Graph theory is an interdisciplinary field of study that has various applications in mathematical modeling and computer science. Research in graph theory depends on the creation of not only theorems but also conjectures. Conjecture-refuting algorithms attempt to refute conjectures by searching for counterexamples to those conjectures, often by maximizing certain score functions on graphs. This study proposes a novel conjecture-refuting algorithm, referred to as the adaptive Monte Carlo search (AMCS) algorithm, obtained by modifying the Monte Carlo tree search algorithm. Evaluated based on its success in finding counterexamples to several graph theory conjectures, AMCS outperforms existing conjecture-refuting algorithms. The algorithm is further utilized to refute six open conjectures, two of which were chemical graph theory conjectures formulated by Liu et al. in 2021 and four of which were formulated by the AutoGraphiX computer system in 2006. Finally, four of the open conjectures are strongly refuted by generalizing the counterexamples obtained by AMCS to produce a family of counterexamples. It is expected that the algorithm can help researchers test graph-theoretic conjectures more effectively.
While sentence simplification is an active research topic in NLP, its adjacent tasks of sentence complexification and same-level paraphrasing are not. To train models on all three tasks, we present two new unsupervised datasets. We compare these datasets, one labeled by a weak classifier and the other by a rule-based approach, with a single supervised dataset. Using these three datasets for training, we perform extensive experiments on both multitasking and prompting strategies. Compared to other systems trained on unsupervised parallel data, models trained on our weak classifier labeled dataset achieve state-of-the-art performance on the ASSET simplification benchmark. Our models also outperform previous work on sentence level targeting. Finally, we establish how a handful of Large Language Models perform on these tasks under a zero-shot setting.
As the development of measuring instruments and computers has accelerated the collection of massive data, functional data analysis (FDA) has gained a surge of attention. FDA is a methodology that treats longitudinal data as a function and performs inference, including regression. Functionalizing data typically involves fitting it with basis functions. However, the number of these functions smaller than the sample size is selected commonly. This paper casts doubt on this convention. Recent statistical theory has witnessed a phenomenon (the so-called double descent) in which excess parameters overcome overfitting and lead to precise interpolation. If we transfer this idea to the choice of the number of bases for functional data, providing an excess number of bases can lead to accurate predictions. We have explored this phenomenon in a functional regression problem and examined its validity through numerical experiments. In addition, through application to real-world datasets, we demonstrated that the double descent goes beyond just theoretical and numerical experiments - it is also important for practical use.
In intelligent reflecting surface (IRS) assisted communication, beam search is usually time-consuming as the multiple-input multiple-output (MIMO) of IRS is usually very large. Hierarchical codebooks is a widely accepted method for reducing the complexity of searching time. The performance of this method strongly depends on the design scheme of beamforming of different beamwidths. In this paper, a non-constant phase difference (NCPD) beamforming algorithm is proposed. To implement the NCPD algorithm, we first model the phase shift of IRS as a continuous function, and then determine the parameters of the continuous function through the analysis of its array factor. Then, we propose a hierarchical codebook and two beam training schemes, namely the joint searching (JS) scheme and direction-wise searching (DWS) scheme by using the NCPD algorithm which can flexibly change the width, direction and shape of the beam formed by the IRS array. Simulation results show that the NCPD algorithm is more accurate with smaller side lobes, and also more stable on IRS of different sizes compared to other wide beam algorithms. The misalignment rate of the beam formed by the NCPD method is significantly reduced. The time complexity of the NCPD algorithm is constant, thus making it more suitable for solving the beamforming design problem with practically large IRS.
We present SEIF, a methodology that combines static analysis with symbolic execution to verify and explicate information flow paths in a hardware design. SEIF begins with a statically built model of the information flow through a design and uses guided symbolic execution to recognize and eliminate non-flows with high precision or to find corresponding paths through the design state for true flows. We evaluate SEIF on two open-source CPUs, an AES core, and the AKER access control module. SEIF can exhaustively explore 10-12 clock cycles deep in 4-6 seconds on average, and can automatically account for 86-90% of the paths in the statically built model. Additionally, SEIF can be used to find multiple violating paths for security properties, providing a new angle for security verification.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
Triple extraction is an essential task in information extraction for natural language processing and knowledge graph construction. In this paper, we revisit the end-to-end triple extraction task for sequence generation. Since generative triple extraction may struggle to capture long-term dependencies and generate unfaithful triples, we introduce a novel model, contrastive triple extraction with a generative transformer. Specifically, we introduce a single shared transformer module for encoder-decoder-based generation. To generate faithful results, we propose a novel triplet contrastive training object. Moreover, we introduce two mechanisms to further improve model performance (i.e., batch-wise dynamic attention-masking and triple-wise calibration). Experimental results on three datasets (i.e., NYT, WebNLG, and MIE) show that our approach achieves better performance than that of baselines.
Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.
It is important to detect anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance. We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.
We introduce a generic framework that reduces the computational cost of object detection while retaining accuracy for scenarios where objects with varied sizes appear in high resolution images. Detection progresses in a coarse-to-fine manner, first on a down-sampled version of the image and then on a sequence of higher resolution regions identified as likely to improve the detection accuracy. Built upon reinforcement learning, our approach consists of a model (R-net) that uses coarse detection results to predict the potential accuracy gain for analyzing a region at a higher resolution and another model (Q-net) that sequentially selects regions to zoom in. Experiments on the Caltech Pedestrians dataset show that our approach reduces the number of processed pixels by over 50% without a drop in detection accuracy. The merits of our approach become more significant on a high resolution test set collected from YFCC100M dataset, where our approach maintains high detection performance while reducing the number of processed pixels by about 70% and the detection time by over 50%.