We have developed a new embedding method for solving scalar hyperbolic conservation laws on surfaces. The approach represents the interface implicitly by a signed distance function following the typical level set method and some embedding methods. Instead of solving the equation explicitly on the surface, we introduce a modified partial differential equation in a small neighborhood of the interface. This embedding equation is developed based on a push-forward operator that can extend any tangential flux vectors from the surface to a neighboring level surface. This operator is easy to compute and involves only the level set function and the corresponding Hessian. The resulting solution is constant in the normal direction of the interface. To demonstrate the accuracy and effectiveness of our method, we provide some two- and three-dimensional examples.
Graph neural networks (GNNs) have achieved tremendous success in the task of graph classification and its diverse downstream real-world applications. Despite the huge success in learning graph representations, current GNN models have demonstrated their vulnerability to potentially existent adversarial examples on graph-structured data. Existing approaches are either limited to structure attacks or restricted to local information, urging for the design of a more general attack framework on graph classification, which faces significant challenges due to the complexity of generating local-node-level adversarial examples using the global-graph-level information. To address this "global-to-local" attack challenge, we present a novel and general framework to generate adversarial examples via manipulating graph structure and node features. Specifically, we make use of Graph Class Activation Mapping and its variant to produce node-level importance corresponding to the graph classification task. Then through a heuristic design of algorithms, we can perform both feature and structure attacks under unnoticeable perturbation budgets with the help of both node-level and subgraph-level importance. Experiments towards attacking four state-of-the-art graph classification models on six real-world benchmarks verify the flexibility and effectiveness of our framework.
Robotic manipulation tasks, such as object rearrangement, play a crucial role in enabling robots to interact with complex and arbitrary environments. Existing work focuses primarily on single-level rearrangement planning and, even if multiple levels exist, dependency relations among substructures are geometrically simpler, like tower stacking. We propose Structural Concept Learning (SCL), a deep learning approach that leverages graph attention networks to perform multi-level object rearrangement planning for scenes with structural dependency hierarchies. It is trained on a self-generated simulation data set with intuitive structures, works for unseen scenes with an arbitrary number of objects and higher complexity of structures, infers independent substructures to allow for task parallelization over multiple manipulators, and generalizes to the real world. We compare our method with a range of classical and model-based baselines to show that our method leverages its scene understanding to achieve better performance, flexibility, and efficiency. The dataset, supplementary details, videos, and code implementation are available at: //manavkulshrestha.github.io/scl
Compared to traditional intelligent reflecting surfaces(IRS), aerial IRS (AIRS) has unique advantages, such as more flexible deployment and wider service coverage. However, modeling AIRS in the channel presents new challenges due to their mobility. In this paper, a three-dimensional (3D) wideband channel model for AIRS and IRS joint-assisted multiple-input multiple-output (MIMO) communication system is proposed, where considering the rotational degrees of freedom in three directions and the motion angles of AIRS in space. Based on the proposed model, the channel impulse response (CIR), correlation function, and channel capacity are derived, and several feasible joint phase shifts schemes for AIRS and IRS units are proposed. Simulation results show that the proposed model can capture the channel characteristics accurately, and the proposed phase shifts methods can effectively improve the channel statistical characteristics and increase the system capacity. Additionally, we observe that in certain scenarios, the paths involving the IRS and the line-of-sight (LoS) paths exhibit similar characteristics. These findings provide valuable insights for the future development of intelligent communication systems.
Robots must make and break contact to interact with the world and perform useful tasks. However, planning and control through contact remains a formidable challenge. In this work, we achieve real-time contact-implicit model predictive control with a surprisingly simple method: inverse dynamics trajectory optimization. While trajectory optimization with inverse dynamics is not new, we introduce a series of incremental innovations that collectively enable fast model predictive control on a variety of challenging manipulation and locomotion tasks. We implement these innovations in an open-source solver, and present a variety of simulation examples to support the effectiveness of the proposed approach. Additionally, we demonstrate contact-implicit model predictive control on hardware at over 100 Hz for a 20 degree-of-freedom bi-manual manipulation task.
As surgical interventions trend towards minimally invasive approaches, Concentric Tube Robots (CTRs) have been explored for various interventions such as brain, eye, fetoscopic, lung, cardiac and prostate surgeries. Arranged concentrically, each tube is rotated and translated independently to move the robot end-effector position, making kinematics and control challenging. Classical model-based approaches have been previously investigated with developments in deep learning based approaches outperforming more classical approaches in both forward kinematics and shape estimation. We propose a deep reinforcement learning approach to control where we generalise across two to four systems, an element not yet achieved in any other deep learning approach for CTRs. In this way we explore the likely robustness of the control approach. Also investigated is the impact of rotational constraints applied on tube actuation and the effects on error metrics. We evaluate inverse kinematics errors and tracking error for path following tasks and compare the results to those achieved using state of the art methods. Additionally, as current results are performed in simulation, we also investigate a domain transfer approach known as domain randomization and evaluate error metrics as an initial step towards hardware implementation. Finally, we compare our method to a Jacobian approach found in literature.
This paper presents a taxonomy for analytical spreadsheet models. It considers both the use case that a spreadsheet is meant to serve, and the engineering resources devoted to its development. We extend a previous three-type taxonomy, to identify nine types of spreadsheet models, that encompass the many analytical spreadsheet models seen in the literature. We connect disparate research literature to distinguish between an "analytical solution" and an "industrial-quality analytical spreadsheet model". We explore the nature of each of the nine types, propose definitions for some, relate them to the literature, and hypothesize on how they might arise. The taxonomy aids in identifying where various spreadsheet development guidelines are most useful, provides a lens for viewing spreadsheet errors and risk, and offers a structure for understanding how spreadsheets change over time. This taxonomy opens the door to many interesting research questions, including refinements to itself.
Large Language Models (LLMs) have emerged as powerful tools in the field of Natural Language Processing (NLP) and have recently gained significant attention in the domain of Recommendation Systems (RS). These models, trained on massive amounts of data using self-supervised learning, have demonstrated remarkable success in learning universal representations and have the potential to enhance various aspects of recommendation systems by some effective transfer techniques such as fine-tuning and prompt tuning, and so on. The crucial aspect of harnessing the power of language models in enhancing recommendation quality is the utilization of their high-quality representations of textual features and their extensive coverage of external knowledge to establish correlations between items and users. To provide a comprehensive understanding of the existing LLM-based recommendation systems, this survey presents a taxonomy that categorizes these models into two major paradigms, respectively Discriminative LLM for Recommendation (DLLM4Rec) and Generative LLM for Recommendation (GLLM4Rec), with the latter being systematically sorted out for the first time. Furthermore, we systematically review and analyze existing LLM-based recommendation systems within each paradigm, providing insights into their methodologies, techniques, and performance. Additionally, we identify key challenges and several valuable findings to provide researchers and practitioners with inspiration.
Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the distributions of given graphs and generating more novel graphs. Owing to their wide range of applications, generative models for graphs, which have a rich history, however, are traditionally hand-crafted and only capable of modeling a few statistical properties of graphs. Recent advances in deep generative models for graph generation is an important step towards improving the fidelity of generated graphs and paves the way for new kinds of applications. This article provides an extensive overview of the literature in the field of deep generative models for graph generation. Firstly, the formal definition of deep generative models for the graph generation and the preliminary knowledge are provided. Secondly, taxonomies of deep generative models for both unconditional and conditional graph generation are proposed respectively; the existing works of each are compared and analyzed. After that, an overview of the evaluation metrics in this specific domain is provided. Finally, the applications that deep graph generation enables are summarized and five promising future research directions are highlighted.
Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.
Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.