This paper conducts a comprehensive benchmarking analysis of the performance of two innovative cryptographic schemes: Homomorphic Polynomial Public Key (HPPK)-Key Encapsulation Mechanism (KEM) and Digital Signature (DS), recently proposed by Kuang et al. These schemes represent a departure from traditional cryptographic paradigms, with HPPK leveraging the security of homomorphic symmetric encryption across two hidden rings without reliance on NP-hard problems. HPPK can be viewed as a specialized variant of Multivariate Public Key Cryptography (MPKC), intricately associated with two vector spaces: the polynomial vector space for the secret exchange and the multivariate vector space for randomized encapsulation. The unique integration of asymmetric, symmetric, and homomorphic cryptography within HPPK necessitates a careful examination of its performance metrics. This study focuses on the thorough benchmarking of HPPK KEM and DS across key cryptographic operations, encompassing key generation, encapsulation, decapsulation, signing, and verification. The results highlight the exceptional efficiency of HPPK, characterized by compact key sizes, cipher sizes, and signature sizes. The use of symmetric encryption in HPPK enhances its overall performance. Key findings underscore the outstanding performance of HPPK KEM and DS across various security levels, emphasizing their superiority in crucial cryptographic operations. This research positions HPPK as a promising and competitive solution for post-quantum cryptographic applications in a wide range of applications, including blockchain, digital currency, and Internet of Things (IoT) devices.
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By consolidating scattered knowledge, the literature review provides a comprehensive understanding of the investigated topic. However, excessive reviews, especially in the booming field of pattern analysis and machine intelligence (PAMI), raise concerns for both researchers and reviewers. In response to these concerns, this Analysis aims to provide a thorough review of reviews in the PAMI field from diverse perspectives. First, large language model-empowered bibliometric indicators are proposed to evaluate literature reviews automatically. To facilitate this, a meta-data database dubbed RiPAMI, and a topic dataset are constructed, which are utilized to obtain statistical characteristics of PAMI reviews. Unlike traditional bibliometric measurements, the proposed article-level indicators provide real-time and field-normalized quantified assessments of reviews without relying on user-defined keywords. Second, based on these indicators, the study presents comparative analyses of different reviews, unveiling the characteristics of publications across various fields, periods, and journals. The newly emerging AI-generated literature reviews are also appraised, and the observed differences suggest that most AI-generated reviews still lag behind human-authored reviews in several aspects. Third, we briefly provide a subjective evaluation of representative PAMI reviews and introduce a paper structure-based typology of literature reviews. This typology may improve the clarity and effectiveness for scholars in reading and writing reviews, while also serving as a guide for AI systems in generating well-organized reviews. Finally, this Analysis offers insights into the current challenges of literature reviews and envisions future directions for their development.
This paper provides an introduction to quantum machine learning, exploring the potential benefits of using quantum computing principles and algorithms that may improve upon classical machine learning approaches. Quantum computing utilizes particles governed by quantum mechanics for computational purposes, leveraging properties like superposition and entanglement for information representation and manipulation. Quantum machine learning applies these principles to enhance classical machine learning models, potentially reducing network size and training time on quantum hardware. The paper covers basic quantum mechanics principles, including superposition, phase space, and entanglement, and introduces the concept of quantum gates that exploit these properties. It also reviews classical deep learning concepts, such as artificial neural networks, gradient descent, and backpropagation, before delving into trainable quantum circuits as neural networks. An example problem demonstrates the potential advantages of quantum neural networks, and the appendices provide detailed derivations. The paper aims to help researchers new to quantum mechanics and machine learning develop their expertise more efficiently.
Contextualized embeddings are the preferred tool for modeling Lexical Semantic Change (LSC). Current evaluations typically focus on a specific task known as Graded Change Detection (GCD). However, performance comparison across work are often misleading due to their reliance on diverse settings. In this paper, we evaluate state-of-the-art models and approaches for GCD under equal conditions. We further break the LSC problem into Word-in-Context (WiC) and Word Sense Induction (WSI) tasks, and compare models across these different levels. Our evaluation is performed across different languages on eight available benchmarks for LSC, and shows that (i) APD outperforms other approaches for GCD; (ii) XL-LEXEME outperforms other contextualized models for WiC, WSI, and GCD, while being comparable to GPT-4; (iii) there is a clear need for improving the modeling of word meanings, as well as focus on how, when, and why these meanings change, rather than solely focusing on the extent of semantic change.
