S1.1 Step-by-step derivation of min-max optimization in Section 2.2.1 By substituting Eq. 2 into Eq. 1 in the main manuscript, we can obtain the objective function of subscript z (we temporarily drop ifor clarity): J(z) = max Since z might be in high dimensional space, solving such a large system of linear equations under the constraint |z| 1is oftentimes computationally challenging. In order to find a practical solution for z that satisfies the constrained minimization problem in Eq. By setting zl as point of coincidence, we can find a separable majorizer of M(z) by adding the non-negative function (z zl) (βI Gx Gx)(z zl) (S6) 37th Conference on Neural Information Processing Systems (NeurIPS 2023). Note, to unify the format, we use the matrix transpose property in Eq. Then, the next step is to find z RN that minimizes z z 2bz subject to the constraint |z| 1. Let's first consider the simplest case where z is a scalar: argmin If b 1, then the solution is z = b.

Graphs are ubiquitous in various domains, such as social networks and biological systems. Despite the great successes of graph neural networks (GNNs) in modeling and analyzing complex graph data, the inductive bias of locality assumption, which involves exchanging information only within neighboring connected nodes, restricts GNNs in capturing long-range dependencies and global patterns in graphs. Inspired by the classic Brachistochrone problem, we seek how to devise a new inductive bias for cutting-edge graph application and present a general framework through the lens of variational analysis. The backbone of our framework is a two-way mapping between the discrete GNN model and continuous diffusion functional, which allows us to design application-specific objective function in the continuous domain and engineer discrete deep model with mathematical guarantees. First, we address over-smoothing in current GNNs.

With the rapidly increasing demand for oriented object detection, e.g. in autonomous driving and remote sensing, the recently proposed paradigm involving weakly-supervised detector H2RBox for learning rotated box (RBox) from the more readily-available horizontal box (HBox) has shown promise. This paper presents H2RBox-v2, to further bridge the gap between HBox-supervised and RBox-supervised oriented object detection. Specifically, we propose to leverage the reflection symmetry via flip and rotate consistencies, using a weakly-supervised network branch similar to H2RBox, together with a novel self-supervised branch that learns orientations from the symmetry inherent in visual objects. The detector is further stabilized and enhanced by practical techniques to cope with peripheral issues e.g.

Neural Radiance Field (NeRF) is an implicit 3D reconstruction method that has shown immense potential and has gained significant attention for its ability to reconstruct 3D scenes solely from a set of photographs. However, its real-time rendering capability, especially for interactive real-time rendering of large-scale scenes, has significant limitations. To address this challenge, we propose a novel neural rendering system called UE4-NeRF that is designed for real-time rendering of large-scale scenes. Our proposed approach partitions large scenes into subNeRFs, and uses polygonal meshes to represent them. In order to represent the partitioned independent scene, we initialize polygonal meshes by constructing multiple regular octahedra within the scene and the vertices of the polygonal faces are continuously optimized during the training process. Drawing inspiration from the Level of Detail (LOD) techniques, we train meshes with varying levels of detail for different observation levels. Our approach combines with the rasterization pipeline in Unreal Engine 4 (UE4), achieving real-time rendering of large-scale scenes at 4K resolution with a frame rate of up to 43 FPS. Our experimental results demonstrate that our method attains rendering quality on par with state-of-the-art approaches, while additionally offering the advantage of real-time performance.

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The streamline shape is still more aerodynamic than most cars today. 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. In 1930, English engineer Sir Dennis Burney told Popular Science that his teardrop-shaped car would cut fuel consumption in half. Breakthroughs, discoveries, and DIY tips sent six days a week. From the start, cars were built wrong. At least, that's what Chrysler's head of automotive research, Carl Breer, thought in 1930. Automobiles had never been built to be aerodynamic, he posited, and he was right.

We find that the distribution shift settings in previous studies commonly lack adequate challenges, hindering the accurate evaluation of OOD robustness. To address these issues, we propose a benchmark construction protocol that ensures clear differentiation and challenging distribution shifts. Then we introduce BOSS, a Benchmark suite for Out-of-distribution robustneSS evaluation covering 5 tasks and 20 datasets. Based on BOSS, we conduct a series of experiments on pretrained language models for analysis and evaluation of OOD robustness. First, for vanilla fine-tuning, we examine the relationship between in-distribution (ID) and OOD performance. We identify three typical types that unveil the inner learning mechanism, which could potentially facilitate the forecasting of OOD robustness, correlating with the advancements on ID datasets. Then, we evaluate 5 classic methods on BOSS and find that, despite exhibiting some effectiveness in specific cases, they do not offer significant improvement compared to vanilla fine-tuning. Further, we evaluate 5 LLMs with various adaptation paradigms and find that when sufficient ID data is available, fine-tuning domain-specific models outperform LLMs on ID examples significantly.

A diversity of tasks use language models trained on semantic similarity data. While there are a variety of datasets that capture semantic similarity, they are either constructed from modern web data or are relatively small datasets created in the past decade by human annotators.