Hypergraphs model higher-order interactions, but realistic hypergraph generation remains difficult because incidence, hyperedge-size heterogeneity, and overlap structure are not faithfully captured by pairwise reductions. We propose \HEDGE, a generative model defined directly on relaxed incidence matrices via a structured stochastic diffusion. The forward process combines a hypergraph-specific two-sided heat operator with an Ornstein--Uhlenbeck component, preserving structure-aware noising near the data while yielding an explicit Gaussian terminal law. Conditional on an observed hypergraph, this forward process is linear-Gaussian, so conditional means, covariances, scores, and reverse-drift targets are available in closed form. We therefore learn a permutation-equivariant state-only reverse-drift field in incidence space by regressing onto exact conditional targets, and generate samples by simulating a learned reverse-time SDE from the Gaussian base law. We establish exactness in the ideal state-only setting together with finite-horizon stability guarantees, and empirically show improved hypergraph generation quality relative to strong baselines.

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors can be represented by a Gaussian graphical model, the structure of the predictor graph can be exploited during regularization. Our proposed model exploits this underlying predictor graph structure by decomposing the estimated coefficient vector into a sum of latent variables that correspond to the sum of each node contribution to the coefficient vector. Regularization is then performed on the latent variables rather than on the coefficient vector directly. We use a penalty function that permits a clear user-defined trade-off between the L1 and L2 penalties and propose a novel proximal projection during optimization. Further, our implementation computes the projection operator for the intersection of selected groups, which conserves more computing resources compared to predictor duplication methods, especially for high-dimensional data. Through simulation, we evaluate the performance of our approach under different graph structures and node counts, and present results on real-world data. Results suggest that our method exhibits stable performance relative to other singly or doubly sparse graphical regression models.

We develop a framework for task-specific active next-best-view selection in 3D reconstruction from point clouds, by casting the problem in the language of Bayesian decision theory. Our framework works by (a) placing a prior distribution over the space of implicit surfaces, (b) using recently-developed stochastic surface reconstruction methods to calculate the resulting posterior distribution, then (c) using the posterior distribution to carefully reason about which view to scan next. This enables us to perform camera selection in a manner that is directly optimized for the intended use of the reconstructed data - meaning, we reduce uncertainty only in those regions that make a difference in the task at hand, as opposed to prior approaches that reduce it uniformly across space. We evaluate our method across three distinct downstream tasks: semantic classification, segmentation, and PDE-guided physics simulation. Experimental results demonstrate that our framework achieves superior task performance with fewer views compared to commonly used baselines and prior general uncertainty-reduction techniques.

How many key-value associations can a $d\times d$ linear memory store? We show that the answer depends not only on the $d^2$ degrees of freedom in the memory matrix, but also on the retrieval criterion. In an isotropic Gaussian model for the stored pairs, we show that top-1 retrieval, where every signal must beat its largest distractor, requires the logarithmic model-size scale $d^2\asymp n\log n$. We prove that the correlation matrix memory construction, which stores associations by superposing key-target outer products, achieves this scale through a sharp phase transition, and that the same scaling is necessary for any linear memory. Thus the logarithm is the intrinsic extreme-value price of winner-take-all decoding. We next consider listwise retrieval, where the correct target need not be the unique top-scoring item but should remain among the strongest candidates. To formalize this regime, we propose the Tail-Average Margin (TAM), a convex upper-tail criterion that certifies inclusion of the correct target in a controlled candidate list. Under this listwise retrieval criterion, the capacity follows the quadratic scale $d^2\asymp n$. At load $n/d^2\toα$, we develop an exact asymptotic theory for the TAM empirical-risk minimizer through a two-parameter scalar variational principle. The theory has a rich phenomenology: in the ridgeless limit it yields a closed-form critical load separating satisfiable and unsatisfiable phases, and it predicts the limiting laws of true scores, competitor scores, margins, and percentile profiles. Finally, a small-tail extrapolation further leads to the conjectural sharp top-1 threshold $d^2\sim 2n\log n$.

To stop children from bypassing its age checks, Meta is revamping its age-verification tools with an AI system that analyzes images and videos for "visual cues," such as height and bone structure. Meta is beefing up its age-verification mechanisms with an AI system that analyzes images and videos on Instagram and Facebook for "visual cues," such as height and bone structure, to identify and delete accounts of users under the age of 13. The company announced the move amid a wave of cases in which hundreds of children have managed to evade social network access restrictions, even through simple tricks such as drawing on a mustache. The new approach is part of a series of measures Meta adopted as part of an AI-based security strategy designed to correct the limitations of traditional methods, which rely heavily on self-reported age. With this change, the company seeks to reduce the ease with which minors access platforms that, in theory, are restricted to them.

In an unexpected turn, the two companies signed a deal for Anthropic to use computing resources from Elon Musk's xAI. Anthropic and Elon Musk's SpaceX said on Wednesday that the two entities have signed an agreement for Anthropic to use computing resources from xAI's data center in Memphis, Tennessee. It's the latest tie up in an industry that is scrambling to find enough computers to run complex AI software. SpaceX and xAI were previously separate companies, but the two merged earlier this year. The combined entity, also owned by Musk, is called SpaceXAI.

New research suggests that reliance on AI assistants can have a negative impact on people's ability to think and problem solve. Using AI chatbots for even just for 10 minutes may have a shockingly negative impact on people's ability to think and problem-solve, according to a new study from researchers at Carnegie Mellon, MIT, Oxford, and UCLA. Researchers tasked people with solving various problems, including simple fractions and reading comprehension, through an online platform that paid them for their work. They conducted three experiments, each involving several hundred people. Some participants were given access to an AI assistant capable of solving the problem autonomously.

Plus a roller coaster'thoosie' and other weird things we learned this week. 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. An 800-year-old Latin chant called the Dies irae will hit your feels. Breakthroughs, discoveries, and DIY tips sent six days a week. What's the weirdest thing you learned this week?

Hackers and other cybercriminals are complaining about "AI shit" flooding platforms where they discuss cyberattacks and other illegal activity. "I'm disappointed that you are working to incorporate AI garbage into the site," one annoyed person, posting anonymously, said in an online message. "No-one is asking for this--we want you to improve the site, stop charging for new features." Only, this is not a regular internet user moaning about AI being forced into their favorite app . Instead, they are complaining about a cybercrime forum's plans to introduce more generative AI.

It probably looked as cool as you think. 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. Gold ligature surrounding the left central incisor and the right lateral incisor on the mandible of an adult male buried in the East Kirk of the parish church of St Nicholas, Aberdeen, Scotland. Breakthroughs, discoveries, and DIY tips sent six days a week. Today, extensive tooth repair or replacement often requires the installation of a dental bridge made from durable resin and metal.