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Cops and Robbers is a well-studied pursuit-evasion game in which a set of cops seeks to catch a robber in a graph G, where cops and robber move along edges of G. The cop number of G is the minimum number of cops that is sufficient to catch the robber. Every planar graph has cop number at most three, and there are planar graphs for which three cops are necessary [Aigner and Fromme, DAM 1984]. We study the problem for beyond-planar graphs, that is, graphs that can be drawn in the plane with few crossings. In particular, we focus on 1-planar graphs, that is, graphs that can be drawn in the plane with at most one crossing per edge. In contrast to planar graphs, we show that some 1-planar graphs have unbounded cop number. Meanwhile, for maximal 1-planar graphs, we prove that three cops are always sufficient and sometimes necessary. In addition, we characterize outer 1-planar graphs with respect to their cop number.

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Ontologies often require knowledge representation on multiple levels of abstraction, but description logics (DLs) are not well-equipped for supporting this. We propose an extension of DLs in which abstraction levels are first-class citizens and which provides explicit operators for the abstraction and refinement of concepts and roles across multiple abstraction levels, based on conjunctive queries. We prove that reasoning in the resulting family of DLs is decidable while several seemingly harmless variations turn out to be undecidable. We also pinpoint the precise complexity of our logics and several relevant fragments.

We address a benchmark task in agile robotics: catching objects thrown at high-speed. This is a challenging task that involves tracking, intercepting, and cradling a thrown object with access only to visual observations of the object and the proprioceptive state of the robot, all within a fraction of a second. We present the relative merits of two fundamentally different solution strategies: (i) Model Predictive Control using accelerated constrained trajectory optimization, and (ii) Reinforcement Learning using zeroth-order optimization. We provide insights into various performance trade-offs including sample efficiency, sim-to-real transfer, robustness to distribution shifts, and whole-body multimodality via extensive on-hardware experiments. We conclude with proposals on fusing "classical" and "learning-based" techniques for agile robot control. Videos of our experiments may be found at //sites.google.com/view/agile-catching

As one of the three main pillars of fine-grained complexity theory, the 3SUM problem explains the hardness of many diverse polynomial-time problems via fine-grained reductions. Many of these reductions are either directly based on or heavily inspired by P\u{a}tra\c{s}cu's framework involving additive hashing and are thus randomized. Some selected reductions were derandomized in previous work [Chan, He; SOSA'20], but the current techniques are limited and a major fraction of the reductions remains randomized. In this work we gather a toolkit aimed to derandomize reductions based on additive hashing. Using this toolkit, we manage to derandomize almost all known 3SUM-hardness reductions. As technical highlights we derandomize the hardness reductions to (offline) Set Disjointness, (offline) Set Intersection and Triangle Listing -- these questions were explicitly left open in previous work [Kopelowitz, Pettie, Porat; SODA'16]. The few exceptions to our work fall into a special category of recent reductions based on structure-versus-randomness dichotomies. We expect that our toolkit can be readily applied to derandomize future reductions as well. As a conceptual innovation, our work thereby promotes the theory of deterministic 3SUM-hardness. As our second contribution, we prove that there is a deterministic universe reduction for 3SUM. Specifically, using additive hashing it is a standard trick to assume that the numbers in 3SUM have size at most $n^3$. We prove that this assumption is similarly valid for deterministic algorithms.

In the wake of Masked Image Modeling (MIM), a diverse range of plain, non-hierarchical Vision Transformer (ViT) models have been pre-trained with extensive datasets, offering new paradigms and significant potential for semantic segmentation. Current state-of-the-art systems incorporate numerous inductive biases and employ cumbersome decoders. Building upon the original motivations of plain ViTs, which are simplicity and generality, we explore high-performance `minimalist' systems to this end. Our primary purpose is to provide simple and efficient baselines for practical semantic segmentation with plain ViTs. Specifically, we first explore the feasibility and methodology for achieving high-performance semantic segmentation using the last feature map. As a result, we introduce the PlainSeg, a model comprising only three 3$\times$3 convolutions in addition to the transformer layers (either encoder or decoder). In this process, we offer insights into two underlying principles: (i) high-resolution features are crucial to high performance in spite of employing simple up-sampling techniques and (ii) the slim transformer decoder requires a much larger learning rate than the wide transformer decoder. On this basis, we further present the PlainSeg-Hier, which allows for the utilization of hierarchical features. Extensive experiments on four popular benchmarks demonstrate the high performance and efficiency of our methods. They can also serve as powerful tools for assessing the transfer ability of base models in semantic segmentation. Code is available at \url{//github.com/ydhongHIT/PlainSeg}.

