Using equations based on orbital speeds, distances in space and the physics of turbulence, Dr Nathanael-Israel Israel claimed he uncovered evidence that the biblical account of creation was literally true. His calculations suggested that the Earth formed in 2.82 days and that the sun and moon were completed in 3.69 days, figures he said closely mirrored the timeline laid out in Genesis. Israel clarified that his formula produced separate figures of 3.32 days for the moon and 3.69 days for the sun, placing the completion of both celestial bodies on the fourth day. Because he believed no other major religion offered the same sequence of events, he argued that his work pointed specifically to the existence of the Christian God. 'People say you can't prove God, but the question is, "How can you prove God?" I'm the first person in history to offer this mathematical framework,' Dr Israel told the Daily Mail.

The company has drawn governments, a major chipmaker, and the Pentagon into an effort to control fragile photons and build a useful quantum machine. It aims to be the first. PsiQuantum aims to build a quantum computer that can solve some of science's hardest problems. Its chips, cut from wafers like the one shown here, will perform computations using photons, the particles of light. The machine that could change the world will be housed in a room that looks like a data center crossed with an ice cream factory. Inside will be some 100 stainless-steel cabinets, each about six feet tall and connected to a supply of liquid helium that keeps them only a few degrees above absolute zero. Inside those cabinets will be hundreds of chips, and on those, thousands of particles of light flying through a maze of optical switches and beam splitters.

Power companies are pushing aggressive time-based use pricing. Here's how a regular consumer can benefit. I like to keep my home at a cool and comfortable 68 degrees year-round. This preference would be fine if I lived near the Pacific Ocean, or in a small home, or in a newer home that's insulated with modern mineral wool instead of tissue paper and horsehair. I, however, live in a 2,000-plus-square-foot home built in 1906.

We study how the choice of default prior for a common Gaussian scale affects high-dimensional shrinkage risk, highlighting the role played by high-dimensional geometry. Formally, we consider a high-dimensional setting in which the near-zero behavior of the common scale prior has first-order consequences for shrinkage risk, and show that priors that are flat on the variance and those flat on the standard deviation allocate markedly different mass near the zero-scale boundary, leading to distinct shrinkage behavior and informing principled default prior selection. Specifically, under a radial-power benchmark, we establish that the SD-flat benchmark has a one-unit asymptotic risk advantage near the origin, crosses over in the critical regime, and is second-order equivalent to the variance-flat benchmark for strong signals. Proper single global-scale hyperpriors and bounded coordinate-multiplier mixtures inherit these limits through the near-zero exponent of their SD-scale density. For heavier-tailed or sparse priors, that exponent still classifies the common global-scale component, while local-scale tails, model-size priors, or allocation priors can also affect risk.

Curriculum learning is a class of training strategies that organizes the data being exposed to a model by difficulty, gradually from simpler to more complex examples. This research explores a reverse curriculum generation approach that recursively decomposes complex datasets into simpler, more learnable components. We propose a teacher-student framework where the teacher is equipped with the ability to reason step-by-step, which is used to recursively generate easier versions of examples, enabling the student model to progressively master difficult tasks. We propose a novel scoring system to measure data difficulty based on its structural complexity and conceptual depth, allowing curriculum construction over decomposed data. Experiments on math datasets (MATH and AIME) and code generation datasets demonstrate that models trained with curricula generated by our approach exhibit superior performance compared to standard training on original datasets.

Existing molecular machine learning force fields (MLFFs) generally focus on the learning of atoms, molecules, and simple quantum chemical properties (such as energy and force), but ignore the importance of electron density (ED) ρ(r) in accurately understanding molecular force fields (MFFs). ED describes the probability of finding electrons at specific locations around atoms or molecules, which uniquely determines all ground state properties (such as energy, molecular structure, etc.) of interactive multi-particle systems according to the HohenbergKohn theorem. However, the calculation of ED relies on the time-consuming first-principles density functional theory (DFT), which leads to the lack of largescale ED data and limits its application in MLFFs. In this paper, we introduce EDBench, a large-scale, high-quality dataset of ED designed to advance learningbased research at the electronic scale. Built upon the PCQM4Mv2, EDBench provides accurate ED data, covering 3.3 million molecules. To comprehensively evaluate the ability of models to understand and utilize electronic information, we design a suite of ED-centric benchmark tasks spanning prediction, retrieval, and generation. Our evaluation of several state-of-the-art methods demonstrates that learning from EDBench is not only feasible but also achieves high accuracy. Moreover, we show that learning-based methods can efficiently calculate ED with comparable precision while significantly reducing the computational cost relative to traditional DFT calculations. All data and benchmarks from EDBench will be freely available, laying a robust foundation for ED-driven drug discovery and materials science.

