner . This final enterprise version of Atlas can perform a wide array of industrial tasks, according to Boston Dynamics, and is specifically designed with consistency and reliability in mind.

Hyundai Motor Group says it will roll out human-like robots in its factories from 2028, as major companies race to use the new technology. The South Korean firm showed off Atlas, a humanoid robot developed by Boston Dynamics, at the Consumer Electronics Show (CES) in Las Vegas on Monday. Hyundai says it plans to integrate Atlas across its global network, including a plant in the US state of Georgia that was involved in a massive immigration raid in 2025 . Other firms that have said they will use humanoid robots in their operations include Amazon, Tesla and Chinese car making giant BYD. The Atlas robots will gradually take on more tasks, said Hyundai.

The new Atlas will be deployed at Hyundai and Google DeepMind first. After years of testing its humanoid robot (and forcing it to dance), Boston Dynamics' Atlas is entering production . The robotics company says the final product version of the robot is being built now, and the first companies that will receive deployments are Hyundai, Boston Dynamics' majority shareholder, and Google DeepMind, the firm's newly minted AI partner. This final enterprise version of Atlas can perform a wide array of industrial tasks, according to Boston Dynamics, and is specifically designed with consistency and reliability in mind. Atlas can work autonomously, via a teleoperator or with a tablet steering interface, and the robot is both strong and durable.