Related papers: MLPs and KANs for data-driven learning in physical…
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)…
We introduce the Kolmogorov-Arnold Network for Dynamics (KANDy) as a zero-depth, wide neural architecture capable of discovering governing equations in chaotic and complex dynamical systems. Building on the foundation of Kolmogorov-Arnold…
Continual learning (CL), the ability of a model to learn new tasks without forgetting previously acquired knowledge, remains a critical challenge in artificial intelligence, particularly for vision transformers (ViTs) utilizing Multilayer…
Recent developments have introduced Kolmogorov-Arnold Networks (KAN), an innovative architectural paradigm capable of replicating conventional deep neural network (DNN) capabilities while utilizing significantly reduced parameter counts…
Multi-scale PDE problems present significant challenges in scientific computing. While conventional MLP-based deep learning methods exhibit spectral bias in resolving multi-scale features, the physics-informed Kolmogorov-Arnold network…
Kolmogorov-Arnold Networks (KANs) have recently emerged as a compelling alternative to multilayer perceptrons, offering enhanced interpretability via functional decomposition. However, existing KAN architectures, including spline-,…
Recently, a novel model named Kolmogorov-Arnold Networks (KAN) has been proposed with the potential to achieve the functionality of traditional deep neural networks (DNNs) using orders of magnitude fewer parameters by parameterized B-spline…
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…
While most modern machine learning methods offer speed and accuracy, few promise interpretability or explainability -- two key features necessary for highly sensitive industries, like medicine, finance, and engineering. Using eight datasets…
Recent advancements in deep learning for image classification predominantly rely on convolutional neural networks (CNNs) or Transformer-based architectures. However, these models face notable challenges in medical imaging, particularly in…
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,…
Symbolic discovery of governing equations is a long-standing goal in scientific machine learning, yet a fundamental trade-off persists between interpretability and scalable learning. Classical symbolic regression methods yield explicit…
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…
Interpreting complex datasets remains a major challenge for scientists, particularly due to high dimensionality and collinearity among variables. We introduce a novel application of Kolmogorov-Arnold Networks (KANs) to enhance…
Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network's training process as soft constraints, becoming an important…
Massive number of applications involve data with underlying relationships embedded in non-Euclidean space. Graph neural networks (GNNs) are utilized to extract features by capturing the dependencies within graphs. Despite groundbreaking…
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…
Reinforcement learning (RL) has been increasingly applied to network control problems, such as load balancing. However, existing RL approaches often suffer from lack of interpretability and difficulty in extracting controller equations. In…
The highly nonlinear degradation process, complex physical interactions, and various sources of uncertainty render single-image Super-resolution (SR) a particularly challenging task. Existing interpretable SR approaches, whether based on…
Multivariate time series forecasting is a crucial task that predicts the future states based on historical inputs. Related techniques have been developing in parallel with the machine learning community, from early statistical learning…