We consider multilevel low rank (MLR) matrices, defined as a row and column permutation of a sum of matrices, each one a block diagonal refinement of the previous one, with all blocks low rank given in factored form. MLR matrices extend low rank matrices but share many of their properties, such as the total storage required and complexity of matrix-vector multiplication. We address three problems that arise in fitting a given matrix by an MLR matrix in the Frobenius norm. The first problem is factor fitting, where we adjust the factors of the MLR matrix. The second is rank allocation, where we choose the ranks of the blocks in each level, subject to the total rank having a given value, which preserves the total storage needed for the MLR matrix. The final problem is to choose the hierarchical partition of rows and columns, along with the ranks and factors. This paper is accompanied by an open source package that implements the proposed methods.
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As the number and complexity of malware attacks continue to increase, there is an urgent need for effective malware detection systems. While deep learning models are effective at detecting malware, they are vulnerable to adversarial attacks. Attacks like this can create malicious files that are resistant to detection, creating a significant cybersecurity risk. Recent research has seen the development of several adversarial attack and response approaches aiming at strengthening deep learning models' resilience to such attacks. This survey study offers an in-depth look at current research in adversarial attack and defensive strategies for malware classification in cybersecurity. The methods are classified into four categories: generative models, feature-based approaches, ensemble methods, and hybrid tactics. The article outlines cutting-edge procedures within each area, assessing their benefits and drawbacks. Each topic presents cutting-edge approaches and explores their advantages and disadvantages. In addition, the study discusses the datasets and assessment criteria that are often utilized on this subject. Finally, it identifies open research difficulties and suggests future study options. This document is a significant resource for malware categorization and cyber security researchers and practitioners.
Several sensing techniques have been proposed for silent speech recognition (SSR); however, many of these methods require invasive processes or sensor attachment to the skin using adhesive tape or glue, rendering them unsuitable for frequent use in daily life. By contrast, impulse radio ultra-wideband (IR-UWB) radar can operate without physical contact with users' articulators and related body parts, offering several advantages for SSR. These advantages include high range resolution, high penetrability, low power consumption, robustness to external light or sound interference, and the ability to be embedded in space-constrained handheld devices. This study demonstrated IR-UWB radar-based contactless SSR using four types of speech stimuli (vowels, consonants, words, and phrases). To achieve this, a novel speech feature extraction algorithm specifically designed for IR-UWB radar-based SSR is proposed. Each speech stimulus is recognized by applying a classification algorithm to the extracted speech features. Two different algorithms, multidimensional dynamic time warping (MD-DTW) and deep neural network-hidden Markov model (DNN-HMM), were compared for the classification task. Additionally, a favorable radar antenna position, either in front of the user's lips or below the user's chin, was determined to achieve higher recognition accuracy. Experimental results demonstrated the efficacy of the proposed speech feature extraction algorithm combined with DNN-HMM for classifying vowels, consonants, words, and phrases. Notably, this study represents the first demonstration of phoneme-level SSR using contactless radar.
While the problem of computing the genus of a knot is now fairly well understood, no algorithm is known for its four-dimensional variants, both in the smooth and in the topological locally flat category. In this article, we investigate a class of knots and links called Hopf arborescent links, which are obtained as the boundaries of some iterated plumbings of Hopf bands. We show that for such links, computing the genus defects, which measure how much the four-dimensional genera differ from the classical genus, is decidable. Our proof is non-constructive, and is obtained by proving that Seifert surfaces of Hopf arborescent links under a relation of minors defined by containment of their Seifert surfaces form a well-quasi-order.
The prevalence of the powerful multilingual models, such as Whisper, has significantly advanced the researches on speech recognition. However, these models often struggle with handling the code-switching setting, which is essential in multilingual speech recognition. Recent studies have attempted to address this setting by separating the modules for different languages to ensure distinct latent representations for languages. Some other methods considered the switching mechanism based on language identification. In this study, a new attention-guided adaptation is proposed to conduct parameter-efficient learning for bilingual ASR. This method selects those attention heads in a model which closely express language identities and then guided those heads to be correctly attended with their corresponding languages. The experiments on the Mandarin-English code-switching speech corpus show that the proposed approach achieves a 14.2% mixed error rate, surpassing state-of-the-art method, where only 5.6% additional parameters over Whisper are trained.
In approval-based committee (ABC) voting, the goal is to choose a subset of predefined size of the candidates based on the voters' approval preferences over the candidates. While this problem has attracted significant attention in recent years, the incentives for voters to participate in an election for a given ABC voting rule have been neglected so far. This paper is thus the first to explicitly study this property, typically called participation, for ABC voting rules. In particular, we show that all ABC scoring rules even satisfy group participation, whereas most sequential rules severely fail participation. We furthermore explore several escape routes to the impossibility for sequential ABC voting rules: we prove for many sequential rules that (i) they satisfy participation on laminar profiles, (ii) voters who approve none of the elected candidates cannot benefit by abstaining, and (iii) it is NP-hard for a voter to decide whether she benefits from abstaining.
Proper scoring rules evaluate the quality of probabilistic predictions, playing an essential role in the pursuit of accurate and well-calibrated models. Every proper score decomposes into two fundamental components -- proper calibration error and refinement -- utilizing a Bregman divergence. While uncertainty calibration has gained significant attention, current literature lacks a general estimator for these quantities with known statistical properties. To address this gap, we propose a method that allows consistent, and asymptotically unbiased estimation of all proper calibration errors and refinement terms. In particular, we introduce Kullback--Leibler calibration error, induced by the commonly used cross-entropy loss. As part of our results, we prove the relation between refinement and f-divergences, which implies information monotonicity in neural networks, regardless of which proper scoring rule is optimized. Our experiments validate empirically the claimed properties of the proposed estimator and suggest that the selection of a post-hoc calibration method should be determined by the particular calibration error of interest.
Conflict transformation and management are complex decision processes with extremely high stakes at hand and could greatly benefit from formal approaches to decision support. For this purpose we develop a general framework about how to use problem structuring methods for such purposes. More precisely we show how to transform cognitive maps to value trees in order to promote a more design-oriented approach to decision support aiming at constructing innovative solutions for conflict management purposes. We show that our findings have a much wider validity since they allow to move from a descriptive representation of a problem situation to a more prescriptive one using formal procedures and models.
Temporal characteristics are prominently evident in a substantial volume of knowledge, which underscores the pivotal role of Temporal Knowledge Graphs (TKGs) in both academia and industry. However, TKGs often suffer from incompleteness for three main reasons: the continuous emergence of new knowledge, the weakness of the algorithm for extracting structured information from unstructured data, and the lack of information in the source dataset. Thus, the task of Temporal Knowledge Graph Completion (TKGC) has attracted increasing attention, aiming to predict missing items based on the available information. In this paper, we provide a comprehensive review of TKGC methods and their details. Specifically, this paper mainly consists of three components, namely, 1)Background, which covers the preliminaries of TKGC methods, loss functions required for training, as well as the dataset and evaluation protocol; 2)Interpolation, that estimates and predicts the missing elements or set of elements through the relevant available information. It further categorizes related TKGC methods based on how to process temporal information; 3)Extrapolation, which typically focuses on continuous TKGs and predicts future events, and then classifies all extrapolation methods based on the algorithms they utilize. We further pinpoint the challenges and discuss future research directions of TKGC.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
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