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Quantum computing has emerged as a powerful tool for solving complex problems intractable for classical computers, particularly in popular fields such as cryptography, optimization, and neurocomputing. In this paper, we present a new quantum-based approach named the Hierarchical Quantum Control Gates (HQCG) method for efficient understanding of Functional Magnetic Resonance Imaging (fMRI) data. This approach includes two novel modules: the Local Quantum Control Gate (LQCG) and the Global Quantum Control Gate (GQCG), which are designed to extract local and global features of fMRI signals, respectively. Our method operates end-to-end on a quantum machine, leveraging quantum mechanics to learn patterns within extremely high-dimensional fMRI signals, such as 30,000 samples which is a challenge for classical computers. Empirical results demonstrate that our approach significantly outperforms classical methods. Additionally, we found that the proposed quantum model is more stable and less prone to overfitting than the classical methods.

In the first part of this paper, we develop a general framework that permits a comparison between explicit class field theories for a family of rational function fields $\mathbb{F}_s(t)$ over arbitrary constant fields $\mathbb{F}_s$ and explicit class field theory for the rational function field $\mathfrak{K}(t)$ over the nonprincipal ultraproduct $\mathfrak{K}$ of the constant fields $\mathbb{F}_s$. Under an additional assumption that the constant fields $\mathbb{F}_s$ are perfect procyclic fields, we prove a correspondence between ramifications of primes $P$ in $\mathfrak{K}(t)$ and ramifications of primes $P_s$ in $\mathbb{F}_s(t)$, where the $P_s$ are primes in $\mathbb{F}_s(t)$ whose nonprincipal ultraproduct coincides with $P$. In the second part of the paper, we are mainly concerned with rational function fields over a large class of fields, called $n$-th level ultra-finite fields that are a generalization of finite fields. At the $0$-th level, ultra-finite fields are simply finite fields, and for an arbitrary positive integer $n$, an $n$-th level ultra-finite field is inductively defined as a nonprincipal ultraproduct of $(n - 1)$-th level ultra-finite fields. We develop an analogue of cyclotomic function fields for rational function fields over $n$-th level ultra-finite fields that generalize the works of Carlitz and Hayes for rational function fields over finite fields such that these cyclotomic function fields are in complete analogy with the classical cyclotomic fields $\mathbb{Q}(\zeta)$ of the rationals $\mathbb{Q}$. The main result in the second part of the paper is an analogue of the Kronecker--Weber theorem for rational function fields over $n$-th level ultra-finite fields that explicitly describes, from a model-theoretic viewpoint, the maximal abelian extension of the rational function field over a given $n$-th level ultra-finite field for all $n \ge 1$.

This paper examines the pricing issue of margin-call stock loans with finite maturities under the Black-Scholes-Merton framework. In particular, using a Fourier Sine transform method, we reduce the partial differential equation governing the price of a margin-call stock loan into an ordinary differential equation, the solution of which can be easily found (in the Fourier Sine space) and analytically inverted into the original space. As a result, we obtain an integral representation of the value of the stock loan in terms of the unknown optimal exit prices, which are, in turn, governed by a Volterra integral equation. We thus can break the pricing problem of margin-call stock loans into two steps: 1) finding the optimal exit prices by solving numerically the governing Volterra integral equation and 2) calculating the values of margin-call stock loans based on the obtained optimal exit prices. By validating and comparing with other available numerical methods, we show that our proposed numerical scheme offers a reliable and efficient way to calculate the service fee of a margin-call stock loan contract, track the contract value over time, and compute the level of stock price above which it is optimal to exit the contract. The effects of the margin-call feature on the loan contract are also examined and quantified.

Parameterized Quantum Circuits (PQCs) have been acknowledged as a leading strategy to utilize near-term quantum advantages in multiple problems, including machine learning and combinatorial optimization. When applied to specific tasks, the parameters in the quantum circuits are trained to minimize the target function. Although there have been comprehensive studies to improve the performance of the PQCs on practical tasks, the errors caused by the quantum noise downgrade the performance when running on real quantum computers. In particular, when the quantum state is transformed through multiple quantum circuit layers, the effect of the quantum noise happens cumulatively and becomes closer to the maximally mixed state or complete noise. This paper studies the relationship between the quantum noise and the diffusion model. Then, we propose a novel diffusion-inspired learning approach to mitigate the quantum noise in the PQCs and reduce the error for specific tasks. Through our experiments, we illustrate the efficiency of the learning strategy and achieve state-of-the-art performance on classification tasks in the quantum noise scenarios.

