Time Evidence Fusion Network: Multi-source View in Long-Term Time Series Forecasting

In real-world scenarios, time series forecasting often demands timeliness, making research on model backbones a perennially hot topic. To meet these performance demands, we propose a novel backbone from the perspective of information fusion. Introducing the Basic Probability Assignment (BPA) Module and the Time Evidence Fusion Network (TEFN), based on evidence theory, allows us to achieve superior performance. On the other hand, the perspective of multi-source information fusion effectively improves the accuracy of forecasting. Due to the fact that BPA is generated by fuzzy theory, TEFN also has considerable interpretability. In real data experiments, the TEFN partially achieved state-of-the-art, with low errors comparable to PatchTST, and operating efficiency surpass performance models such as Dlinear. Meanwhile, TEFN has high robustness and small error fluctuations in the random hyperparameter selection. TEFN is not a model that achieves the ultimate in single aspect, but a model that balances performance, accuracy, stability, and interpretability.

Isopignistic Canonical Decomposition via Belief Evolution Network

Developing a general information processing model in uncertain environments is fundamental for the advancement of explainable artificial intelligence. Dempster-Shafer theory of evidence is a well-known and effective reasoning method for representing epistemic uncertainty, which is closely related to subjective probability theory and possibility theory. Although they can be transformed to each other under some particular belief structures, there remains a lack of a clear and interpretable transformation process, as well as a unified approach for information processing. In this paper, we aim to address these issues from the perspectives of isopignistic belief functions and the hyper-cautious transferable belief model. Firstly, we propose an isopignistic transformation based on the belief evolution network. This transformation allows for the adjustment of the information granule while retaining the potential decision outcome. The isopignistic transformation is integrated with a hyper-cautious transferable belief model to establish a new canonical decomposition. This decomposition offers a reverse path between the possibility distribution and its isopignistic mass functions. The result of the canonical decomposition, called isopignistic function, is an identical information content distribution to reflect the propensity and relative commitment degree of the BPA. Furthermore, this paper introduces a method to reconstruct the basic belief assignment by adjusting the isopignistic function. It explores the advantages of this approach in modeling and handling uncertainty within the hyper-cautious transferable belief model. More general, this paper establishes a theoretical basis for building general models of artificial intelligence based on probability theory, Dempster-Shafer theory, and possibility theory.

Random Walk in Random Permutation Set Theory

Random walk is an explainable approach for modeling natural processes at the molecular level. The Random Permutation Set Theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer Theory. Recent explorations indicate a promising link between RPST and random walk. In this study, we conduct an analysis and construct a random walk model based on the properties of RPST, with Monte Carlo simulations of such random walk. Our findings reveal that the random walk generated through RPST exhibits characteristics similar to those of a Gaussian random walk and can be transformed into a Wiener process through a specific limiting scaling procedure. This investigation establishes a novel connection between RPST and random walk theory, thereby not only expanding the applicability of RPST, but also demonstrating the potential for combining the strengths of both approaches to improve problem-solving abilities.

Learnable WSN Deployment of Evidential Collaborative Sensing Model

In wireless sensor networks (WSNs), coverage and deployment are two most crucial issues when conducting detection tasks. However, the detection information collected from sensors is oftentimes not fully utilized and efficiently integrated. Such sensing model and deployment strategy, thereby, cannot reach the maximum quality of coverage, particularly when the amount of sensors within WSNs expands significantly. In this article, we aim at achieving the optimal coverage quality of WSN deployment. We develop a collaborative sensing model of sensors to enhance detection capabilities of WSNs, by leveraging the collaborative information derived from the combination rule under the framework of evidence theory. In this model, the performance evaluation of evidential fusion systems is adopted as the criterion of the sensor selection. A learnable sensor deployment network (LSDNet) considering both sensor contribution and detection capability, is proposed for achieving the optimal deployment of WSNs. Moreover, we deeply investigate the algorithm for finding the requisite minimum number of sensors that realizes the full coverage of WSNs. A series of numerical examples, along with an application of forest area monitoring, are employed to demonstrate the effectiveness and the robustness of the proposed algorithms.

Limit of the Maximum Random Permutation Set Entropy

The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been proposed. Exploring the maximum entropy provides a possible way of understanding the physical meaning of RPS. In this paper, a new concept, the envelope of entropy function, is defined. In addition, the limit of the envelope of RPS entropy is derived and proved. Compared with the existing method, the computational complexity of the proposed method to calculate the envelope of RPS entropy decreases greatly. The result shows that when $N \to \infty$, the limit form of the envelope of the entropy of RPS converges to $e \times (N!)^2$, which is highly connected to the constant $e$ and factorial. Finally, numerical examples validate the efficiency and conciseness of the proposed envelope, which provides a new insight into the maximum entropy function.

