This supplementary material provides further elaboration and discussion on our work, including additional details that support our findings.

We consider a non-convex constrained optimization problem, where the objective function is weakly convex and the constraint function is either convex or weakly convex. To solve this problem, we consider the classical switching subgradient method, which is an intuitive and easily implementable first-order method whose oracle complexity was only known for convex problems. This paper provides the first analysis on the oracle complexity of the switching subgradient method for finding a nearly stationary point of non-convex problems. Our results are derived separately for convex and weakly convex constraints. Compared to existing approaches, especially the double-loop methods, the switching gradient method can be applied to non-smooth problems and achieves the same complexity using only a single loop, which saves the effort on tuning the number of inner iterations.

The weaponry highlights a coastal Belgian city's longtime strategic location. 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. Breakthroughs, discoveries, and DIY tips sent six days a week. Renovations on government buildings in the coastal Belgian town of Nieuwpoort are currently on hold after surveyors discovered an impressive archaeological trove: dozens of carefully crafted stone cannonballs dating as far back as the 14th century. However, the medieval ammunition backstock wasn't the only weaponry buried roughly 70 miles west of Brussels.

AI chatbots trained to be warm and friendly when interacting with users may also be more prone to inaccuracies, new research suggests. Oxford Internet Institute (OII) researchers analysed more than 400,000 responses from five AI systems which had been tweaked to communicate in a more empathetic way. Friendlier answers contained more mistakes - from giving inaccurate medical advice to reaffirming user's false beliefs, the study found. The findings raise further questions over the trustworthiness of AI models, which are often deliberately designed to be warm and human-like in order to increase engagement. Such concerns are accentuated by AI chatbots being used for support and even intimacy, as developers seek to broaden their appeal.

In some applications of reinforcement learning, a dataset of pre-collected experience is already available but it is also possible to acquire some additional online data to help improve the quality of the policy. However, it may be preferable to gather additional data with a single, non-reactive exploration policy and avoid the engineering costs associated with switching policies. In this paper we propose an algorithm with provable guarantees that can leverage an offline dataset to design a single non-reactive policy for exploration. We theoretically analyze the algorithm and measure the quality of the final policy as a function of the local coverage of the original dataset and the amount of additional data collected.

The recent popularity of text-to-image diffusion models (DM) can largely be attributed to the intuitive interface they provide to users. The intended generation can be expressed in natural language, with the model producing faithful interpretations of text prompts. However, expressing complex or nuanced ideas in text alone can be difficult.

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.

The McKean-Vlasov equation (MVE) describes the collective behavior of particles subject to drift, diffusion, and mean-field interaction. In physical systems, the interaction term can be singular, i.e. it diverges when two particles collide. Notable examples of such interactions include the Coulomb interaction, fundamental in plasma physics, and the Biot-Savart interaction, present in the vorticity formulation of the 2DNavier-Stokes equation (NSE) in fluid dynamics. Solving MVEs that involve singular interaction kernels presents a significant challenge, especially when aiming to provide rigorous theoretical guarantees. In this work, we propose a novel approach based on the concept of entropy dissipation in the underlying system.

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.