Conjucyclic codes are part of a family of codes that includes cyclic, constacyclic, and quasi-cyclic codes, among others. Despite their importance in quantum error correction, they have not received much attention in the literature. This paper focuses on additive conjucyclic (ACC) codes over $\mathbb{F}_4$ and investigates their properties. Specifically, we derive the duals of ACC codes using a trace inner product and obtain the trace hull and its dimension. Also, establish a necessary and sufficient condition for an additive code to have a complementary dual (ACD). Additionally, we identify a necessary condition for an additive conjucyclic complementary pair of codes over $\mathbb{F}_4$. Furthermore, we show that the trace code of an ACC code is cyclic and provide a condition for the trace code of an ACC code to be LCD. To demonstrate the practical application of our findings, we construct some good entanglement-assisted quantum error-correcting (EAQEC) codes using the trace code of ACC codes.
Explainable recommender systems (RS) have traditionally followed a one-size-fits-all approach, delivering the same explanation level of detail to each user, without considering their individual needs and goals. Further, explanations in RS have so far been presented mostly in a static and non-interactive manner. To fill these research gaps, we aim in this paper to adopt a user-centered, interactive explanation model that provides explanations with different levels of detail and empowers users to interact with, control, and personalize the explanations based on their needs and preferences. We followed a user-centered approach to design interactive explanations with three levels of detail (basic, intermediate, and advanced) and implemented them in the transparent Recommendation and Interest Modeling Application (RIMA). We conducted a qualitative user study (N=14) to investigate the impact of providing interactive explanations with varying level of details on the users' perception of the explainable RS. Our study showed qualitative evidence that fostering interaction and giving users control in deciding which explanation they would like to see can meet the demands of users with different needs, preferences, and goals, and consequently can have positive effects on different crucial aspects in explainable recommendation, including transparency, trust, satisfaction, and user experience.
Translation-based AMR parsers have recently gained popularity due to their simplicity and effectiveness. They predict linearized graphs as free texts, avoiding explicit structure modeling. However, this simplicity neglects structural locality in AMR graphs and introduces unnecessary tokens to represent coreferences. In this paper, we introduce new target forms of AMR parsing and a novel model, CHAP, which is equipped with causal hierarchical attention and the pointer mechanism, enabling the integration of structures into the Transformer decoder. We empirically explore various alternative modeling options. Experiments show that our model outperforms baseline models on four out of five benchmarks in the setting of no additional data.
Scientific imaging problems are often severely ill-posed, and hence have significant intrinsic uncertainty. Accurately quantifying the uncertainty in the solutions to such problems is therefore critical for the rigorous interpretation of experimental results as well as for reliably using the reconstructed images as scientific evidence. Unfortunately, existing imaging methods are unable to quantify the uncertainty in the reconstructed images in a manner that is robust to experiment replications. This paper presents a new uncertainty quantification methodology based on an equivariant formulation of the parametric bootstrap algorithm that leverages symmetries and invariance properties commonly encountered in imaging problems. Additionally, the proposed methodology is general and can be easily applied with any image reconstruction technique, including unsupervised training strategies that can be trained from observed data alone, thus enabling uncertainty quantification in situations where there is no ground truth data available. We demonstrate the proposed approach with a series of numerical experiments and through comparisons with alternative uncertainty quantification strategies from the state-of-the-art, such as Bayesian strategies involving score-based diffusion models and Langevin samplers. In all our experiments, the proposed method delivers remarkably accurate high-dimensional confidence regions and outperforms the competing approaches in terms of estimation accuracy, uncertainty quantification accuracy, and computing time.
Nested simulation encompasses the estimation of functionals linked to conditional expectations through simulation techniques. In this paper, we treat conditional expectation as a function of the multidimensional conditioning variable and provide asymptotic analyses of general Least Squared Estimators on sieve, without imposing specific assumptions on the function's form. Our study explores scenarios in which the convergence rate surpasses that of the standard Monte Carlo method and the one recently proposed based on kernel ridge regression. We also delve into the conditions that allow for achieving the best possible square root convergence rate among all methods. Numerical experiments are conducted to support our statements.
In the field of Artificial (General) Intelligence (AI), the several recent advancements in Natural language processing (NLP) activities relying on Large Language Models (LLMs) have come to encourage the adoption of LLMs as scientific models of language. While the terminology employed for the characterization of LLMs favors their embracing as such, it is not clear that they are in a place to offer insights into the target system they seek to represent. After identifying the most important theoretical and empirical risks brought about by the adoption of scientific models that lack transparency, we discuss LLMs relating them to every scientific model's fundamental components: the object, the medium, the meaning and the user. We conclude that, at their current stage of development, LLMs hardly offer any explanations for language, and then we provide an outlook for more informative future research directions on this topic.
Many modern datasets, such as those in ecology and geology, are composed of samples with spatial structure and dependence. With such data violating the usual independent and identically distributed (IID) assumption in machine learning and classical statistics, it is unclear a priori how one should measure the performance and generalization of models. Several authors have empirically investigated cross-validation (CV) methods in this setting, reaching mixed conclusions. We provide a class of unbiased estimation methods for general quadratic errors, correlated Gaussian response, and arbitrary prediction function $g$, for a noise-elevated version of the error. Our approach generalizes the coupled bootstrap (CB) from the normal means problem to general normal data, allowing correlation both within and between the training and test sets. CB relies on creating bootstrap samples that are intelligently decoupled, in the sense of being statistically independent. Specifically, the key to CB lies in generating two independent "views" of our data and using them as stand-ins for the usual independent training and test samples. Beginning with Mallows' $C_p$, we generalize the estimator to develop our generalized $C_p$ estimators (GC). We show at under only a moment condition on $g$, this noise-elevated error estimate converges smoothly to the noiseless error estimate. We show that when Stein's unbiased risk estimator (SURE) applies, GC converges to SURE as in the normal means problem. Further, we use these same tools to analyze CV and provide some theoretical analysis to help understand when CV will provide good estimates of error. Simulations align with our theoretical results, demonstrating the effectiveness of GC and illustrating the behavior of CV methods. Lastly, we apply our estimator to a model selection task on geothermal data in Nevada.
Although large language models (LLMs) are impressive in solving various tasks, they can quickly be outdated after deployment. Maintaining their up-to-date status is a pressing concern in the current era. This paper provides a comprehensive review of recent advances in aligning LLMs with the ever-changing world knowledge without re-training from scratch. We categorize research works systemically and provide in-depth comparisons and discussion. We also discuss existing challenges and highlight future directions to facilitate research in this field. We release the paper list at //github.com/hyintell/awesome-refreshing-llms
A community reveals the features and connections of its members that are different from those in other communities in a network. Detecting communities is of great significance in network analysis. Despite the classical spectral clustering and statistical inference methods, we notice a significant development of deep learning techniques for community detection in recent years with their advantages in handling high dimensional network data. Hence, a comprehensive overview of community detection's latest progress through deep learning is timely to both academics and practitioners. This survey devises and proposes a new taxonomy covering different categories of the state-of-the-art methods, including deep learning-based models upon deep neural networks, deep nonnegative matrix factorization and deep sparse filtering. The main category, i.e., deep neural networks, is further divided into convolutional networks, graph attention networks, generative adversarial networks and autoencoders. The survey also summarizes the popular benchmark data sets, model evaluation metrics, and open-source implementations to address experimentation settings. We then discuss the practical applications of community detection in various domains and point to implementation scenarios. Finally, we outline future directions by suggesting challenging topics in this fast-growing deep learning field.
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.
While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.