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We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). Formally, we prove lower bounds against the accuracy of FPC-interpretations that map Unique Games instances (encoded as relational structures) to rational numbers giving the approximate fraction of constraints that can be satisfied. We prove two new FPC-inexpressibility results for Unique Games: the existence of a (1/2, 1/3 + $\delta$)-inapproximability gap, and inapproximability to within any constant factor. Previous recent work has established similar FPC-inapproximability results for a small handful of other problems. Our construction builds upon some of these ideas, but contains a novel technique. While most FPC-inexpressibility results are based on variants of the CFI-construction, ours is significantly different. We start with a graph of very large girth and label the edges with random affine vector spaces over $\ff_2$ that determine the constraints in the two structures. Duplicator's strategy involves maintaining a partial isomorphism over a minimal tree that spans the pebbled vertices of the graph.

We study the problem of Out-of-Distribution (OOD) detection, that is, detecting whether a learning algorithm's output can be trusted at inference time. While a number of tests for OOD detection have been proposed in prior work, a formal framework for studying this problem is lacking. We propose a definition for the notion of OOD that includes both the input distribution and the learning algorithm, which provides insights for the construction of powerful tests for OOD detection. We propose a multiple hypothesis testing inspired procedure to systematically combine any number of different statistics from the learning algorithm using conformal p-values. We further provide strong guarantees on the probability of incorrectly classifying an in-distribution sample as OOD. In our experiments, we find that threshold-based tests proposed in prior work perform well in specific settings, but not uniformly well across different types of OOD instances. In contrast, our proposed method that combines multiple statistics performs uniformly well across different datasets and neural networks.

Identifiability of discrete statistical models with latent variables is known to be challenging to study, yet crucial to a model's interpretability and reliability. This work presents a general algebraic technique to investigate identifiability of complicated discrete models with latent and graphical components. Specifically, motivated by diagnostic tests collecting multivariate categorical data, we focus on discrete models with multiple binary latent variables. In the considered model, the latent variables can have arbitrary dependencies among themselves while the latent-to-observed measurement graph takes a "star-forest" shape. We establish necessary and sufficient graphical criteria for identifiability, and reveal an interesting and perhaps surprising phenomenon of blessing-of-dependence geometry: under the minimal conditions for generic identifiability, the parameters are identifiable if and only if the latent variables are not statistically independent. Thanks to this theory, we can perform formal hypothesis tests of identifiability in the boundary case by testing certain marginal independence of the observed variables. Our results give new understanding of statistical properties of graphical models with latent variables. They also entail useful implications for designing diagnostic tests or surveys that measure binary latent traits.

This paper delves into the intersection of computational theory and music, examining the concept of undecidability and its significant, yet overlooked, implications within the realm of modern music composition and production. It posits that undecidability, a principle traditionally associated with theoretical computer science, extends its relevance to the music industry. The study adopts a multidimensional approach, focusing on five key areas: (1) the Turing completeness of Ableton, a widely used digital audio workstation, (2) the undecidability of satisfiability in sound creation utilizing an array of effects, (3) the undecidability of constraints on polymeters in musical compositions, (4) the undecidability of satisfiability in just intonation harmony constraints, and (5) the undecidability of "new ordering systems". In addition to providing theoretical proof for these assertions, the paper elucidates the practical relevance of these concepts for practitioners outside the field of theoretical computer science. The ultimate aim is to foster a new understanding of undecidability in music, highlighting its broader applicability and potential to influence contemporary computer-assisted (and traditional) music making.

This paper investigates the performance of a singleuser fluid antenna system (FAS), by exploiting a class of elliptical copulas to describe the structure of dependency amongst the fluid antenna ports. By expressing Jakes' model in terms of the Gaussian copula, we consider two cases: (i) the general case, i.e., any arbitrary correlated fading distribution; and (ii) the specific case, i.e., correlated Nakagami-m fading. For both scenarios, we first derive analytical expressions for the cumulative distribution function (CDF) and probability density function (PDF) of the equivalent channel in terms of multivariate normal distribution. Then, we obtain the outage probability (OP) and the delay outage rate (DOR) to analyze the performance of the FAS. By employing the popular rank correlation coefficients such as Spearman's \{rho} and Kendall's {\tau}, we measure the degree of dependency in correlated arbitrary fading channels and illustrate how the Gaussian copula can be accurately connected to Jakes' model in FAS without complicated mathematical analysis. Numerical results show that increasing the fluid antenna size provides lower OP and DOR, but the system performance saturates as the number of antenna ports increases. In addition, our results indicate that FAS provides better performance compared to conventional single-fixed antenna systems even when the size of fluid antenna is small.

