The anticipated launch of the High Luminosity Large Hadron Collider (HL-LHC) [1] by CERN at the end of this decade is expected to generate an unprecedented volume of data, necessitating advanced computational frameworks and strategies to handle, process, and analyze this immense dataset efficiently. Classical computing resources, while effective, face significant limitations in scaling to the data and computational demands projected by such high-dimensional tasks. Addressing this challenge, quantum machine learning (QML) [2, 3] has emerged as a promising solution. Quantum vision transformers (QViTs) [4, 5, 6, 7] have recently been proposed as hybrid architectures that integrate quantum circuits within classical vision transformer (ViT) [8] frameworks to reduce time complexity and improve performance in machine learning tasks involving high-dimensional data. Traditional ViTs employ self-attention mechanisms [9] and multi-layer perceptrons (MLPs) [10] to learn from image data, which has shown promising results in computer vision tasks across various domains.

DNA microarray gene-expression data has been widely used to identify cancerous gene signatures. Microarray can increase the accuracy of cancer diagnosis and prognosis. However, analyzing the large amount of gene expression data from microarray chips pose a challenge for current machine learning researches. One of the challenges lie within classification of healthy and cancerous tissues is high dimensionality of gene expressions. High dimensionality decreases the accuracy of the classification. This research aims to apply a hybrid model of Genetic Algorithm and Neural Network to overcome the problem during subset selection of informative genes. Whereby, a Genetic Algorithm (GA) reduced dimensionality during feature selection and then a Multi-Layer perceptron Neural Network (MLP) is applied to classify selected genes. The performance evaluated by considering to the accuracy and the number of selected genes. Experimental results show the proposed method suggested high accuracy and minimum number of selected genes in comparison with other machine learning algorithms.

In recent years, imitation learning using neural networks has enabled robots to perform flexible tasks. However, since neural networks operate in a feedforward structure, they do not possess a mechanism to compensate for output errors. To address this limitation, we developed a feedback mechanism to correct these errors. By employing a hierarchical structure for neural networks comprising lower and upper layers, the lower layer was controlled to follow the upper layer. Additionally, using a multi-layer perceptron in the lower layer, which lacks an internal state, enhanced the error feedback. In the character-writing task, this model demonstrated improved accuracy in writing previously untrained characters. In the character-writing task, this model demonstrated improved accuracy in writing previously untrained characters. Through autonomous control with error feedback, we confirmed that the lower layer could effectively track the output of the upper layer. This study represents a promising step toward integrating neural networks with control theories.

Virtual Reality (VR) has been a beneficial training tool in fields such as advanced manufacturing. However, users may experience a high cognitive load due to various factors, such as the use of VR hardware or tasks within the VR environment. Studies have shown that eye-tracking has the potential to detect cognitive load, but in the context of VR and complex spatiotemporal tasks (e.g., assembly and disassembly), it remains relatively unexplored. Here, we present an ongoing study to detect users' cognitive load using an eye-tracking-based machine learning approach. We developed a VR training system for cold spray and tested it with 22 participants, obtaining 19 valid eye-tracking datasets and NASA-TLX scores. We applied Multi-Layer Perceptron (MLP) and Random Forest (RF) models to compare the accuracy of predicting cognitive load (i.e., NASA-TLX) using pupil dilation and fixation duration. Our preliminary analysis demonstrates the feasibility of using eye tracking to detect cognitive load in complex spatiotemporal VR experiences and motivates further exploration.

The problem of learning halfspaces is one of the classical and most well-studied problems in machine learning--going back to the Perceptron algorithm [Ros58]--and has had great impact on many other influential techniques, including SVMs [Vap98] and AdaBoost [FS97]. Here we focus on learning halfspaces from random labeled examples. The computational complexity of this task crucially depends on the choice of the underlying model. For example, in the realizable PAC model (i.e., with clean labels), the problem is known to be efficiently solvable (see, e.g., [MT94]) via a reduction to linear programming. Unfortunately, this method is quite fragile and breaks down in the presence of noisy labels. In the noisy setting, the computational complexity of the problem depends on the choice of noise model and distributional assumptions. In this work, we study the problem of distribution-specific PAC learning of halfspaces, with respect to Gaussian marginals, in the reliable agnostic model of [KKM12]. Formally, we have the following definition.