We introduce a novel concept of convergence for Markovian processes within Orlicz spaces, extending beyond the conventional approach associated with $L_p$ spaces. After showing that Markovian operators are contractive in Orlicz spaces, our key technical contribution is an upper bound on their contraction coefficient, which admits a closed-form expression. The bound is tight in some settings, and it recovers well-known results, such as the connection between contraction and ergodicity, ultra-mixing and Doeblin's minorisation. Specialising our approach to $L_p$ spaces leads to a significant improvement upon classical Riesz-Thorin's interpolation methods. Furthermore, by exploiting the flexibility offered by Orlicz spaces, we can tackle settings where the stationary distribution is heavy-tailed, a severely under-studied setup. As an application of the framework put forward in the paper, we introduce tighter bounds on the mixing time of Markovian processes, better exponential concentration bounds for MCMC methods, and better lower bounds on the burn-in period. To conclude, we show how our results can be used to prove the concentration of measure phenomenon for a sequence of Markovian random variables.
We propose a novel approach to the problem of controller design for environments modeled as Markov decision processes (MDPs). Specifically, we consider a hierarchical MDP a graph with each vertex populated by an MDP called a "room". We first apply deep reinforcement learning (DRL) to obtain low-level policies for each room, scaling to large rooms of unknown structure. We then apply reactive synthesis to obtain a high-level planner that chooses which low-level policy to execute in each room. The central challenge in synthesizing the planner is the need for modeling rooms. We address this challenge by developing a DRL procedure to train concise "latent" policies together with PAC guarantees on their performance. Unlike previous approaches, ours circumvents a model distillation step. Our approach combats sparse rewards in DRL and enables reusability of low-level policies. We demonstrate feasibility in a case study involving agent navigation amid moving obstacles.
When constructing parametric models to predict the cost of future claims, several important details have to be taken into account: (i) models should be designed to accommodate deductibles, policy limits, and coinsurance factors, (ii) parameters should be estimated robustly to control the influence of outliers on model predictions, and (iii) all point predictions should be augmented with estimates of their uncertainty. The methodology proposed in this paper provides a framework for addressing all these aspects simultaneously. Using payment-per-payment and payment-per-loss variables, we construct the adaptive version of method of winsorized moments (MWM) estimators for the parameters of truncated and censored lognormal distribution. Further, the asymptotic distributional properties of this approach are derived and compared with those of the maximum likelihood estimator (MLE) and method of trimmed moments (MTM) estimators. The latter being a primary competitor to MWM. Moreover, the theoretical results are validated with extensive simulation studies and risk measure sensitivity analysis. Finally, practical performance of these methods is illustrated using the well-studied data set of 1500 U.S. indemnity losses. With this real data set, it is also demonstrated that the composite models do not provide much improvement in the quality of predictive models compared to a stand-alone fitted distribution specially for truncated and censored sample data.
This paper details an empirical investigation into using Graph Contrastive Learning (GCL) to generate mathematical equation representations, a critical aspect of Mathematical Information Retrieval (MIR). Our findings reveal that this simple approach consistently exceeds the performance of the current leading formula retrieval model, TangentCFT. To support ongoing research and development in this field, we have made our source code accessible to the public at //github.com/WangPeiSyuan/GCL-Formula-Retrieval/.
This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of working on a weighted space by establishing operator-norm bounds for finite element and graph-based discretizations of Mat\'ern-type priors and deconvolution forward models. For linear-Gaussian inverse problems, we develop a general theory to characterize the error in the approximation to the posterior. We also embed the computational framework into ensemble Kalman methods and MAP estimators for nonlinear inverse problems. Our operator-norm bounds for prior discretizations guarantee the scalability and accuracy of these algorithms under mesh refinement.
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
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