Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of stochastic optimization algorithms to cope with large-scale OT problems. These methods can handle arbitrary distributions (either discrete or continuous) as long as one is able to draw samples from them, which is the typical setup in highdimensional learning problems.

Figure 10: Visual results on Pascal validation set with 60 labels.

West Midlands Police has admitted it overstated the evidence used to make the decision to ban Israeli fans from a match in Birmingham. Craig Guildford, its former chief constable, retired earlier this month after damning criticism of the ban on Maccabi Tel Aviv fans from the Europa League match against Aston Villa, last November. In newly released documents, the force also said we did not engage early enough with the local Jewish community, and indicated there was now a ban on AI use after its evidence included a match that did not take place. Furthermore, it said its operations would have lasted four days, involved multiple forces, and cost more than £5m, if 2,500 away fans had attended. The documents were released ahead of a public meeting on Tuesday, at which Police and Crime Commissioner for the West Midlands, Simon Foster, will discuss at his accountability and governance board, the decision to ban the Maccabi fans.

Attention maps are popular tools for explaining the decisions of convolutional neural networks (CNNs) for image classification. Typically, for each image of interest, a single attention map is produced, which assigns weights to pixels based on their importance to the classification. We argue that a single attention map provides an incomplete understanding since there are often many other maps that explain a classification equally well. In this paper, we propose to utilize a beam search algorithm to systematically search for multiple explanations for each image. Results show that there are indeed multiple relatively localized explanations for many images. However, naively showing multiple explanations to users can be overwhelming and does not reveal their common and distinct structures.

The Vision Pro Was an Expensive Misstep. Having reportedly shelved work on a cheaper Vision Pro, Apple is apparently pivoting its focus to smart glasses--and hoping it's not too late. If Apple wants to match the grip Meta has on the smart glasses market, it just might have to simplify its face computers. According to an internal announcement reported in Bloomberg by serial Apple leaker Mark Gurman, Apple has deprioritized efforts to make a lighter, more affordable version of its Vision Pro headset in favor of focusing on AI-enabled smart glasses . Apple now seems to be aiming to launch a pair of Meta-style smart glasses in 2027, with another pair featuring a display on the lens aimed for release in 2028--if not before.

Saliency maps are popular tools for explaining the decisions of convolutional neural networks (CNNs) for image classification.

Human teaching effort is a significant bottleneck for the broader applicability of interactive imitation learning. To reduce the number of required queries, existing methods employ active learning to query the human teacher only in uncertain, risky, or novel situations. However, during these queries, the novice's planned actions are not utilized despite containing valuable information, such as the novice's capabilities, as well as corresponding uncertainty levels. To this end, we allow the novice to say: "I plan to do this, but I am uncertain." We introduce the Active Skill-level Data Aggregation (ASkDAgger) framework, which leverages teacher feedback on the novice plan in three key ways: (1) S-Aware Gating (SAG): Adjusts the gating threshold to track sensitivity, specificity, or a minimum success rate; (2) Foresight Interactive Experience Replay (FIER), which recasts valid and relabeled novice action plans into demonstrations; and (3) Prioritized Interactive Experience Replay (PIER), which prioritizes replay based on uncertainty, novice success, and demonstration age. Together, these components balance query frequency with failure incidence, reduce the number of required demonstration annotations, improve generalization, and speed up adaptation to changing domains. We validate the effectiveness of ASkDAgger through language-conditioned manipulation tasks in both simulation and real-world environments. Code, data, and videos are available at https://askdagger.github.io.

Satellite internet is blasting off right now. Nations and states are inking deals with satellite providers to fill in service gaps for their residents and keep their critical infrastructure connected. Phone makers are building satellite capabilities into their handsets. Airlines are partnering with satellite operators to keep your in-flight Netflix stream stutter-free. And the race to blast the satellites powering these networks into orbit is helping the rocket business thrive.

Ubiquitous geometric objects can be precisely and efficiently represented as polyhedra. The transformation of a polyhedron into a vector, known as polyhedra representation learning, is crucial for manipulating these shapes with mathematical and statistical tools for tasks like classification, clustering, and generation. Recent years have witnessed significant strides in this domain, yet most efforts focus on the vertex sequence of a polyhedron, neglecting the complex surface modeling crucial in real-world polyhedral objects. This study proposes PolyhedronNet, a general framework tailored for learning representations of 3D polyhedral objects. We propose the concept of the surface-attributed graph to seamlessly model the vertices, edges, faces, and their geometric interrelationships within a polyhedron. To effectively learn the representation of the entire surface-attributed graph, we first propose to break it down into local rigid representations to effectively learn each local region's relative positions against the remaining regions without geometric information loss. Subsequently, we propose PolyhedronGNN to hierarchically aggregate the local rigid representation via intra-face and inter-face geometric message passing modules, to obtain a global representation that minimizes information loss while maintaining rotation and translation invariance. Our experimental evaluations on four distinct datasets, encompassing both classification and retrieval tasks, substantiate PolyhedronNet's efficacy in capturing comprehensive and informative representations of 3D polyhedral objects. In mathematics and computational geometry Yu et al. (2025), a polyhedron is defined as a threedimensional (3D) solid formed by flat polygon faces joined at edges and vertices. Ubiquitous geometric shapes can be precisely and efficiently modeled as polyhedra, ranging from basic 3D shapes (e.g., cubic, pyramid, and truncated tetrahedron) to compositions of them (e.g., shapes of buildings, furniture, and digital objects in CAD) as exemplified Figure 1 (a). In the real world, there are many tasks surrounding polyhedra such as classification (e.g., convex or concave); clustering polyhedra into different types (e.g., Platonic solids and prisms); as well as generation and optimization (e.g., use faceted facades to break up flat surfaces) of polyhedra for design needs.