Graph), a comprehensive benchmark of graph-based problem solving designed in natural language.

In this section, we provide an open-ended discussion on how the prior distribution ( i.e., imbalanced

Here we cover the full specification of the experiments. Some details were omitted from the main text. If there were separate training and test sets, they were combined before creating the random 10-fold split. All attributes are normalized to mean 0 and standard deviation 1. Additional details for each model type follow.

Accurate localization represents a fundamental challenge in robotic navigation. Traditional methodologies, such as Lidar or QR-code-based systems, suffer from inherent scalability and adaptability constraints, particularly in complex environments. In this work, we propose an innovative localization framework that harnesses flooring characteristics by employing graph-based representations and Graph Convolutional Networks (GCNs). Our method uses graphs to represent floor features, which helps localize the robot more accurately ( 0. 64 cm error) and more efficiently than comparing individual image features. Additionally, this approach successfully addresses the kidnapped robot problem in every frame without requiring complex filtering processes.

This paper introduces GraphOmni, a comprehensive benchmark designed to evaluate the reasoning capabilities of LLMs on graph-theoretic tasks articulated in natural language. GraphOmni encompasses diverse graph types, serialization formats, and prompting schemes, significantly exceeding prior efforts in both scope and depth. Through extensive systematic evaluation, we identify critical interactions among these dimensions, demonstrating their substantial impact on model performance. Our experiments reveal that state-of-the-art models like Claude-3.5 and o4-mini consistently outperform other models, yet even these leading models exhibit substantial room for improvement. Performance variability is evident depending on the specific combinations of factors we considered, underscoring the necessity of comprehensive evaluations across these interconnected dimensions. Additionally, we observe distinct impacts of serialization and prompting strategies between open-source and closed-source models, encouraging the development of tailored approaches. Motivated by the findings, we also propose a reinforcement learning-inspired framework that adaptively selects the optimal factors influencing LLM reasoning capabilities. This flexible and extendable benchmark not only deepens our understanding of LLM performance on structured tasks but also provides a robust foundation for advancing research in LLM-based graph reasoning. The code and datasets are available at https://github.com/GAI-Community/GraphOmni.

Although gossip and random walk-based learning algorithms are widely known for decentralized learning, there has been limited theoretical and experimental analysis to understand their relative performance for different graph topologies and data heterogeneity. We first design and analyze a random walk-based learning algorithm with multiple streams (walks), which we name asynchronous "Multi-Walk (MW)". We provide a convergence analysis for MW w.r.t iteration (computation), wall-clock time, and communication. We also present a convergence analysis for "Asynchronous Gossip", noting the lack of a comprehensive analysis of its convergence, along with the computation and communication overhead, in the literature. Our results show that MW has better convergence in terms of iterations as compared to Asynchronous Gossip in graphs with large diameters (e.g., cycles), while its relative performance, as compared to Asynchronous Gossip, depends on the number of walks and the data heterogeneity in graphs with small diameters (e.g., complete graphs). In wall-clock time analysis, we observe a linear speed-up with the number of walks and nodes in MW and Asynchronous Gossip, respectively. Finally, we show that MW outperforms Asynchronous Gossip in communication overhead, except in small-diameter topologies with extreme data heterogeneity. These results highlight the effectiveness of each algorithm in different graph topologies and data heterogeneity. Our codes are available for reproducibility.

Deep Neural Networks (DNNs) have revolutionized artificial intelligence, achieving impressive results on diverse data types, including images, videos, and texts. However, DNNs still lag behind Gradient Boosting Decision Trees (GBDT) on tabular data, a format extensively utilized across various domains. In this paper, we propose DOFEN, short for \textbf{D}eep \textbf{O}blivious \textbf{F}orest \textbf{EN}semble, a novel DNN architecture inspired by oblivious decision trees. DOFEN constructs relaxed oblivious decision trees (rODTs) by randomly combining conditions for each column and further enhances performance with a two-level rODT forest ensembling process. By employing this approach, DOFEN achieves state-of-the-art results among DNNs and further narrows the gap between DNNs and tree-based models on the well-recognized benchmark: Tabular Benchmark \citep{grinsztajn2022tree}, which includes 73 total datasets spanning a wide array of domains. The code of DOFEN is available at: \url{https://github.com/Sinopac-Digital-Technology-Division/DOFEN}.