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The membership and threshold problems for recurrence sequences are fundamental open decision problems in automated verification. The former problem asks whether a chosen target is an element of a sequence, whilst the latter asks whether every term in a sequence is bounded from below by a given value. A rational-valued sequence $\langle u_n \rangle_n$ is hypergeometric if it satisfies a first-order linear recurrence of the form $p(n)u_{n+1} = q(n)u_{n}$ with polynomial coefficients $p,q\in\mathbb{Z}[x]$. In this note we establish decidability results for the aforementioned problems for restricted classes of hypergeometric sequences. For example, we establish decidability for the aforementioned problems under the assumption that the polynomial coefficients $p,q\in\mathbb{Z}[x]$ are monic and split over an imaginary rational extension of $\mathbb{Q}$. We also establish conditional decidability results; that is, conditional on Schanuel's conjecture, when the irreducible factors of the monic polynomial coefficients $p,q\in\mathbb{Z}[x]$ are either linear or quadratic.

Legal question-answering (QA) systems have the potential to revolutionize the way legal professionals interact with case law documents. This paper conducts a comparative analysis of existing artificial intelligence models for their utility in answering legal questions within the Indian legal system, specifically focusing on Indian Legal Question Answering (AILQA) and our study investigates the efficacy of different retrieval and QA algorithms currently available. Utilizing the OpenAI GPT model as a benchmark, along with query prompts, our investigation shows that existing AILQA systems can automatically interpret natural language queries from users and generate highly accurate responses. This research is particularly focused on applications within the Indian criminal justice domain, which has its own set of challenges due to its complexity and resource constraints. In order to rigorously assess the performance of these models, empirical evaluations are complemented by feedback from practicing legal professionals, thereby offering a multifaceted view on the capabilities and limitations of AI in the context of Indian legal question-answering.

Understanding the fundamental principles behind the success of deep neural networks is one of the most important open questions in the current literature. To this end, we study the training problem of deep neural networks and introduce an analytic approach to unveil hidden convexity in the optimization landscape. We consider a deep parallel ReLU network architecture, which also includes standard deep networks and ResNets as its special cases. We then show that pathwise regularized training problems can be represented as an exact convex optimization problem. We further prove that the equivalent convex problem is regularized via a group sparsity inducing norm. Thus, a path regularized parallel ReLU network can be viewed as a parsimonious convex model in high dimensions. More importantly, since the original training problem may not be trainable in polynomial-time, we propose an approximate algorithm with a fully polynomial-time complexity in all data dimensions. Then, we prove strong global optimality guarantees for this algorithm. We also provide experiments corroborating our theory.

Recent research efforts on semantic communication have mostly considered accuracy as a main problem for optimizing goal-oriented communication systems. However, these approaches introduce a paradox: the accuracy of artificial intelligence (AI) tasks should naturally emerge through training rather than being dictated by network constraints. Acknowledging this dilemma, this work introduces an innovative approach that leverages the rate-distortion theory to analyze distortions induced by communication and semantic compression, thereby analyzing the learning process. Specifically, we examine the distribution shift between the original data and the distorted data, thus assessing its impact on the AI model's performance. Founding upon this analysis, we can preemptively estimate the empirical accuracy of AI tasks, making the goal-oriented semantic communication problem feasible. To achieve this objective, we present the theoretical foundation of our approach, accompanied by simulations and experiments that demonstrate its effectiveness. The experimental results indicate that our proposed method enables accurate AI task performance while adhering to network constraints, establishing it as a valuable contribution to the field of signal processing. Furthermore, this work advances research in goal-oriented semantic communication and highlights the significance of data-driven approaches in optimizing the performance of intelligent systems.

Reinforcement Learning (RL)-based recommender systems (RSs) have garnered considerable attention due to their ability to learn optimal recommendation policies and maximize long-term user rewards. However, deploying RL models directly in online environments and generating authentic data through A/B tests can pose challenges and require substantial resources. Simulators offer an alternative approach by providing training and evaluation environments for RS models, reducing reliance on real-world data. Existing simulators have shown promising results but also have limitations such as simplified user feedback, lacking consistency with real-world data, the challenge of simulator evaluation, and difficulties in migration and expansion across RSs. To address these challenges, we propose KuaiSim, a comprehensive user environment that provides user feedback with multi-behavior and cross-session responses. The resulting simulator can support three levels of recommendation problems: the request level list-wise recommendation task, the whole-session level sequential recommendation task, and the cross-session level retention optimization task. For each task, KuaiSim also provides evaluation protocols and baseline recommendation algorithms that further serve as benchmarks for future research. We also restructure existing competitive simulators on the KuaiRand Dataset and compare them against KuaiSim to future assess their performance and behavioral differences. Furthermore, to showcase KuaiSim's flexibility in accommodating different datasets, we demonstrate its versatility and robustness when deploying it on the ML-1m dataset.

Choosing an appropriate representation of the environment for the underlying decision-making process of the RL agent is not always straightforward. The state representation should be inclusive enough to allow the agent to informatively decide on its actions and compact enough to increase sample efficiency for policy training. Given this outlook, this work examines the effect of various state representations in incentivizing the agent to solve a specific robotic task: antipodal and planar object grasping. A continuum of state representation abstractions is defined, starting from a model-based approach with complete system knowledge, through hand-crafted numerical, to image-based representations with decreasing level of induced task-specific knowledge. We examine the effects of each representation in the ability of the agent to solve the task in simulation and the transferability of the learned policy to the real robot. The results show that RL agents using numerical states can perform on par with non-learning baselines. Furthermore, we find that agents using image-based representations from pre-trained environment embedding vectors perform better than end-to-end trained agents, and hypothesize that task-specific knowledge is necessary for achieving convergence and high success rates in robot control.

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.

Generative commonsense reasoning which aims to empower machines to generate sentences with the capacity of reasoning over a set of concepts is a critical bottleneck for text generation. Even the state-of-the-art pre-trained language generation models struggle at this task and often produce implausible and anomalous sentences. One reason is that they rarely consider incorporating the knowledge graph which can provide rich relational information among the commonsense concepts. To promote the ability of commonsense reasoning for text generation, we propose a novel knowledge graph augmented pre-trained language generation model KG-BART, which encompasses the complex relations of concepts through the knowledge graph and produces more logical and natural sentences as output. Moreover, KG-BART can leverage the graph attention to aggregate the rich concept semantics that enhances the model generalization on unseen concept sets. Experiments on benchmark CommonGen dataset verify the effectiveness of our proposed approach by comparing with several strong pre-trained language generation models, particularly KG-BART outperforms BART by 5.80, 4.60, in terms of BLEU-3, 4. Moreover, we also show that the generated context by our model can work as background scenarios to benefit downstream commonsense QA tasks.

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.

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.