Deep learning models have witnessed depth and pose estimation framework on unannotated datasets as a effective pathway to succeed in endoscopic navigation. Most current techniques are dedicated to developing more advanced neural networks to improve the accuracy. However, existing methods ignore the special properties of endoscopic images, resulting in an inability to fully unleash the power of neural networks. In this study, we conduct a detail analysis of the properties of endoscopic images and improve the compatibility of images and neural networks, to unleash the power of current neural networks. First, we introcude the Mask Image Modelling (MIM) module, which inputs partial image information instead of complete image information, allowing the network to recover global information from partial pixel information. This enhances the network' s ability to perceive global information and alleviates the phenomenon of local overfitting in convolutional neural networks due to local artifacts. Second, we propose a lightweight neural network to enhance the endoscopic images, to explicitly improve the compatibility between images and neural networks. Extensive experiments are conducted on the three public datasets and one inhouse dataset, and the proposed modules improve baselines by a large margin. Furthermore, the enhanced images we proposed, which have higher network compatibility, can serve as an effective data augmentation method and they are able to extract more stable feature points in traditional feature point matching tasks and achieve outstanding performance.

In a pre-registered randomized experiment, we found that, relative to a reverse-chronological baseline, Twitter's engagement-based ranking algorithm may amplify emotionally charged, out-group hostile content and contribute to affective polarization. Furthermore, we critically examine the claim that the algorithm shows users what they want to see, discovering that users do *not* prefer the political tweets selected by the algorithm. Finally, we explore the implications of an alternative approach to ranking content based on users' stated preferences and find a reduction in angry, partisan, and out-group hostile content but also a potential reinforcement of echo chambers. The evidence underscores the necessity for a more nuanced approach to content ranking that balances engagement, users' stated preferences, and sociopolitical outcomes.

Knowledge graph reasoning (KGR), aiming to deduce new facts from existing facts based on mined logic rules underlying knowledge graphs (KGs), has become a fast-growing research direction. It has been proven to significantly benefit the usage of KGs in many AI applications, such as question answering and recommendation systems, etc. According to the graph types, the existing KGR models can be roughly divided into three categories, \textit{i.e.,} static models, temporal models, and multi-modal models. The early works in this domain mainly focus on static KGR and tend to directly apply general knowledge graph embedding models to the reasoning task. However, these models are not suitable for more complex but practical tasks, such as inductive static KGR, temporal KGR, and multi-modal KGR. To this end, multiple works have been developed recently, but no survey papers and open-source repositories comprehensively summarize and discuss models in this important direction. To fill the gap, we conduct a survey for knowledge graph reasoning tracing from static to temporal and then to multi-modal KGs. Concretely, the preliminaries, summaries of KGR models, and typical datasets are introduced and discussed consequently. Moreover, we discuss the challenges and potential opportunities. The corresponding open-source repository is shared on GitHub: //github.com/LIANGKE23/Awesome-Knowledge-Graph-Reasoning.

Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.

Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics system, learning molecular fingerprints, predicting protein interface, and classifying diseases require that a model to learn from graph inputs. In other domains such as learning from non-structural data like texts and images, reasoning on extracted structures, like the dependency tree of sentences and the scene graph of images, is an important research topic which also needs graph reasoning models. Graph neural networks (GNNs) are connectionist models that capture the dependence of graphs via message passing between the nodes of graphs. Unlike standard neural networks, graph neural networks retain a state that can represent information from its neighborhood with an arbitrary depth. Although the primitive graph neural networks have been found difficult to train for a fixed point, recent advances in network architectures, optimization techniques, and parallel computation have enabled successful learning with them. In recent years, systems based on graph convolutional network (GCN) and gated graph neural network (GGNN) have demonstrated ground-breaking performance on many tasks mentioned above. In this survey, we provide a detailed review over existing graph neural network models, systematically categorize the applications, and propose four open problems for future research.