Although quantum machine learning has been introduced for a while, its applications in computer vision are still limited. This paper, therefore, revisits the quantum visual encoding strategies, the initial step in quantum machine learning. Investigating the root cause, we uncover that the existing quantum encoding design fails to ensure information preservation of the visual features after the encoding process, thus complicating the learning process of the quantum machine learning models. In particular, the problem, termed "Quantum Information Gap" (QIG), leads to a gap of information between classical and corresponding quantum features. We provide theoretical proof and practical demonstrations of that found and underscore the significance of QIG, as it directly impacts the performance of quantum machine learning algorithms. To tackle this challenge, we introduce a simple but efficient new loss function named Quantum Information Preserving (QIP) to minimize this gap, resulting in enhanced performance of quantum machine learning algorithms. Extensive experiments validate the effectiveness of our approach, showcasing superior performance compared to current methodologies and consistently achieving state-of-the-art results in quantum modeling., Comment: Accepted to Quantum Machine Intelligence

Unsupervised vision clustering, a cornerstone in computer vision, has been studied for decades, yielding significant outcomes across numerous vision tasks. However, these algorithms involve substantial computational demands when confronted with vast amounts of unlabeled data. Conversely, quantum computing holds promise in expediting unsupervised algorithms when handling large-scale databases. In this study, we introduce QClusformer, a pioneering Transformer-based framework leveraging quantum machines to tackle unsupervised vision clustering challenges. Specifically, we design the Transformer architecture, including the self-attention module and transformer blocks, from a quantum perspective to enable execution on quantum hardware. In addition, we present QClusformer, a variant based on the Transformer architecture, tailored for unsupervised vision clustering tasks. By integrating these elements into an end-to-end framework, QClusformer consistently outperforms previous methods running on classical computers. Empirical evaluations across diverse benchmarks, including MS-Celeb-1M and DeepFashion, underscore the superior performance of QClusformer compared to state-of-the-art methods.

In recent years, Large Language Models (LLMs) have become integrated into our daily lives, serving as invaluable assistants in completing tasks. Widely embraced by users, the abuse of LLMs is inevitable, particularly in using them to generate text content for various purposes, leading to difficulties in distinguishing between text generated by LLMs and that written by humans. In this study, we present a dataset named ViDetect, comprising 6.800 samples of Vietnamese essay, with 3.400 samples authored by humans and the remainder generated by LLMs, serving the purpose of detecting text generated by AI. We conducted evaluations using state-of-the-art methods, including ViT5, BartPho, PhoBERT, mDeberta V3, and mBERT. These results contribute not only to the growing body of research on detecting text generated by AI but also demonstrate the adaptability and effectiveness of different methods in the Vietnamese language context. This research lays the foundation for future advancements in AI-generated text detection and provides valuable insights for researchers in the field of natural language processing.

Action recognition has become one of the popular research topics in computer vision. There are various methods based on Convolutional Networks and self-attention mechanisms as Transformers to solve both spatial and temporal dimensions problems of action recognition tasks that achieve competitive performances. However, these methods lack a guarantee of the correctness of the action subject that the models give attention to, i.e., how to ensure an action recognition model focuses on the proper action subject to make a reasonable action prediction. In this paper, we propose a multi-view attention consistency method that computes the similarity between two attentions from two different views of the action videos using Directed Gromov-Wasserstein Discrepancy. Furthermore, our approach applies the idea of Neural Radiance Field to implicitly render the features from novel views when training on single-view datasets. Therefore, the contributions in this work are three-fold. Firstly, we introduce the multi-view attention consistency to solve the problem of reasonable prediction in action recognition. Secondly, we define a new metric for multi-view consistent attention using Directed Gromov-Wasserstein Discrepancy. Thirdly, we built an action recognition model based on Video Transformers and Neural Radiance Fields. Compared to the recent action recognition methods, the proposed approach achieves state-of-the-art results on three large-scale datasets, i.e., Jester, Something-Something V2, and Kinetics-400.