Kolmogorov-Arnold Networks (KANs) have seen great success in scientific domains thanks to spline activation functions, becoming an alternative to Multi-Layer Perceptrons (MLPs). However, spline functions may not respect symmetry in tasks, which is crucial prior knowledge in machine learning. Previously, equivariant networks embed symmetry into their architectures, achieving better performance in specific applications. Among these, Equivariant Multi-Layer Perceptrons (EMLP) introduce arbitrary matrix group equivariance into MLPs, providing a general framework for constructing equivariant networks layer by layer. In this paper, we propose Equivariant Kolmogorov-Arnold Networks (EKAN), a method for incorporating matrix group equivariance into KANs, aiming to broaden their applicability to more fields. First, we construct gated spline basis functions, which form the EKAN layer together with equivariant linear weights. We then define a lift layer to align the input space of EKAN with the feature space of the dataset, thereby building the entire EKAN architecture. Compared with baseline models, EKAN achieves higher accuracy with smaller datasets or fewer parameters on symmetry-related tasks, such as particle scattering and the three-body problem, often reducing test MSE by several orders of magnitude. Even in non-symbolic formula scenarios, such as top quark tagging with three jet constituents, EKAN achieves comparable results with EMLP using only $26\%$ of the parameters, while KANs do not outperform MLPs as expected.

The curse of dimensionality poses a significant challenge to modern multilayer perceptron-based architectures, often causing performance stagnation and scalability issues. Addressing this limitation typically requires vast amounts of data. In contrast, Kolmogorov-Arnold Networks have gained attention in the machine learning community for their bold claim of being unaffected by the curse of dimensionality. This paper explores the Kolmogorov-Arnold representation theorem and the mathematical principles underlying Kolmogorov-Arnold Networks, which enable their scalability and high performance in high-dimensional spaces. We begin with an introduction to foundational concepts necessary to understand Kolmogorov-Arnold Networks, including interpolation methods and Basis-splines, which form their mathematical backbone. This is followed by an overview of perceptron architectures and the Universal approximation theorem, a key principle guiding modern machine learning. This is followed by an overview of the Kolmogorov-Arnold representation theorem, including its mathematical formulation and implications for overcoming dimensionality challenges. Next, we review the architecture and error-scaling properties of Kolmogorov-Arnold Networks, demonstrating how these networks achieve true freedom from the curse of dimensionality. Finally, we discuss the practical viability of Kolmogorov-Arnold Networks, highlighting scenarios where their unique capabilities position them to excel in real-world applications. This review aims to offer insights into Kolmogorov-Arnold Networks' potential to redefine scalability and performance in high-dimensional learning tasks.

Radiologists have preferred visual impressions or 'styles' of X-ray images that are manually adjusted to their needs to support their diagnostic performance. In this work, we propose an automatic and interpretable X-ray style transfer by introducing a trainable version of the Local Laplacian Filter (LLF). From the shape of the LLF's optimized remap function, the characteristics of the style transfer can be inferred and reliability of the algorithm can be ensured. Moreover, we enable the LLF to capture complex X-ray style features by replacing the remap function with a Multi-Layer Perceptron (MLP) and adding a trainable normalization layer. We demonstrate the effectiveness of the proposed method by transforming unprocessed mammographic X-ray images into images that match the style of target mammograms and achieve a Structural Similarity Index (SSIM) of 0.94 compared to 0.82 of the baseline LLF style transfer method from Aubry et al.

Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use multilayer perceptrons (MLPs) as their underlying architecture, recent advancements have explored alternative neural network structures. One such innovation is the Kolmogorov-Arnold Network (KAN), which has demonstrated benefits over traditional MLPs, including faster neural scaling and better interpretability. The application of KANs to physics-informed learning has led to the development of Physics-Informed KANs (PIKANs), enabling the use of KANs to solve PDEs. However, despite their advantages, KANs often suffer from slower training speeds, particularly in higher-dimensional problems where the number of collocation points grows exponentially with the dimensionality of the system. To address this challenge, we introduce Separable Physics-Informed Kolmogorov-Arnold Networks (SPIKANs). This novel architecture applies the principle of separation of variables to PIKANs, decomposing the problem such that each dimension is handled by an individual KAN. This approach drastically reduces the computational complexity of training without sacrificing accuracy, facilitating their application to higher-dimensional PDEs. Through a series of benchmark problems, we demonstrate the effectiveness of SPIKANs, showcasing their superior scalability and performance compared to PIKANs and highlighting their potential for solving complex, high-dimensional PDEs in scientific computing.

Despite the remarkable success achieved by neural networks, particularly those represented by MLP and Transformer, we reveal that they exhibit potential flaws in the modeling and reasoning of periodicity, i.e., they tend to memorize the periodic data rather than genuinely understanding the underlying principles of periodicity. However, periodicity is a crucial trait in various forms of reasoning and generalization, underpinning predictability across natural and engineered systems through recurring patterns in observations. In this paper, we propose FAN, a novel network architecture based on Fourier Analysis, which empowers the ability to efficiently model and reason about periodic phenomena. By introducing Fourier Series, the periodicity is naturally integrated into the structure and computational processes of the neural network, thus achieving a more accurate expression and prediction of periodic patterns. As a promising substitute to multi-layer perceptron (MLP), FAN can seamlessly replace MLP in various models with fewer parameters and FLOPs. Through extensive experiments, we demonstrate the effectiveness of FAN in modeling and reasoning about periodic functions, and the superiority and generalizability of FAN across a range of real-world tasks, including symbolic formula representation, time series forecasting, and language modeling.