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This paper introduces a new neural-network-based approach, namely In-Context Operator Networks (ICON), to simultaneously learn operators from the prompted data and apply it to new questions during the inference stage, without any weight update. Existing methods are limited to using a neural network to approximate a specific equation solution or a specific operator, requiring retraining when switching to a new problem with different equations. By training a single neural network as an operator learner, we can not only get rid of retraining (even fine-tuning) the neural network for new problems, but also leverage the commonalities shared across operators so that only a few demos in the prompt are needed when learning a new operator. Our numerical results show the neural network's capability as a few-shot operator learner for a diversified type of differential equation problems, including forward and inverse problems of ordinary differential equations (ODEs), partial differential equations (PDEs), and mean-field control (MFC) problems, and also show that it can generalize its learning capability to operators beyond the training distribution.

Our research explores the use of natural language processing (NLP) methods to automatically classify entities for the purpose of knowledge graph population and integration with food system ontologies. We have created NLP models that can automatically classify organizations with respect to categories associated with environmental issues as well as Standard Industrial Classification (SIC) codes, which are used by the U.S. government to characterize business activities. As input, the NLP models are provided with text snippets retrieved by the Google search engine for each organization, which serves as a textual description of the organization that is used for learning. Our experimental results show that NLP models can achieve reasonably good performance for these two classification tasks, and they rely on a general framework that could be applied to many other classification problems as well. We believe that NLP models represent a promising approach for automatically harvesting information to populate knowledge graphs and aligning the information with existing ontologies through shared categories and concepts.

This paper considers a generalization of the Path Finding (PF) with refueling constraints referred to as the Refuelling Path Finding (RF-PF) problem. Just like PF, the RF-PF problem is defined over a graph, where vertices are gas stations with known fuel prices, and edge costs depend on the gas consumption between the corresponding vertices. RF-PF seeks a minimum-cost path from the start to the goal vertex for a robot with a limited gas tank and a limited number of refuelling stops. While RF-PF is polynomial-time solvable, it remains a challenge to quickly compute an optimal solution in practice since the robot needs to simultaneously determine the path, where to make the stops, and the amount to refuel at each stop. This paper develops a heuristic search algorithm called Refuel A* (RF-A* ) that iteratively constructs partial solution paths from the start to the goal guided by a heuristic function while leveraging dominance rules for state pruning during planning. RF-A* is guaranteed to find an optimal solution and runs more than an order of magnitude faster than the existing state of the art (a polynomial time algorithm) when tested in large city maps with hundreds of gas stations.

Recommender systems usually leverage multi-task learning methods to simultaneously optimize several objectives because of the multi-faceted user behavior data. The typical way of conducting multi-task learning is to establish appropriate parameter sharing across multiple tasks at lower layers while reserving a separate task tower for each task at upper layers. Since the task towers exert direct impact on the prediction results, we argue that the architecture of standalone task towers is sub-optimal for promoting positive knowledge sharing. Accordingly, we propose the framework of Deep Mutual Learning across task towers, which is compatible with various backbone multi-task networks. Extensive offline experiments and online AB tests are conducted to evaluate and verify the proposed approach's effectiveness.

This paper presents a knowledge graph construction method for legal case documents and related laws, aiming to organize legal information efficiently and enhance various downstream tasks. Our approach consists of three main steps: data crawling, information extraction, and knowledge graph deployment. First, the data crawler collects a large corpus of legal case documents and related laws from various sources, providing a rich database for further processing. Next, the information extraction step employs natural language processing techniques to extract entities such as courts, cases, domains, and laws, as well as their relationships from the unstructured text. Finally, the knowledge graph is deployed, connecting these entities based on their extracted relationships, creating a heterogeneous graph that effectively represents legal information and caters to users such as lawyers, judges, and scholars. The established baseline model leverages unsupervised learning methods, and by incorporating the knowledge graph, it demonstrates the ability to identify relevant laws for a given legal case. This approach opens up opportunities for various applications in the legal domain, such as legal case analysis, legal recommendation, and decision support.

This study investigates the outage performance of an under-laying wireless-powered secondary system that reuses the primary users (PU) spectrum in a multiple-input multiple-output (MIMO) cognitive radio (CR) network. Each secondary user (SU) harvests energy and receives information simultaneously by applying power splitting (PS) protocol. The communication between SUs is aided by a two-way (TW) decode and forward (DF) relay. We formulate a problem to design the PS ratios at SUs, the power control factor at the secondary relay, and beamforming matrices at all nodes to minimize the secondary network's outage probability. To address this problem, we propose a two-step solution. The first step establishes closedform expressions for the PS ratios at each SU and secondary relay's power control factor. Furthermore, in the second step, interference alignment (IA) is used to design proper precoding and decoding matrices for managing the interference between secondary and primary networks. We choose IA matrices based on the minimum mean square error (MMSE) iterative algorithm. The simulation results demonstrate a significant decrease in the outage probability for the proposed scheme compared to the benchmark schemes, with an average reduction of more than two orders of magnitude achieved.

Visual Inertial Odometry (VIO) is an essential component of modern Augmented Reality (AR) applications. However, VIO only tracks the relative pose of the device, leading to drift over time. Absolute pose estimation methods infer the device's absolute pose, but their accuracy depends on the input quality. This paper introduces VIO-APR, a new framework for markerless mobile AR that combines an absolute pose regressor (APR) with a local VIO tracking system. VIO-APR uses VIO to assess the reliability of the APR and the APR to identify and compensate for VIO drift. This feedback loop results in more accurate positioning and more stable AR experiences. To evaluate VIO-APR, we created a dataset that combines camera images with ARKit's VIO system output for six indoor and outdoor scenes of various scales. Over this dataset, VIO-APR improves the median accuracy of popular APR by up to 36\% in position and 29\% in orientation, increases the percentage of frames in the high ($0.25 m, 2^{\circ}$) accuracy level by up to 112\% and reduces the percentage of frames predicted below the low ($5 m, 10^\circ$) accuracy greatly. We implement VIO-APR into a mobile AR application using Unity to demonstrate its capabilities. VIO-APR results in noticeably more accurate localization and a more stable overall experience.

To address the issue of poor embedding performance in the knowledge graph of a programming design course, a joint represen-tation learning model that combines entity neighborhood infor-mation and description information is proposed. Firstly, a graph at-tention network is employed to obtain the features of entity neigh-boring nodes, incorporating relationship features to enrich the structural information. Next, the BERT-WWM model is utilized in conjunction with attention mechanisms to obtain the representation of entity description information. Finally, the final entity vector representation is obtained by combining the vector representations of entity neighborhood information and description information. Experimental results demonstrate that the proposed model achieves favorable performance on the knowledge graph dataset of the pro-gramming design course, outperforming other baseline models.

Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.

Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.