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Graph-based interactive theorem provers offer a visual representation of proofs, explicitly representing the dependencies and inferences between each of the proof steps in a graph or hypergraph format. The number and complexity of these dependency links can determine how long it takes to verify the validity of the entire proof. Towards this end, we present a set of parallel algorithms for the formal verification of graph-based natural-deduction (ND) style proofs. We introduce a definition of layering that captures dependencies between the proof steps (nodes). Nodes in each layer can then be verified in parallel as long as prior layers have been verified. To evaluate the performance of our algorithms on proof graphs, we propose a framework for finding the performance bounds and patterns using directed acyclic network topologies (DANTs). This framework allows us to create concrete instances of DANTs for empirical evaluation of our algorithms. With this, we compare our set of parallel algorithms against a serial implementation with two experiments: one scaling both the problem size and the other scaling the number of threads. Our findings show that parallelization results in improved verification performance for certain DANT instances. We also show that our algorithms scale for certain DANT instances with respect to the number of threads.

Implementing precise detection of oil leaks in peak load equipment through image analysis can significantly enhance inspection quality and ensure the system's safety and reliability. However, challenges such as varying shapes of oil-stained regions, background noise, and fluctuating lighting conditions complicate the detection process. To address this, the integration of logical rule-based discrimination into image recognition has been proposed. This approach involves recognizing the spatial relationships among objects to semantically segment images of oil spills using a Mask RCNN network. The process begins with histogram equalization to enhance the original image, followed by the use of Mask RCNN to identify the preliminary positions and outlines of oil tanks, the ground, and areas of potential oil contamination. Subsequent to this identification, the spatial relationships between these objects are analyzed. Logical rules are then applied to ascertain whether the suspected areas are indeed oil spills. This method's effectiveness has been confirmed by testing on images captured from peak power equipment in the field. The results indicate that this approach can adeptly tackle the challenges in identifying oil-contaminated areas, showing a substantial improvement in accuracy compared to existing methods.

The accessibility of documents within a collection holds a pivotal role in Information Retrieval, signifying the ease of locating specific content in a collection of documents. This accessibility can be achieved via two distinct avenues. The first is through some retrieval model using a keyword or other feature-based search, and the other is where a document can be navigated using links associated with them, if available. Metrics such as PageRank, Hub, and Authority illuminate the pathways through which documents can be discovered within the network of content while the concept of Retrievability is used to quantify the ease with which a document can be found by a retrieval model. In this paper, we compare these two perspectives, PageRank and retrievability, as they quantify the importance and discoverability of content in a corpus. Through empirical experimentation on benchmark datasets, we demonstrate a subtle similarity between retrievability and PageRank particularly distinguishable for larger datasets.

Fast Hough transform is a widely used algorithm in pattern recognition. The algorithm relies on approximating lines using a specific discrete line model called dyadic lines. The worst-case deviation of a dyadic line from the ideal line it used to construct grows as $O(log(n))$, where $n$ is the linear size of the image. But few lines actually reach the worst-case bound. The present paper addresses a statistical analysis of the deviation of a dyadic line from its ideal counterpart. Specifically, our findings show that the mean deviation is zero, and the variance grows as $O(log(n))$. As $n$ increases, the distribution of these (suitably normalized) deviations converges towards a normal distribution with zero mean and a small variance. This limiting result makes an essential use of ergodic theory.

The increasing demand for heterogeneous functionality in the automotive industry and the evolution of chip manufacturing processes have led to the transition from federated to integrated critical real-time embedded systems (CRTESs). This leads to higher integration challenges of conventional timing predictability techniques due to access contention on shared resources, which can be resolved by providing system-level observability and controllability in hardware. We focus on the interconnect as a shared resource and propose AXI-REALM, a lightweight, modular, and technology-independent real-time extension to industry-standard AXI4 interconnects, available open-source. AXI-REALM uses a credit-based mechanism to distribute and control the bandwidth in a multi-subordinate system on periodic time windows, proactively prevents denial of service from malicious actors in the system, and tracks each manager's access and interference statistics for optimal budget and period selection. We provide detailed performance and implementation cost assessment in a 12nm node and an end-to-end functional case study implementing AXI-REALM into an open-source Linux-capable RISC-V SoC. In a system with a general-purpose core and a hardware accelerator's DMA engine causing interference on the interconnect, AXI-REALM achieves fair bandwidth distribution among managers, allowing the core to recover 68.2 % of its performance compared to the case without contention. Moreover, near-ideal performance (above 95 %) can be achieved by distributing the available bandwidth in favor of the core, improving the worst-case memory access latency from 264 to below eight cycles. Our approach minimizes buffering compared to other solutions and introduces only 2.45 % area overhead compared to the original SoC.

The transformer neural network architecture uses a form of attention in which the dot product of query and key is divided by the square root of the key dimension before applying softmax. This scaling of the dot product is designed to avoid the absolute value of the dot products becoming so large that applying softmax leads to vanishing gradients. In this paper, we propose some alternative scalings, including dividing the dot product instead by the sum of the key lengths before applying softmax. We use simulated keys and queries to show that in many situations this appears to be more effective at avoiding regions where applying softmax leads to vanishing gradients.

Machine Translation (MT) continues to improve in quality and adoption, yet the inadvertent perpetuation of gender bias remains a significant concern. Despite numerous studies into gender bias in translations from gender-neutral languages such as Turkish into more strongly gendered languages like English, there are no benchmarks for evaluating this phenomenon or for assessing mitigation strategies. To address this gap, we introduce GATE X-E, an extension to the GATE (Rarrick et al., 2023) corpus, that consists of human translations from Turkish, Hungarian, Finnish, and Persian into English. Each translation is accompanied by feminine, masculine, and neutral variants for each possible gender interpretation. The dataset, which contains between 1250 and 1850 instances for each of the four language pairs, features natural sentences with a wide range of sentence lengths and domains, challenging translation rewriters on various linguistic phenomena. Additionally, we present an English gender rewriting solution built on GPT-3.5 Turbo and use GATE X-E to evaluate it. We open source our contributions to encourage further research on gender debiasing.

Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from using traditional methods to infer potential causal structures from observational data to the field of pattern recognition involved in deep learning. The rapid accumulation of massive data promotes the emergence of causal search methods with brilliant scalability. Existing summaries of causal discovery methods mainly focus on traditional methods based on constraints, scores and FCMs, there is a lack of perfect sorting and elaboration for deep learning-based methods, also lacking some considers and exploration of causal discovery methods from the perspective of variable paradigms. Therefore, we divide the possible causal discovery tasks into three types according to the variable paradigm and give the definitions of the three tasks respectively, define and instantiate the relevant datasets for each task and the final causal model constructed at the same time, then reviews the main existing causal discovery methods for different tasks. Finally, we propose some roadmaps from different perspectives for the current research gaps in the field of causal discovery and point out future research directions.

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.

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.