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The Hurst exponent is a significant indicator for characterizing the self-similarity and long-term memory properties of time sequences. It has wide applications in physics, technologies, engineering, mathematics, statistics, economics, psychology and so on. Currently, available methods for estimating the Hurst exponent of time sequences can be divided into different categories: time-domain methods and spectrum-domain methods based on the representation of time sequence, linear regression methods and Bayesian methods based on parameter estimation methods. Although various methods are discussed in literature, there are still some deficiencies: the descriptions of the estimation algorithms are just mathematics-oriented and the pseudo-codes are missing; the effectiveness and accuracy of the estimation algorithms are not clear; the classification of estimation methods is not considered and there is a lack of guidance for selecting the estimation methods. In this work, the emphasis is put on thirteen dominant methods for estimating the Hurst exponent. For the purpose of decreasing the difficulty of implementing the estimation methods with computer programs, the mathematical principles are discussed briefly and the pseudo-codes of algorithms are presented with necessary details. It is expected that the survey could help the researchers to select, implement and apply the estimation algorithms of interest in practical situations in an easy way.

Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component of prevalent deep neural network architectures to achieve chosen equivariance is a difficult problem and can result in a computationally expensive network during both training and inference. A recently proposed alternative towards equivariance that removes the architectural constraints is to use a simple canonicalization network that transforms the input to a canonical form before feeding it to an unconstrained prediction network. We show here that this approach can effectively be used to make a large pretrained network equivariant. However, we observe that the produced canonical orientations can be misaligned with those of the training distribution, hindering performance. Using dataset-dependent priors to inform the canonicalization function, we are able to make large pretrained models equivariant while maintaining their performance. This significantly improves the robustness of these models to deterministic transformations of the data, such as rotations. We believe this equivariant adaptation of large pretrained models can help their domain-specific applications with known symmetry priors.

Large Language Models (LLMs) exhibit impressive performance on a range of NLP tasks, due to the general-purpose linguistic knowledge acquired during pretraining. Existing model interpretability research (Tenney et al., 2019) suggests that a linguistic hierarchy emerges in the LLM layers, with lower layers better suited to solving syntactic tasks and higher layers employed for semantic processing. Yet, little is known about how encodings of different linguistic phenomena interact within the models and to what extent processing of linguistically-related categories relies on the same, shared model representations. In this paper, we propose a framework for testing the joint encoding of linguistic categories in LLMs. Focusing on syntax, we find evidence of joint encoding both at the same (related part-of-speech (POS) classes) and different (POS classes and related syntactic dependency relations) levels of linguistic hierarchy. Our cross-lingual experiments show that the same patterns hold across languages in multilingual LLMs.

Despite the advancements in high-performance computing and modern numerical algorithms, the cost remains prohibitive for multi-query kinetic plasma simulations. In this work, we develop data-driven reduced-order models (ROM) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by principal proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution into multiple time windows using a physical-time indicator and creating a temporally-local ROM. Applied to 1D-1V simulations, specifically the benchmark two-stream instability case, our time-windowed reduced-order model (TW-ROM) with the tensorial approach solves the equation approximately 450 times faster than Eulerian simulations while maintaining a maximum relative error of 3% for the training data and 12% for the testing data.

Semantic text similarity plays an important role in software engineering tasks in which engineers are requested to clarify the semantics of descriptive labels (e.g., business terms, table column names) that are often consists of too short or too generic words and appears in their IT systems. We formulate this type of problem as a task of matching descriptive labels to glossary descriptions. We then propose a framework to leverage an existing semantic text similarity measurement (STS) and augment it using semantic label enrichment and set-based collective contextualization where the former is a method to retrieve sentences relevant to a given label and the latter is a method to compute similarity between two contexts each of which is derived from a set of texts (e.g., column names in the same table). We performed an experiment on two datasets derived from publicly available data sources. The result indicated that the proposed methods helped the underlying STS correctly match more descriptive labels with the descriptions.

