Guaranteed Multidimensional Time Series Prediction via Deterministic Tensor Completion Theory

In recent years, the prediction of multidimensional time series data has become increasingly important due to its wide-ranging applications. Tensor-based prediction methods have gained attention for their ability to preserve the inherent structure of such data. However, existing approaches, such as tensor autoregression and tensor decomposition, often have consistently failed to provide clear assertions regarding the number of samples that can be exactly predicted. While matrix-based methods using nuclear norms address this limitation, their reliance on matrices limits accuracy and increases computational costs when handling multidimensional data. To overcome these challenges, we reformulate multidimensional time series prediction as a deterministic tensor completion problem and propose a novel theoretical framework. Specifically, we develop a deterministic tensor completion theory and introduce the Temporal Convolutional Tensor Nuclear Norm (TCTNN) model. By convolving the multidimensional time series along the temporal dimension and applying the tensor nuclear norm, our approach identifies the maximum forecast horizon for exact predictions. Additionally, TCTNN achieves superior performance in prediction accuracy and computational efficiency compared to existing methods across diverse real-world datasets, including climate temperature, network flow, and traffic ride data. Our implementation is publicly available at https://github.com/HaoShu2000/TCTNN.

Pixel-Wise Feature Selection for Perceptual Edge Detection without post-processing

Although deep convolutional neutral networks (CNNs) have significantly enhanced performance in image edge detection (ED), current models remain highly dependent on post-processing techniques such as non-maximum suppression (NMS), and often fail to deliver satisfactory perceptual results, while the performance will deteriorate significantly if the allowed error toleration distance decreases. These limitations arise from the uniform fusion of features across all pixels, regardless of their specific characteristics, such as the distinction between textural and edge areas. If the features extracted by the ED models are selected more meticulously and encompass greater diversity, the resulting predictions are expected to be more accurate and perceptually meaningful. Motivated by this observation, this paper proposes a novel feature selection paradigm for deep networks that facilitates the differential selection of features and can be seamlessly integrated into existing ED models. By incorporating this additional structure, the performance of conventional ED models is substantially enhanced without post-processing, while simultaneously enhancing the perceptual quality of the predictions. Extensive experimental evaluations validate the effectiveness of the proposed model.

Improving Generated and Retrieved Knowledge Combination Through Zero-shot Generation

Open-domain Question Answering (QA) has garnered substantial interest by combining the advantages of faithfully retrieved passages and relevant passages generated through Large Language Models (LLMs). However, there is a lack of definitive labels available to pair these sources of knowledge. In order to address this issue, we propose an unsupervised and simple framework called Bi-Reranking for Merging Generated and Retrieved Knowledge (BRMGR), which utilizes re-ranking methods for both retrieved passages and LLM-generated passages. We pair the two types of passages using two separate re-ranking methods and then combine them through greedy matching. We demonstrate that BRMGR is equivalent to employing a bipartite matching loss when assigning each retrieved passage with a corresponding LLM-generated passage. The application of our model yielded experimental results from three datasets, improving their performance by +1.7 and +1.6 on NQ and WebQ datasets, respectively, and obtaining comparable result on TriviaQA dataset when compared to competitive baselines.

More precise edge detections

Image Edge detection (ED) is a base task in computer vision. While the performance of the ED algorithm has been improved greatly by introducing CNN-based models, current models still suffer from unsatisfactory precision rates especially when only a low error toleration distance is allowed. Therefore, model architecture for more precise predictions still needs an investigation. On the other hand, the unavoidable noise training data provided by humans would lead to unsatisfactory model predictions even when inputs are edge maps themselves, which also needs improvement. In this paper, more precise ED models are presented with cascaded skipping density blocks (CSDB). Our models obtain state-of-the-art(SOTA) predictions in several datasets, especially in average precision rate (AP), which is confirmed by extensive experiments. Moreover, our models do not include down-sample operations, demonstrating those widely believed operations are not necessary. Also, a novel modification on data augmentation for training is employed, which allows noiseless data to be employed in model training and thus improves the performance of models predicting on edge maps themselves.

SDC-HSDD-NDSA: Structure Detecting Cluster by Hierarchical Secondary Directed Differential with Normalized Density and Self-Adaption

Density-based clustering could be the most popular clustering algorithm since it can identify clusters of arbitrary shape as long as different (high-density) clusters are separated by low-density regions. However, the requirement of the separateness of clusters by low-density regions is not trivial since a high-density region might have different structures which should be clustered into different groups. Such a situation demonstrates the main flaw of all previous density-based clustering algorithms we have known--structures in a high-density cluster could not be detected. Therefore, this paper aims to provide a density-based clustering scheme that not only has the ability previous ones have but could also detect structures in a high-density region not separated by low-density ones. The algorithm employs secondary directed differential, hierarchy, normalized density, as well as the self-adaption coefficient, and thus is called Structure Detecting Cluster by Hierarchical Secondary Directed Differential with Normalized Density and Self-Adaption, dubbed by SDC-HSDD-NDSA for short. To illustrate its effectiveness, we run the algorithm in several data sets. The results verify its validity in structure detection, robustness over noises, as well as independence of granularities, and demonstrate that it could outperform previous ones. The Python code of the paper could be found on https://github.com/Hao-B-Shu/SDC-HSDD-NDSA.