We push each class to its supernode, then apply majority vote to determine the final class.

Machine learning models--including prominent zero-shot models--are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them.

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

We consider the problem of searching for an intruder in a geometric domain by utilizing multiple search robots. The domain is a simply connected orthogonal polygon with edges parallel to the cartesian coordinate axes. Each robot has a limited sensing capability. We study the problem for both static and mobile intruders. It turns out that the problem of finding an intruder is NP-hard, even for a stationary intruder. Given this intractability, we turn our attention towards developing efficient and robust algorithms, namely methods based on space-filling curves, random search, and cooperative random search. Moreover, for each proposed algorithm, we evaluate the trade-off between the number of search robots and the time required for the robots to complete the search process while considering the geometric properties of the connected orthogonal search area.

Reasoning capability is essential to ensure the factual correctness of the responses of transformer-based Large Language Models (LLMs), and robust reasoning about transitive relations is instrumental in many settings, such as causal inference. Hence, it is essential to investigate the capability of transformers in the task of inferring transitive relations (e.g., knowing A causes B and B causes C, then A causes C). The task of inferring transitive relations is equivalent to the task of connectivity in directed graphs (e.g., knowing there is a path from A to B, and there is a path from B to C, then there is a path from A to C). Past research focused on whether transformers can learn to infer transitivity from in-context examples provided in the input prompt. However, transformers' capability to infer transitive relations from training examples and how scaling affects the ability is unexplored. In this study, we seek to answer this question by generating directed graphs to train transformer models of varying sizes and evaluate their ability to infer transitive relations for various graph sizes. Our findings suggest that transformers are capable of learning connectivity on "grid-like'' directed graphs where each node can be embedded in a low-dimensional subspace, and connectivity is easily inferable from the embeddings of the nodes. We find that the dimensionality of the underlying grid graph is a strong predictor of transformers' ability to learn the connectivity task, where higher-dimensional grid graphs pose a greater challenge than low-dimensional grid graphs. In addition, we observe that increasing the model scale leads to increasingly better generalization to infer connectivity over grid graphs. However, if the graph is not a grid graph and contains many disconnected components, transformers struggle to learn the connectivity task, especially when the number of components is large.

Image datasets such as MNIST are a key benchmark for testing Graph Neural Network (GNN) architectures. The images are traditionally represented as a grid graph with each node representing a pixel and edges connecting neighboring pixels (vertically and horizontally). The graph signal is the values (intensities) of each pixel in the image. The graphs are commonly used as input to graph neural networks (e.g., Graph Convolutional Neural Networks (Graph CNNs) [1, 2], Graph Attention Networks (GAT) [3], GatedGCN [4]) to classify the images. In this work, we improve the accuracy of downstream graph neural network tasks by finding alternative graphs to the grid graph and superpixel methods to represent the dataset images, following the approach in [5, 6]. We find row correlation, column correlation, and product graphs for each image in MNIST and Fashion-MNIST using correlations between the pixel values building on the method in [5, 6]. Experiments show that using these different graph representations and features as input into downstream GNN models improves the accuracy over using the traditional grid graph and superpixel methods in the literature.

We propose a new family of efficient and expressive deep generative models of graphs, called Graph Recurrent Attention Networks (GRANs).

Abstract--We study Multi-Robot Coverage Path Planning (MCPP) on a 4-neighbor 2D grid G, which aims to compute paths for multiple robots to cover all cells of G. Traditional approaches are limited as they first compute coverage trees on a quadrant coarsened grid H and then employ the Spanning Tree Coverage (STC) paradigm to generate paths on G, making them inapplicable to grids with partially obstructed 2 2 blocks. To address this limitation, we reformulate the problem directly on G, revolutionizing grid-based MCPP solving and establishing new NP-hardness results. We introduce Extended-STC (ESTC), a novel paradigm that extends STC to ensure complete coverage with bounded suboptimality, even when H includes partially obstructed blocks. These methods then apply the Spanning Tree Coverage (STC) [17] paradigm to generate coverage I. Coverage Path Planning (CPP) addresses the problem of determining However, operating exclusively on the coarsened grid H has a path that fully covers a designated workspace [1]. First, it fails in cases where H is This problem is essential for a broad spectrum of robotic incomplete--that is, when any 2 2 blocks contain obstructed applications, from indoor tasks like vacuum cleaning [2] and grid cells absent from G. Second, even optimal coverage trees inspection [3] to outdoor activities such as automated harvesting on H do not necessarily result in an optimal MCPP solution (as [4], planetary exploration [5], and environmental monitoring illustrated in Figure 1-(b) and (c)), as evidenced by an asymptotic [6]. Multi-Robot Coverage Path Planning (MCPP) is an suboptimality ratio of four for makespan minimization [14], extension of CPP tailored for multi-robot systems, aiming to since the paths derived from circumnavigating coverage trees coordinate the paths of multiple robots to collectively cover the of H constitute only a subset of all possible sets of coverage given workspace, thereby enhancing both task efficiency [7] The authors are with the School of Computing Science, Simon to discuss the structure and topology of G more precisely, especially in the Fraser University, Burnaby, BC V5A1S6, Canada. The robots require a cost of 1 to traverse between adjacent vertices of G. (a) Single-robot coverage path LS-MCPP but also those generated by existing MCPP methods, to effectively resolve conflicts between robots We revolutionize solving MCPP on grid graphs, overcoming and accounts for turning costs, further enhancing the the above limitations through a two-phase approach that first practicability of the solutions. Our algorithmic contribution are detailed in real-world robotics applications.