Random Graph Set and Evidence Pattern Reasoning Model

Evidence theory is widely used in decision-making and reasoning systems. In previous research, Transferable Belief Model (TBM) is a commonly used evidential decision making model, but TBM is a non-preference model. In order to better fit the decision making goals, the Evidence Pattern Reasoning Model (EPRM) is proposed. By defining pattern operators and decision making operators, corresponding preferences can be set for different tasks. Random Permutation Set (RPS) expands order information for evidence theory. It is hard for RPS to characterize the complex relationship between samples such as cycling, paralleling relationships. Therefore, Random Graph Set (RGS) were proposed to model complex relationships and represent more event types. In order to illustrate the significance of RGS and EPRM, an experiment of aircraft velocity ranking was designed and 10,000 cases were simulated. The implementation of EPRM called Conflict Resolution Decision optimized 18.17\% of the cases compared to Mean Velocity Decision, effectively improving the aircraft velocity ranking. EPRM provides a unified solution for evidence-based decision making.

An Embeddable Implicit IUVD Representation for Part-based 3D Human Surface Reconstruction

To reconstruct a 3D human surface from a single image, it is important to consider human pose, shape and clothing details simultaneously. In recent years, a combination of parametric body models (such as SMPL) that capture body pose and shape prior, and neural implicit functions that learn flexible clothing details, has been used to integrate the advantages of both approaches. However, the combined representation introduces additional computation, e.g. signed distance calculation, in 3D body feature extraction, which exacerbates the redundancy of the implicit query-and-infer process and fails to preserve the underlying body shape prior. To address these issues, we propose a novel IUVD-Feedback representation, which consists of an IUVD occupancy function and a feedback query algorithm. With this representation, the time-consuming signed distance calculation is replaced by a simple linear transformation in the IUVD space, leveraging the SMPL UV maps. Additionally, the redundant query points in the query-and-infer process are reduced through a feedback mechanism. This leads to more reasonable 3D body features and more effective query points, successfully preserving the parametric body prior. Moreover, the IUVD-Feedback representation can be embedded into any existing implicit human reconstruction pipelines without modifying the trained neural networks. Experiments on THuman2.0 dataset demonstrate that the proposed IUVD-Feedback representation improves result robustness and achieves three times faster acceleration in the query-and-infer process. Furthermore, this representation has the potential to be used in generative applications by leveraging its inherited semantic information from the parametric body model.

Linear-time online visibility graph transformation algorithm: for both natural and horizontal visibility criteria

Visibility graph (VG) transformation is a technique used to convert a time series into a graph based on specific visibility criteria. It has attracted increasing interest in the fields of time series analysis, forecasting, and classification. Optimizing the VG transformation algorithm to accelerate the process is a critical aspect of VG-related research, as it enhances the applicability of VG transformation in latency-sensitive areas and conserves computational resources. In the real world, many time series are presented in the form of data streams. Despite the proposal of the concept of VG's online functionality, previous studies have not thoroughly explored the acceleration of VG transformation by leveraging the characteristics of data streams. In this paper, we propose that an efficient online VG algorithm should adhere to two criteria and develop a linear-time method, termed the LOT framework, for both natural and horizontal visibility graph transformations in data stream scenarios. Experiments are conducted on two datasets, comparing our approach with five existing methods as baselines. The results demonstrate the validity and promising computational efficiency of our framework.

Differential Convolutional Fuzzy Time Series Forecasting

Fuzzy time series forecasting (FTSF) is a typical forecasting method with wide application. Traditional FTSF is regarded as an expert system which leads to lose the ability to recognize undefined feature. The mentioned is main reason of poor forecasting with FTSF. To solve the problem, the proposed model Differential Fuzzy Convolutional Neural Network (DFCNN) utilizes convolution neural network to re-implement FTSF with learnable ability. DFCNN is capable of recognizing the potential information and improve the forecasting accuracy. Thanks to learnable ability of neural network, length of fuzzy rules established in FTSF is expended to arbitrary length which expert is not able to be handle by expert system. At the same time, FTSF usually cannot achieve satisfactory performance of non-stationary time series due to trend of non-stationary time series. The trend of non-stationary time series causes the fuzzy set established by FTSF to invalid and cause the forecasting to fail. DFCNN utilizes the Difference algorithm to weaken the non-stationarity of time series, so that DFCNN can forecast the non-stationary time series with low error that FTSF cannot forecast in satisfactory performance. After mass of experiments, DFCNN has excellent prediction effect, which is ahead of the existing FTSF and common time series forecasting algorithms. Finally, DFCNN provides further ideas for improving FTSF and holds continued research value.

Towards Better Instruction Following Language Models for Chinese: Investigating the Impact of Training Data and Evaluation

Recently, significant public efforts have been directed towards developing low-cost models with capabilities akin to ChatGPT, thereby fostering the growth of open-source conversational models. However, there remains a scarcity of comprehensive and in-depth evaluations of these models' performance. In this study, we examine the influence of training data factors, including quantity, quality, and linguistic distribution, on model performance. Our analysis is grounded in several publicly accessible, high-quality instruction datasets, as well as our own Chinese multi-turn conversations. We assess various models using a evaluation set of 1,000 samples, encompassing nine real-world scenarios. Our goal is to supplement manual evaluations with quantitative analyses, offering valuable insights for the continued advancement of open-source chat models. Furthermore, to enhance the performance and training and inference efficiency of models in the Chinese domain, we extend the vocabulary of LLaMA - the model with the closest open-source performance to proprietary language models like GPT-3 - and conduct secondary pre-training on 3.4B Chinese words. We make our model, data, as well as code publicly available.