Related papers: A preliminary study on continual learning in compu…

This paper explores alternative formulations of the Kolmogorov Superposition Theorem (KST) as a foundation for neural network design. The original KST formulation, while mathematically elegant, presents practical challenges due to its…

The memory wall problem arises due to the disparity between fast processors and slower memory, causing significant delays in data access, even more so on edge devices. Data prefetching is a key strategy to address this, with traditional…

Image-to-Image translation in Generative Artificial Intelligence (Generative AI) has been a central focus of research, with applications spanning healthcare, remote sensing, physics, chemistry, photography, and more. Among the numerous…

Physics-Informed Neural Networks (PINNs) have become a popular and powerful framework for solving partial differential equations (PDEs), leveraging neural networks to approximate solutions while embedding PDE constraints, boundary…

As key models in geometric deep learning, graph neural networks have demonstrated enormous power in molecular data analysis. Recently, a specially-designed learning scheme, known as Kolmogorov-Arnold Network (KAN), shows unique potential…

We propose a Kolmogorov-Arnold Representation-based Hamiltonian Neural Network (KAR-HNN) that replaces the Multilayer Perceptrons (MLPs) with univariate transformations. While Hamiltonian Neural Networks (HNNs) ensure energy conservation by…

Deeply stacked KANs are practically impossible due to high training difficulties and substantial memory requirements. Consequently, existing studies can only incorporate few KAN layers, hindering the comprehensive exploration of KANs. This…

Efforts to improve Kolmogorov--Arnold networks (KANs) with architectural enhancements have been stymied by the complexity those enhancements bring, undermining the interpretability that makes KANs attractive in the first place. Here we…

Kolmogorov-Arnold Networks (KANs) have gained attention for their potential to outperform Multi-Layer Perceptrons (MLPs) in terms of parameter efficiency and interpretability. Unlike traditional MLPs, KANs use learnable non-linear…

The domain of laser fusion presents a unique and challenging predictive modeling application landscape for machine learning methods due to high problem complexity and limited training data. Data-driven approaches utilizing prescribed…

We firstly simulated disease dynamics by KAN (Kolmogorov-Arnold Networks) nearly 4 years ago, but the kernel functions in the edge include the exponential number of infected and discharged people and is also in line with the…

Catastrophic forgetting remains the central obstacle in continual learning (CL): parameters shared across tasks interfere with one another, and existing regularization methods such as EWC and SI apply uniform penalties without awareness of…

The Kolmogorov-Arnold Network (KAN) is a novel multi-layer network model recognized for its efficiency in neuromorphic computing, where synapses between neurons are trained linearly. Computations in KAN are performed by generating a…

Kolmogorov Arnold Networks (KANs) are neural architectures inspired by the Kolmogorov Arnold representation theorem that leverage B Spline parameterizations for flexible, locally adaptive function approximation. Although KANs can capture…

Discovering causal relationships in time series data is central in many scientific areas, ranging from economics to climate science. Granger causality is a powerful tool for causality detection. However, its original formulation is limited…

Deep learning-based medical image segmentation has shown remarkable success; however, it typically requires extensive pixel-level annotations, which are both expensive and time-intensive. Semi-supervised medical image segmentation (SSMIS)…

In the fields of computational mathematics and artificial intelligence, the need for precise data modeling is crucial, especially for predictive machine learning tasks. This paper explores further XNet, a novel algorithm that employs the…

Time series forecasting has long been a focus of research across diverse fields, including economics, energy, healthcare, and traffic management. Recent works have introduced innovative architectures for time series models, such as the…

Traditional constitutive models rely on hand-crafted parametric forms with limited expressivity and generalizability, while neural network-based models can capture complex material behavior but often lack interpretability. To balance these…

Complex dynamical systems governed by holomorphic maps such as $z^2 + c$ exhibit fractal boundaries with extreme sensitivity to initial conditions. Accurately modelling these structures from data requires methods that respect the underlying…