Kolmogorov-Arnold Networks

Also known as KAN

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Latest papers 118

13 papers in the last four weeks, up 8% on the four weeks before. 0.1% of all new papers.

Apr 11, 2026

Gait Recognition with Temporal Kolmogorov-Arnold Networks

Gait recognition is a biometric modality that identifies individuals from their characteristic walking patterns. Unlike conventional biometric traits, gait can be acquired at a distance and without active subject cooperation, making it suitable for surveillance and public safety applications. Nevertheless, silhouette-based temporal models remain sensitive to long sequences, observation noise, and appearance-related covariates. Recurrent architectures often struggle to preserve information from earlier frames and are inherently sequential to optimize, whereas transformer-based models typically require greater computational resources and larger training sets and may be sensitive to irregular sequence lengths and noisy inputs. These limitations reduce robustness under clothing variation, carrying conditions, and view changes, while also hindering the joint modeling of local gait cycles and longer-term motion trends. To address these challenges, we introduce a Temporal Kolmogorov-Arnold Network (TKAN) for gait recognition. The proposed model replaces fixed edge weights with learnable one-dimensional functions and incorporates a two-level memory mechanism consisting of short-term RKAN sublayers and a gated long-term pathway. This design enables efficient modeling of both cycle-level dynamics and broader temporal context while maintaining a compact backbone. Experiments on the CASIA-B dataset indicate that the proposed CNN+TKAN framework achieves strong recognition performance under the reported evaluation setting.

Mohammed Asad, Dinesh Kumar Vishwakarma

Multi-Modal Data Analytics Lab, Department of Information Technology, Delhi Technological University, Delhi, 110042, India

Gait Recognition Kolmogorov-Arnold Networks

Apr 9, 2026

Small-scale photonic Kolmogorov-Arnold networks using standard telecom nonlinear modules

Photonic neural networks promise ultrafast inference, yet most architectures rely on linear optical meshes with electronic nonlinearities, reintroducing optical-electrical-optical bottlenecks. Here we introduce small-scale photonic Kolmogorov-Arnold networks (SSP-KANs) implemented entirely with standard telecommunications components. Each network edge employs a trainable nonlinear module composed of a Mach-Zehnder interferometer, semiconductor optical amplifier, and variable optical attenuators, providing a four-parameter transfer function derived from gain saturation and interferometric mixing. Despite the constrained functional form of these optical nonlinearities, SSP-KANs comprising only a few optical modules achieve strong nonlinear inference performance across classification, regression, and image recognition tasks, approaching software baselines with significantly fewer parameters. A four-module network achieves

94.3

% (IQR:

90.3

--

97.4

%, 10~seeds) accuracy on nonlinear classification benchmarks; a seven-module network attains

R^2 = 0.986 \pm 0.015

on six-input regression. Performance remains robust under realistic hardware impairments, maintaining high accuracy down to 6-bit input resolution and 14 dB signal-to-noise ratio. By using a fully differentiable physics model for end-to-end optimisation of optical parameters, this work establishes a practical pathway from simulation to experimental demonstration of photonic KANs using commodity telecom hardware.

Luca Nogueira Calçado, Sergei K. Turitsyn, Egor Manuylovich

Aston Institute of Photonic Technologies (AiPT), Aston University, Birmingham, B4 7ET, United Kingdom.

