's leaf nodes to form Given the definition of our attention in Eq. 9 in the main text, the highest polynomial order is Before providing the proof of Theorem 4, we establish Lemma 1 as its foundation. We follow the principle of Y an et al's work [ Figure 1, we consider two kinds of value functions, i.e., In P AM-Net, we set the number of levels to 2. A grid search is performed over different configurations We conduct grid searches on the dropout rate over {0, 0.1, 0.2} and the initial

Neural approaches for combinatorial optimization (CO) equip a learning mechanism to discover powerful heuristics for solving complex real-world problems. While neural approaches capable of high-quality solutions in a single shot are emerging, state-of-the-art approaches are often unable to take full advantage of the solving time available to them. In contrast, hand-crafted heuristics perform highly effective search well and exploit the computation time given to them, but contain heuristics that are difficult to adapt to a dataset being solved.

This paper addresses the problem of building global topological maps from 3D LiDAR point clouds for autonomous mobile robots operating in large-scale, dynamic, and unknown environments. Adaptive Resonance Theory-based Topological Clustering with Different Topologies (ATC-DT) builds global topological maps represented as graphs while mitigating catastrophic forgetting during sequential processing. However, its winner selection mechanism relies on an exhaustive nearest-neighbor search over all existing nodes, leading to scalability limitations as the map grows. To address this challenge, we propose a hierarchical extension called Multi-Layer ATC (MLATC). MLATC organizes nodes into a hierarchy, enabling the nearest-neighbor search to proceed from coarse to fine resolutions, thereby drastically reducing the number of distance evaluations per query. The number of layers is not fixed in advance. MLATC employs an adaptive layer addition mechanism that automatically deepens the hierarchy when lower layers become saturated, keeping the number of user-defined hyperparameters low. Simulation experiments on synthetic large-scale environments show that MLATC accelerates topological map building compared to the original ATC-DT and exhibits a sublinear, approximately logarithmic scaling of search time with respect to the number of nodes. Experiments on campus-scale real-world LiDAR datasets confirm that MLATC maintains a millisecond-level per-frame runtime and enables real-time global topological map building in large-scale environments, significantly outperforming the original ATC-DT in terms of computational efficiency.

Large language models (LLMs), with the transformer architecture being their core building block, are remarkably successful across a wide range of tasks, in particular reasoning. LLMs excel in solving complex reasoning tasks by iteratively generating intermediate steps [Wei et al., 2022]-- an intriguing approach known as Chain-of-Thought (CoT). Fine-tuning has been shown to be a powerful method to enhance efficient CoT generation in LLMs, which in turn improves the multi-step reasoning performance of LLMs significantly [Wei et al., 2022, Zelikman et al., 2022, Lightman et al., 2024]. A widely adopted approach for fine-tuning to generate CoT is supervised fine-tuning (SFT), where the transformers are trained to minimize a loss over pairs of inputs and labeled outputs. While straightforward, SFT is restricted by the demand of a large amount of labeled CoT data. As a result, fine-tuning approaches based on reinforcement learning (RL) [DeepSeek-AI et al., 2025, Ouyang et al., 2022, Bai et al., 2022, Christiano et al., 2023, Kumar et al., 2024] are increasingly prevalent. Instead of minimizing a loss over labeled CoT data, RL guides transformers to generate CoT to solve complex reasoning tasks by maximizing a reward function via policy gradient methods [Mnih et al., 2016, Schulman et al., 2017, DeepSeek-AI et al., 2025], which has shown significant potential for improving the reasoning capabilities of LLMs.

Asynchronous parallel optimization received substantial successes and extensive attention recently. One of core theoretical questions is how much speedup (or benefit) the asynchronous parallelization can bring to us. This paper provides a comprehensive and generic analysis to study the speedup property for a broad range of asynchronous parallel stochastic algorithms from the zeroth order to the first order methods. Our result recovers or improves existing analysis on special cases, provides more insights for understanding the asynchronous parallel behaviors, and suggests a novel asynchronous parallel zeroth order method for the first time. Our experiments provide novel applications of the proposed asynchronous parallel zeroth order method on hyper parameter tuning and model blending problems.

Neural Information Processing Systems http://nips.cc/

Mean-shift-based approaches have recently emerged as the most effective methods for robot swarm shape assembly tasks. These methods rely on image-based representations of target shapes to compute local density gradients and perform mean-shift exploration, which constitute their core mechanism. However, such image representations incur substantial memory overhead, which can become prohibitive for high-resolution or 3D shapes. To overcome this limitation, we propose a memory-efficient tree map representation that hierarchically encodes user-specified shapes and is applicable to both 2D and 3D scenarios. Building on this representation, we design a behavior-based distributed controller that enables assignment-free shape assembly. Comparative 2D and 3D simulations against a state-of-the-art mean-shift algorithm demonstrate one to two orders of magnitude lower memory usage and two to three times faster shape entry while maintaining comparable uniformity. Finally, we validate the framework through physical experiments with 6 to 7 UAVs, confirming its real-world practicality.

In this paper, we propose a 3D path planning method that integrates the A* algorithm with the octree structure. Unmanned Ground Vehicles (UGVs) and legged robots have been extensively studied, enabling locomotion across a variety of terrains. Advances in mobility have enabled obstacles to be regarded not only as hindrances to be avoided, but also as navigational aids when beneficial. A modified 3D A* algorithm generates an optimal path by leveraging obstacles during the planning process. By incorporating a height-based penalty into the cost function, the algorithm enables the use of traversable obstacles to aid locomotion while avoiding those that are impassable, resulting in more efficient and realistic path generation. The octree-based 3D grid map achieves compression by merging high-resolution nodes into larger blocks, especially in obstacle-free or sparsely populated areas. This reduces the number of nodes explored by the A* algorithm, thereby improving computational efficiency and memory usage, and supporting real-time path planning in practical environments. Benchmark results demonstrate that the use of octree structure ensures an optimal path while significantly reducing memory usage and computation time.