The ability to quickly and accurately compute properties from atomic simulations is critical for advancing a large number of applications in chemistry and materials science including drug discovery, energy storage, and semiconductor manufacturing. To address this need, we present a family of Universal Models for Atoms (UMA), designed to push the frontier of speed, accuracy, and generalization. UMA models are trained on half a billion unique 3D atomic structures (the largest training runs to date) by compiling data across multiple chemical domains, e.g.

Consistency models are a class of generative models that enable few-step generation for diffusion and flow matching models. While consistency models have achieved promising results on Euclidean domains like images, their applications to Riemannian manifolds remain challenging due to the curved geometry. In this work, we propose the Riemannian Consistency Model (RCM), which, for the first time, enables few-step consistency modeling while respecting the intrinsic manifold constraint imposed by the Riemannian geometry. Leveraging the covariant derivative and exponential-map-based parameterization, we derive the closed-form solutions for both discrete-and continuous-time training objectives for RCM. We then demonstrate theoretical equivalence between the two variants of RCM: Riemannian consistency distillation (RCD) that relies on a teacher model to approximate the marginal vector field, and Riemannian consistency training (RCT) that utilizes the conditional vector field for training. We further propose a simplified training objective that eliminates the need for the complicated differential calculation. Finally, we provide a unique kinematics perspective for interpreting the RCM objective, offering new theoretical angles.

Large reasoning models (LRMs) like OpenAI-o1 have shown impressive capabilities in natural language reasoning. However, these models frequently demonstrate inefficiencies or inaccuracies when tackling complex mathematical operations. While integrating computational tools such as Code Interpreters (CIs) offers a promising solution, it introduces a critical challenge: a conflict between the model's internal, probabilistic reasoning and the external, deterministic knowledge provided by the CI, which often leads models to unproductive deliberation. To overcome this, we introduce CoRT (Code-Optimized Reasoning Training), a post-training framework designed to teach LRMs to effectively utilize CIs. We propose Hint-Engineering, a new data synthesis strategy that strategically injects diverse hints at optimal points within reasoning paths. This approach generates high-quality, code-integrated reasoning data specifically tailored to optimize LRMCI interaction. Using this method, we have synthesized 30 high-quality samples to post-train models ranging from 1.5B to 32B parameters through supervised fine-tuning.

Existing molecular machine learning force fields (MLFFs) generally focus on the learning of atoms, molecules, and simple quantum chemical properties (such as energy and force), but ignore the importance of electron density (ED) $\rho(r)$ in accurately understanding molecular force fields (MFFs). ED describes the probability of finding electrons at specific locations around atoms or molecules, which uniquely determines all ground state properties (such as energy, molecular structure, etc.) of interactive multi-particle systems according to the Hohenberg-Kohn theorem. However, the calculation of ED relies on the time-consuming first-principles density functional theory (DFT), which leads to the lack of large-scale ED data and limits its application in MLFFs. In this paper, we introduce EDBench, a large-scale, high-quality dataset of ED designed to advance learning-based research at the electronic scale. Built upon the PCQM4Mv2, EDBench provides accurate ED data, covering 3.3 million molecules. To comprehensively evaluate the ability of models to understand and utilize electronic information, we design a suite of ED-centric benchmark tasks spanning prediction, retrieval, and generation. Our evaluation of several state-of-the-art methods demonstrates that learning from EDBench is not only feasible but also achieves high accuracy. Moreover, we show that learning-based methods can efficiently calculate ED with comparable precision while significantly reducing the computational cost relative to traditional DFT calculations. All data and benchmarks from EDBench will be freely available, laying a robust foundation for ED-driven drug discovery and materials science.