Maximizing the expected value of a concave and strictly increasing utility function defines a fundamental class of discrete optimization problems. Among them, coverage decision problems with diminishing marginal returns under uncertainty, typically modeled via a set-union operator, have been extensively studied. In the classical framework, an item becomes active once it is covered by at least one chosen meta-item. Motivated by increasing robustness requirements in applications such as automated systems, social networks, and emergency response planning, we extend this setting by introducing threshold-based activation. The resulting generalized problem can be formulated as a mixed-integer nonlinear programming problem, for which we further propose three exact algorithms. The first two methods linearize the utility function using submodular cuts (SC) and outer-approximation (OA) techniques, respectively, resulting in formulations that can be solved exactly by off-the-shelf mixed-integer linear programming solvers. The third method builds upon the OA framework and further employs Benders decomposition (BD) to project out the item-related variables, which enables superior performance on ultra-large-scale instances. Extensive computational experiments show that, compared with the SC and BD methods, the OA method exhibits a substantial speed advantage on instances with a size of around 40,000, which can be solved within 100 s. In contrast, for ultra-large-scale instances with more than 100,000 items, the BD method demonstrates superior computational efficiency. These results provide practical guidance for algorithmic strategy selection and further demonstrate the computational tractability of this broader class of utility maximization problems under threshold-based activation.
With the increasing scale and complexity of graph data, graph sampling has become a crucial dimensionality reduction technique, while the evaluation of its effectiveness has also garnered significant attention. However, traditional sampling evaluation methods primarily focus on preserving topological structures while neglecting the integrity of node attributes. To address this, we introduce an attribute-aware evaluation framework for assessing graph sampling differences. First, a novel taxonomy is proposed to categorize sampling differences into two major types: Attribute-Isolation and Attribute-Structure. The former is further divided into Attribute-Distribution and Attribute-Correlation, while the latter includes three subcategories: Attribute-Node, Attribute-Path, and Attribute-Community. Based on this, we design a set of computable metrics to quantify each type of attribute-related differences. Furthermore, we develop an interactive visualization system that integrates multiview visual modules to visualize sampling impacts on attributes and structural correlations. Case studies and quantitative evaluations demonstrate the effectiveness of our method in characterizing the impact of different sampling strategies on attribute information and aiding users in network analysis and strategy selection.
This paper addresses the task of large-scale 3D scene reconstruction from long video sequences. Recent feed-forward reconstruction models have shown promising results by directly regressing 3D geometry from RGB images without explicit 3D priors or geometric constraints. However, these methods often struggle to maintain reconstruction accuracy and consistency over long sequences due to limited memory capacity and the inability to effectively capture global contextual cues. In contrast, humans can naturally exploit the global understanding of the scene to inform local perception. Motivated by this, we propose a novel neural global context representation that efficiently compresses and retains long-range scene information, enabling the model to leverage extensive contextual cues for enhanced reconstruction accuracy and consistency. The context representation is realized through a set of lightweight neural sub-networks that are rapidly adapted during test time via self-supervised objectives, which substantially increases memory capacity without incurring significant computational overhead. The experiments on multiple large-scale benchmarks, including the KITTI Odometry~\cite{Schops 2019 CVPR} and Oxford Spires~\cite{tao2025spires} datasets, demonstrate the effectiveness of our approach in handling ultra-large scenes, achieving state-of-the-art performance in both pose estimation and 3D reconstruction accuracy while maintaining efficiency.
Improving GPU kernel efficiency is crucial for advancing AI systems. Recent work has explored leveraging large language models (LLMs) for GPU kernel generation and optimization. However, existing LLM-based kernel optimization pipelines typically rely on opaque, implicitly learned heuristics within the LLMs to determine optimization strategies. This leads to inefficient trial-and-error and weakly interpretable optimizations. Our key insight is to replace implicit heuristics with expert optimization skills that are knowledge-driven and aware of task trajectories. Specifically, we present KernelSkill, a multi-agent framework with a dual-level memory architecture. KernelSkill operates by coordinating agents with long-term memory of reusable expert skills and short-term memory to prevent repetitive backtracking. On KernelBench Levels 1-3, KernelSkill achieves a 100
Physical principles are fundamental to realistic visual simulation, but remain a significant oversight in video generation. This gap highlights a critical limitation in rendering rigid body motion, a core tenet of classical mechanics. While computer graphics and physics-based simulators can easily model such dynamics using Newton formulas, modern video generative models discard the concept of object rigidity during pixel-level global denoising. Existing methods attempt to tackle this problem through physical data augmentation, dynamics pre-simulation, or reinforcement learning with VLM ratings, but none of these approaches accurately reflect physical principles or enable the model to internalize physical knowledge. Motivated by these considerations, we introduce reinforcement learning with physically verifiable rewards. We design a quantitatively verifiable metric that combines Trajectory Offset and Collision Detection, which can accurately capture rigid-body motion states and assess the quality of generated samples. Subsequently, we extend this paradigm to a unified post-training framework, termed Mimicry-Discovery Cycle, which enables stable training on out-of-distribution scenarios while improving overall model performance. To validate our approach, we construct new benchmark PhysRVGBench and perform extensive qualitative and quantitative experiments to thoroughly assess its effectiveness. The code and demo can be found at https://lucaria-academy.github.io/PhysRVG/ .