Deep networks typically learn concepts via classifiers, which involves setting up a model and training it via gradient descent to fit the concept-labeled data. We will argue instead that learning a concept could be done by looking at its moment statistics matrix to generate a concrete representation or signature of that concept. These signatures can be used to discover structure across the set of concepts and could recursively produce higher-level concepts by learning this structure from those signatures. When the concepts are `intersected', signatures of the concepts can be used to find a common theme across a number of related `intersected' concepts. This process could be used to keep a dictionary of concepts so that inputs could correctly identify and be routed to the set of concepts involved in the (latent) generation of the input.

Graph Neural Networks (GNNs) are state-of-the-art models for performing prediction tasks on graphs. While existing GNNs have shown great performance on various tasks related to graphs, little attention has been paid to the scenario where out-of-distribution (OOD) nodes exist in the graph during training and inference. Borrowing the concept from CV and NLP, we define OOD nodes as nodes with labels unseen from the training set. Since a lot of networks are automatically constructed by programs, real-world graphs are often noisy and may contain nodes from unknown distributions. In this work, we define the problem of graph learning with out-of-distribution nodes. Specifically, we aim to accomplish two tasks: 1) detect nodes which do not belong to the known distribution and 2) classify the remaining nodes to be one of the known classes. We demonstrate that the connection patterns in graphs are informative for outlier detection, and propose Out-of-Distribution Graph Attention Network (OODGAT), a novel GNN model which explicitly models the interaction between different kinds of nodes and separate inliers from outliers during feature propagation. Extensive experiments show that OODGAT outperforms existing outlier detection methods by a large margin, while being better or comparable in terms of in-distribution classification.

Australia is a leading AI nation with strong allies and partnerships. Australia has prioritised robotics, AI, and autonomous systems to develop sovereign capability for the military. Australia commits to Article 36 reviews of all new means and methods of warfare to ensure weapons and weapons systems are operated within acceptable systems of control. Additionally, Australia has undergone significant reviews of the risks of AI to human rights and within intelligence organisations and has committed to producing ethics guidelines and frameworks in Security and Defence. Australia is committed to OECD's values-based principles for the responsible stewardship of trustworthy AI as well as adopting a set of National AI ethics principles. While Australia has not adopted an AI governance framework specifically for Defence; Defence Science has published 'A Method for Ethical AI in Defence' (MEAID) technical report which includes a framework and pragmatic tools for managing ethical and legal risks for military applications of AI.

Multi-agent influence diagrams (MAIDs) are a popular form of graphical model that, for certain classes of games, have been shown to offer key complexity and explainability advantages over traditional extensive form game (EFG) representations. In this paper, we extend previous work on MAIDs by introducing the concept of a MAID subgame, as well as subgame perfect and trembling hand perfect equilibrium refinements. We then prove several equivalence results between MAIDs and EFGs. Finally, we describe an open source implementation for reasoning about MAIDs and computing their equilibria.

Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.

In Multi-Label Text Classification (MLTC), one sample can belong to more than one class. It is observed that most MLTC tasks, there are dependencies or correlations among labels. Existing methods tend to ignore the relationship among labels. In this paper, a graph attention network-based model is proposed to capture the attentive dependency structure among the labels. The graph attention network uses a feature matrix and a correlation matrix to capture and explore the crucial dependencies between the labels and generate classifiers for the task. The generated classifiers are applied to sentence feature vectors obtained from the text feature extraction network (BiLSTM) to enable end-to-end training. Attention allows the system to assign different weights to neighbor nodes per label, thus allowing it to learn the dependencies among labels implicitly. The results of the proposed model are validated on five real-world MLTC datasets. The proposed model achieves similar or better performance compared to the previous state-of-the-art models.

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