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Elliptic reconstruction property, originally introduced by Makridakis and Nochetto for linear parabolic problems, is a well-known tool to derive optimal a posteriori error estimates. No such results are known for nonlinear and nonsmooth problems such as parabolic variational inequalities (VIs). This article establishes the elliptic reconstruction property for parabolic VIs and derives a posteriori error estimates in $L^{\infty}(0,T;L^{2}(\Omega))$ and $L^{\infty}(0,T;L^{\infty}(\Omega))$, respectively. As an application, the residual-type error estimates are presented.

We provide a numerical analysis and computation of neural network projected schemes for approximating one dimensional Wasserstein gradient flows. We approximate the Lagrangian mapping functions of gradient flows by the class of two-layer neural network functions with ReLU (rectified linear unit) activation functions. The numerical scheme is based on a projected gradient method, namely the Wasserstein natural gradient, where the projection is constructed from the $L^2$ mapping spaces onto the neural network parameterized mapping space. We establish theoretical guarantees for the performance of the neural projected dynamics. We derive a closed-form update for the scheme with well-posedness and explicit consistency guarantee for a particular choice of network structure. General truncation error analysis is also established on the basis of the projective nature of the dynamics. Numerical examples, including gradient drift Fokker-Planck equations, porous medium equations, and Keller-Segel models, verify the accuracy and effectiveness of the proposed neural projected algorithm.

Bilingual Lexicon Induction (BLI) is a core task in multilingual NLP that still, to a large extent, relies on calculating cross-lingual word representations. Inspired by the global paradigm shift in NLP towards Large Language Models (LLMs), we examine the potential of the latest generation of LLMs for the development of bilingual lexicons. We ask the following research question: Is it possible to prompt and fine-tune multilingual LLMs (mLLMs) for BLI, and how does this approach compare against and complement current BLI approaches? To this end, we systematically study 1) zero-shot prompting for unsupervised BLI and 2) few-shot in-context prompting with a set of seed translation pairs, both without any LLM fine-tuning, as well as 3) standard BLI-oriented fine-tuning of smaller LLMs. We experiment with 18 open-source text-to-text mLLMs of different sizes (from 0.3B to 13B parameters) on two standard BLI benchmarks covering a range of typologically diverse languages. Our work is the first to demonstrate strong BLI capabilities of text-to-text mLLMs. The results reveal that few-shot prompting with in-context examples from nearest neighbours achieves the best performance, establishing new state-of-the-art BLI scores for many language pairs. We also conduct a series of in-depth analyses and ablation studies, providing more insights on BLI with (m)LLMs, also along with their limitations.

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.

Data processing and analytics are fundamental and pervasive. Algorithms play a vital role in data processing and analytics where many algorithm designs have incorporated heuristics and general rules from human knowledge and experience to improve their effectiveness. Recently, reinforcement learning, deep reinforcement learning (DRL) in particular, is increasingly explored and exploited in many areas because it can learn better strategies in complicated environments it is interacting with than statically designed algorithms. Motivated by this trend, we provide a comprehensive review of recent works focusing on utilizing DRL to improve data processing and analytics. First, we present an introduction to key concepts, theories, and methods in DRL. Next, we discuss DRL deployment on database systems, facilitating data processing and analytics in various aspects, including data organization, scheduling, tuning, and indexing. Then, we survey the application of DRL in data processing and analytics, ranging from data preparation, natural language processing to healthcare, fintech, etc. Finally, we discuss important open challenges and future research directions of using DRL in data processing and analytics.

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.

Named entity recognition (NER) is the task to identify text spans that mention named entities, and to classify them into predefined categories such as person, location, organization etc. NER serves as the basis for a variety of natural language applications such as question answering, text summarization, and machine translation. Although early NER systems are successful in producing decent recognition accuracy, they often require much human effort in carefully designing rules or features. In recent years, deep learning, empowered by continuous real-valued vector representations and semantic composition through nonlinear processing, has been employed in NER systems, yielding stat-of-the-art performance. In this paper, we provide a comprehensive review on existing deep learning techniques for NER. We first introduce NER resources, including tagged NER corpora and off-the-shelf NER tools. Then, we systematically categorize existing works based on a taxonomy along three axes: distributed representations for input, context encoder, and tag decoder. Next, we survey the most representative methods for recent applied techniques of deep learning in new NER problem settings and applications. Finally, we present readers with the challenges faced by NER systems and outline future directions in this area.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.

Recommender System (RS) is a hot area where artificial intelligence (AI) techniques can be effectively applied to improve performance. Since the well-known Netflix Challenge, collaborative filtering (CF) has become the most popular and effective recommendation method. Despite their success in CF, various AI techniques still have to face the data sparsity and cold start problems. Previous works tried to solve these two problems by utilizing auxiliary information, such as social connections among users and meta-data of items. However, they process different types of information separately, leading to information loss. In this work, we propose to utilize Heterogeneous Information Network (HIN), which is a natural and general representation of different types of data, to enhance CF-based recommending methods. HIN-based recommender systems face two problems: how to represent high-level semantics for recommendation and how to fuse the heterogeneous information to recommend. To address these problems, we propose to applying meta-graph to HIN-based RS and solve the information fusion problem with a "matrix factorization (MF) + factorization machine (FM)" framework. For the "MF" part, we obtain user-item similarity matrices from each meta-graph and adopt low-rank matrix approximation to get latent features for both users and items. For the "FM" part, we propose to apply FM with Group lasso (FMG) on the obtained features to simultaneously predict missing ratings and select useful meta-graphs. Experimental results on two large real-world datasets, i.e., Amazon and Yelp, show that our proposed approach is better than that of the state-of-the-art FM and other HIN-based recommending methods.