With the increasing complexity and scope of software systems, their dependability is crucial. The analysis of log data recorded during system execution can enable engineers to automatically predict failures at run time. Several Machine Learning (ML) techniques, including traditional ML and Deep Learning (DL), have been proposed to automate such tasks. However, current empirical studies are limited in terms of covering all main DL types -- Recurrent Neural Network (RNN), Convolutional Neural network (CNN), and transformer -- as well as examining them on a wide range of diverse datasets. In this paper, we aim to address these issues by systematically investigating the combination of log data embedding strategies and DL types for failure prediction. To that end, we propose a modular architecture to accommodate various configurations of embedding strategies and DL-based encoders. To further investigate how dataset characteristics such as dataset size and failure percentage affect model accuracy, we synthesised 360 datasets, with varying characteristics, for three distinct system behavioral models, based on a systematic and automated generation approach. Using the F1 score metric, our results show that the best overall performing configuration is a CNN-based encoder with Logkey2vec. Additionally, we provide specific dataset conditions, namely a dataset size >350 or a failure percentage >7.5%, under which this configuration demonstrates high accuracy for failure prediction.

Video grounding aims to localize the target moment in an untrimmed video corresponding to a given sentence query. Existing methods typically select the best prediction from a set of predefined proposals or directly regress the target span in a single-shot manner, resulting in the absence of a systematical prediction refinement process. In this paper, we propose DiffusionVG, a novel framework with diffusion models that formulates video grounding as a conditional generation task, where the target span is generated from Gaussian noise inputs and interatively refined in the reverse diffusion process. During training, DiffusionVG progressively adds noise to the target span with a fixed forward diffusion process and learns to recover the target span in the reverse diffusion process. In inference, DiffusionVG can generate the target span from Gaussian noise inputs by the learned reverse diffusion process conditioned on the video-sentence representations. Our DiffusionVG follows the encoder-decoder architecture, which firstly encodes the video-sentence features and iteratively denoises the predicted spans in its specialized span refining decoder. Without bells and whistles, our DiffusionVG demonstrates competitive or even superior performance compared to existing well-crafted models on mainstream Charades-STA and ActivityNet Captions benchmarks.

Microarchitectural timing channels are a major threat to computer security. A set of OS mechanisms called time protection was recently proposed as a principled way of preventing information leakage through such channels and prototyped in the seL4 microkernel. We formalise time protection and the underlying hardware mechanisms in a way that allows linking them to the information-flow proofs that showed the absence of storage channels in seL4.

Noisy marginals are a common form of confidentiality-protecting data release and are useful for many downstream tasks such as contingency table analysis, construction of Bayesian networks, and even synthetic data generation. Privacy mechanisms that provide unbiased noisy answers to linear queries (such as marginals) are known as matrix mechanisms. We propose ResidualPlanner, a matrix mechanism for marginals with Gaussian noise that is both optimal and scalable. ResidualPlanner can optimize for many loss functions that can be written as a convex function of marginal variances (prior work was restricted to just one predefined objective function). ResidualPlanner can optimize the accuracy of marginals in large scale settings in seconds, even when the previous state of the art (HDMM) runs out of memory. It even runs on datasets with 100 attributes in a couple of minutes. Furthermore ResidualPlanner can efficiently compute variance/covariance values for each marginal (prior methods quickly run out of memory, even for relatively small datasets).

We study how to generate captions that are not only accurate in describing an image but also discriminative across different images. The problem is both fundamental and interesting, as most machine-generated captions, despite phenomenal research progresses in the past several years, are expressed in a very monotonic and featureless format. While such captions are normally accurate, they often lack important characteristics in human languages - distinctiveness for each caption and diversity for different images. To address this problem, we propose a novel conditional generative adversarial network for generating diverse captions across images. Instead of estimating the quality of a caption solely on one image, the proposed comparative adversarial learning framework better assesses the quality of captions by comparing a set of captions within the image-caption joint space. By contrasting with human-written captions and image-mismatched captions, the caption generator effectively exploits the inherent characteristics of human languages, and generates more discriminative captions. We show that our proposed network is capable of producing accurate and diverse captions across images.