In precision agriculture, the detection and recognition of insects play an essential role in the ability of crops to grow healthy and produce a high-quality yield. The current machine vision model requires a large volume of data to achieve high performance. However, there are approximately 5.5 million different insect species in the world. None of the existing insect datasets can cover even a fraction of them due to varying geographic locations and acquisition costs. In this paper, we introduce a novel "Insect-1M" dataset, a game-changing resource poised to revolutionize insect-related foundation model training. Covering a vast spectrum of insect species, our dataset, including 1 million images with dense identification labels of taxonomy hierarchy and insect descriptions, offers a panoramic view of entomology, enabling foundation models to comprehend visual and semantic information about insects like never before. Then, to efficiently establish an Insect Foundation Model, we develop a micro-feature self-supervised learning method with a Patch-wise Relevant Attention mechanism capable of discerning the subtle differences among insect images. In addition, we introduce Description Consistency loss to improve micro-feature modeling via insect descriptions. Through our experiments, we illustrate the effectiveness of our proposed approach in insect modeling and achieve State-of-the-Art performance on standard benchmarks of insect-related tasks. Our Insect Foundation Model and Dataset promise to empower the next generation of insect-related vision models, bringing them closer to the ultimate goal of precision agriculture.

In this paper, we prove the existence of a first-order definition of the polynomial ring over a nonprincipal ultraproduct of finite fields of unbounded cardinalities in its fraction field by a universal-existential formula in the language of rings augmented by an additional constant symbol $t$. As a consequence, we prove that the full first-order theory of the rational function field over a nonprincipal ultraproduct of finite fields of characteristic $0$ is undecidable., Comment: Added references and a new result regarding undecidability

In this paper, we establish an explicit higher reciprocity law for the polynomial ring over a nonprincipal ultraproduct of finite fields. Such an ultraproduct can be taken over the same finite field, which allows to recover the classical higher reciprocity law for the polynomial ring $\mathbb{F}_q[t]$ over a finite field $\mathbb{F}_q$ that is due to Dedekind, K\"uhne, Artin, and Schmidt. On the other hand, when the ultraproduct is taken over finite fields of unbounded cardinalities, we obtain an explicit higher reciprocity law for the polynomial ring over an infinite field in both characteristics $0$ and $p >0$ for some prime $p$. We then use the higher reciprocity law to prove an analogue of the Grunwald--Wang theorem for such a polynomial ring in both characteristics $0$ and $p > 0$ for some prime $p$., Comment: We revised the first version of the paper to include any nonprincipal ultraproduct of finite fields of both characteristics $0$ and $p >0$. The ultraproduct can be taken over the same finite field $\mathbb{F}_q$, in which case the ultraproduct becomes the finite field $\mathbb{F}_q$, which allows to recover the classical reciprocity law for $\mathbb{F}_q[t]$

Continual semantic segmentation aims to learn new classes while maintaining the information from the previous classes. Although prior studies have shown impressive progress in recent years, the fairness concern in the continual semantic segmentation needs to be better addressed. Meanwhile, fairness is one of the most vital factors in deploying the deep learning model, especially in human-related or safety applications. In this paper, we present a novel Fairness Continual Learning approach to the semantic segmentation problem. In particular, under the fairness objective, a new fairness continual learning framework is proposed based on class distributions. Then, a novel Prototypical Contrastive Clustering loss is proposed to address the significant challenges in continual learning, i.e., catastrophic forgetting and background shift. Our proposed loss has also been proven as a novel, generalized learning paradigm of knowledge distillation commonly used in continual learning. Moreover, the proposed Conditional Structural Consistency loss further regularized the structural constraint of the predicted segmentation. Our proposed approach has achieved State-of-the-Art performance on three standard scene understanding benchmarks, i.e., ADE20K, Cityscapes, and Pascal VOC, and promoted the fairness of the segmentation model., Comment: Accepted to NeurIPS 2023

In their recent work, Gentili and Struppa proposed a different quaternionic analogue of the notion of holomorphic functions in the complex plane, called \textit{slice regular functions}, which has led to several analogues of classical theorems in complex function theory in the quaternionic setting. The quaternionic analogue of meromorphic functions is called \textit{semiregular functions}. Such a function is said to be \textit{slice preserving} if it maps each domain in a complex line to a domain in the same complex line. In this work, we deal with the relation between analytic and algebraic properties of certain fields of semiregular functions in symmetric slice domains of the real quaternions. More precisely, we prove quaternionic analogues of Bers's theorem and Iss'sa's theorem that deal with the algebraic structures of the ring of slice preserving regular functions and of certain fields of slice preserving semiregular functions on symmetric slice domains in the real quaternions.