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Multi-object rearrangement is a crucial skill for service robots, and commonsense reasoning is frequently needed in this process. However, achieving commonsense arrangements requires knowledge about objects, which is hard to transfer to robots. Large language models (LLMs) are one potential source of this knowledge, but they do not naively capture information about plausible physical arrangements of the world. We propose LLM-GROP, which uses prompting to extract commonsense knowledge about semantically valid object configurations from an LLM and instantiates them with a task and motion planner in order to generalize to varying scene geometry. LLM-GROP allows us to go from natural-language commands to human-aligned object rearrangement in varied environments. Based on human evaluations, our approach achieves the highest rating while outperforming competitive baselines in terms of success rate while maintaining comparable cumulative action costs. Finally, we demonstrate a practical implementation of LLM-GROP on a mobile manipulator in real-world scenarios. Supplementary materials are available at: //sites.google.com/view/llm-grop

This letter addresses the problem of trajectory planning in a marsupial robotic system consisting of an unmanned aerial vehicle (UAV) linked to an unmanned ground vehicle (UGV) through a non-taut tether with controllable length. To the best of our knowledge, this is the first method that addresses the trajectory planning of a marsupial UGV-UAV with a non-taut tether. The objective is to determine a synchronized collision-free trajectory for the three marsupial system agents: UAV, UGV, and tether. First, we present a path planning solution based on optimal Rapidly-exploring Random Trees (RRT*) with novel sampling and steering techniques to speed-up the computation. This algorithm is able to obtain collision-free paths for the UAV and the UGV, taking into account the 3D environment and the tether. Then, the letter presents a trajectory planner based on non-linear least squares. The optimizer takes into account aspects not considered in the path planning, like temporal constraints of the motion imposed by limits on the velocities and accelerations of the robots, or raising the tether's clearance. Simulated and field test results demonstrate that the approach generates obstacle-free, smooth, and feasible trajectories for the marsupial system.

Some standardized environments have been designed for partially observable multi-agent cooperation, but we find most current environments are synchronous, whereas real-world agents often have their own action spaces leading to asynchrony. Furthermore, fixed agents number limits the scalability of action space, whereas in reality agents number can change resulting in a flexible action space. In addition, current environments are balanced, which is not always the case in the real world where there may be an ability gap between different parties leading to asymmetry. Finally, current environments tend to have less stochasticity with simple state transitions, whereas real-world environments can be highly stochastic and result in extremely risky. To address this gap, we propose WarGame Challenge (WGC) inspired by the Wargame. WGC is a lightweight, flexible, and easy-to-use environment with a clear framework that can be easily configured by users. Along with the benchmark, we provide MARL baseline algorithms such as QMIX and a toolkit to help algorithms complete performance tests on WGC. Finally, we present baseline experiment results, which demonstrate the challenges of WGC. We think WGC enrichs the partially observable multi-agent cooperation domain and introduces more challenges that better reflect the real-world characteristics. Code is release in //turingai.ia.ac.cn/data\_center/show/10.

A multiverse analysis evaluates all combinations of "reasonable" analytic decisions to promote robustness and transparency, but can lead to a combinatorial explosion of analyses to compute. Long delays before assessing results prevent users from diagnosing errors and iterating early. We contribute (1) approximation algorithms for estimating multiverse sensitivity and (2) monitoring visualizations for assessing progress and controlling execution on the fly. We evaluate how quickly three sampling-based algorithms converge to accurately rank sensitive decisions in both synthetic and real multiverse analyses. Compared to uniform random sampling, round robin and sketching approaches are 2 times faster in the best case, while on average estimating sensitivity accurately using 20% of the full multiverse. To enable analysts to stop early to fix errors or decide when results are "good enough" to move forward, we visualize both effect size and decision sensitivity estimates with confidence intervals, and surface potential issues including runtime warnings and model quality metrics.

We analyze a method for embedding graphs as vectors in a structure-preserving manner, showcasing its rich representational capacity and establishing some of its theoretical properties. Our procedure falls under the bind-and-sum approach, and we show that the tensor product is the most general binding operation that respects the superposition principle. We also establish some precise results characterizing the behavior of our method, and we show that our use of spherical codes achieves a packing upper bound. We establish a link to adjacency matrices, showing that our method is, in some sense, a compression of adjacency matrices with applications towards sparse graph representations.

We consider an atomic congestion game in which each player $i$ either participates in the game with an exogenous and known probability $p_{i}\in(0,1]$, independently of everybody else, or stays out and incurs no cost. We compute the parameterized price of anarchy to characterize the impact of demand uncertainty on the efficiency of selfish behavior, considering two different notions of a social planner. A prophet planner knows the realization of the random participation in the game; the ordinary planner does not. As a consequence, a prophet planner can compute an adaptive social optimum that selects different solutions depending on the players that turn out to be active, whereas an ordinary planner faces the same uncertainty as the players and can only compute social optima with respect to the player participation distribution. For both planners, we derive the precise price of anarchy, which arises from an optimization problem parameterized by the maximum participation probability $q=\max_{i} p_{i}$. For the case of affine costs, we provide an analytic expression for the ordinary and prophet price of anarchy, parameterized as a function of $q$.

Over the years, several memory models have been proposed to capture the subtle concurrency semantics of C/C++.One of the most fundamental problems associated with a memory model M is consistency checking: given an execution X, is X consistent with M? This problem lies at the heart of numerous applications, including specification testing and litmus tests, stateless model checking, and dynamic analyses. As such, it has been explored extensively and its complexity is well-understood for traditional models like SC and TSO. However, less is known for the numerous model variants of C/C++, for which the problem becomes challenging due to the intricacies of their concurrency primitives. In this work we study the problem of consistency checking for popular variants of the C11 memory model, in particular, the RC20 model, its release-acquire (RA) fragment, the strong and weak variants of RA (SRA and WRA), as well as the Relaxed fragment of RC20. Motivated by applications in testing and model checking, we focus on reads-from consistency checking. The input is an execution X specifying a set of events, their program order and their reads-from relation, and the task is to decide the existence of a modification order on the writes of X that makes X consistent in a memory model. We draw a rich complexity landscape for this problem; our results include (i)~nearly-linear-time algorithms for certain variants, which improve over prior results, (ii)~fine-grained optimality results, as well as (iii)~matching upper and lower bounds (NP-hardness) for other variants. To our knowledge, this is the first work to characterize the complexity of consistency checking for C11 memory models. We have implemented our algorithms inside the TruSt model checker and the C11Tester testing tool. Experiments on standard benchmarks show that our new algorithms improve consistency checking, often by a significant margin.

Reinforcement Learning (RL) algorithms are known to scale poorly to environments with many available actions, requiring numerous samples to learn an optimal policy. The traditional approach of considering the same fixed action space in every possible state implies that the agent must understand, while also learning to maximize its reward, to ignore irrelevant actions such as $\textit{inapplicable actions}$ (i.e. actions that have no effect on the environment when performed in a given state). Knowing this information can help reduce the sample complexity of RL algorithms by masking the inapplicable actions from the policy distribution to only explore actions relevant to finding an optimal policy. While this technique has been formalized for quite some time within the Automated Planning community with the concept of precondition in the STRIPS language, RL algorithms have never formally taken advantage of this information to prune the search space to explore. This is typically done in an ad-hoc manner with hand-crafted domain logic added to the RL algorithm. In this paper, we propose a more systematic approach to introduce this knowledge into the algorithm. We (i) standardize the way knowledge can be manually specified to the agent; and (ii) present a new framework to autonomously learn the partial action model encapsulating the precondition of an action jointly with the policy. We show experimentally that learning inapplicable actions greatly improves the sample efficiency of the algorithm by providing a reliable signal to mask out irrelevant actions. Moreover, we demonstrate that thanks to the transferability of the knowledge acquired, it can be reused in other tasks and domains to make the learning process more efficient.

Knowledge graph embedding (KGE) is a increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

Neural networks have shown tremendous growth in recent years to solve numerous problems. Various types of neural networks have been introduced to deal with different types of problems. However, the main goal of any neural network is to transform the non-linearly separable input data into more linearly separable abstract features using a hierarchy of layers. These layers are combinations of linear and nonlinear functions. The most popular and common non-linearity layers are activation functions (AFs), such as Logistic Sigmoid, Tanh, ReLU, ELU, Swish and Mish. In this paper, a comprehensive overview and survey is presented for AFs in neural networks for deep learning. Different classes of AFs such as Logistic Sigmoid and Tanh based, ReLU based, ELU based, and Learning based are covered. Several characteristics of AFs such as output range, monotonicity, and smoothness are also pointed out. A performance comparison is also performed among 18 state-of-the-art AFs with different networks on different types of data. The insights of AFs are presented to benefit the researchers for doing further research and practitioners to select among different choices. The code used for experimental comparison is released at: \url{//github.com/shivram1987/ActivationFunctions}.