Photonic Computing Kolmogorov-Arnold Networks

Apr 6, 2026

Non-monotonic causal discovery with Kolmogorov-Arnold Fuzzy Cognitive Maps

Fuzzy Cognitive Maps constitute a neuro-symbolic paradigm for modeling complex dynamic systems, widely adopted for their inherent interpretability and recurrent inference capabilities. However, the standard FCM formulation, characterized by scalar synaptic weights and monotonic activation functions, is fundamentally constrained in modeling non-monotonic causal dependencies, thereby limiting its efficacy in systems governed by saturation effects or periodic dynamics. To overcome this topological restriction, this research proposes the Kolmogorov-Arnold Fuzzy Cognitive Map (KA-FCM), a novel architecture that redefines the causal transmission mechanism. Drawing upon the Kolmogorov-Arnold representation theorem, static scalar weights are replaced with learnable, univariate B-spline functions located on the model edges. This fundamental modification shifts the non-linearity from the nodes' aggregation phase directly to the causal influence phase. This modification allows for the modeling of arbitrary, non-monotonic causal relationships without increasing the graph density or introducing hidden layers. The proposed architecture is validated against both baselines (standard FCM trained with Particle Swarm Optimization) and universal black-box approximators (Multi-Layer Perceptron) across three distinct domains: non-monotonic inference (Yerkes-Dodson law), symbolic regression, and chaotic time-series forecasting. Experimental results demonstrate that KA-FCMs significantly outperform conventional architectures and achieve competitive accuracy relative to MLPs, while preserving graph- based interpretability and enabling the explicit extraction of mathematical laws from the learned edges.

Jose L. Salmeron

School of Engineering, CUNEF Universidad, Madrid, Spain

Fuzzy Logic Nonmonotonic Reasoning Causal Discovery Kolmogorov-Arnold Networks

Apr 6, 2026

Interpretation of Crystal Energy Landscapes with Kolmogorov-Arnold Networks

Characterizing crystalline energy landscapes is essential to predicting thermodynamic stability, electronic structure, and functional behavior. While machine learning (ML) enables rapid property predictions, the "black-box" nature of most models limits their utility for generating new scientific insights. Here, we introduce Kolmogorov-Arnold Networks (KANs) as an interpretable framework to bridge this gap. Unlike conventional neural networks with fixed activation functions, KANs employ learnable functions that reveal underlying physical relationships. We developed the Element-Weighted KAN, a composition-only model that achieves state-of-the-art accuracy in predicting formation energy, band gap, and work function across large-scale datasets. Crucially, without any explicit physical constraints, KANs uncover interpretable chemical trends aligned with the periodic table and quantum mechanical principles through embedding analysis, correlation studies, and principal component analysis. These results demonstrate that KANs provide a powerful framework with high predictive performance and scientific interpretability, establishing a new paradigm for transparent, chemistry-based materials informatics.

Gen Zu, Ning Mao, Claudia Felser +1

Max Planck Institute for Chemical Physics of Solids, 01187, Dresden, Germany · Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA · Min H. Kao Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, Tennessee 37996, USA

Materials Property Prediction Interpretable ML Kolmogorov-Arnold Networks Computational Materials Science

Apr 3, 2026

Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networks

Kolmogorov-Arnold Networks (KANs) have recently emerged as a powerful architecture for various machine learning applications. However, their unique structure raises significant concerns regarding their computational overhead. Existing studies primarily evaluate KAN complexity in terms of Floating-Point Operations (FLOPs) required for GPU-based training and inference. However, in many latency-sensitive and power-constrained deployment scenarios, such as neural network-driven non-linearity mitigation in optical communications or channel state estimation in wireless communications, training is performed offline and dedicated hardware accelerators are preferred over GPUs for inference. Recent hardware implementation studies report KAN complexity using platform-specific resource consumption metrics, such as Look-Up Tables, Flip-Flops, and Block RAMs. However, these metrics require a full hardware design and synthesis stage that limits their utility for early-stage architectural decisions and cross-platform comparisons. To address this, we derive generalized, platform-independent formulae for evaluating the hardware inference complexity of KANs in terms of Real Multiplications (RM), Bit Operations (BOP), and Number of Additions and Bit-Shifts (NABS). We extend our analysis across multiple KAN variants, including B-spline, Gaussian Radial Basis Function (GRBF), Chebyshev, and Fourier KANs. The proposed metrics can be computed directly from the network structure and enable a fair and straightforward inference complexity comparison between KAN and other neural network architectures.

Bilal Khalid, Pedro Freire, Sergei K. Turitsyn +1

Aston Institute of Photonic Technologies, Aston University, Birmingham, B4 7ET, UK

Efficient Neural Network Inference Kolmogorov-Arnold Networks

Apr 2, 2026

Light-ResKAN: A Parameter-Sharing Lightweight KAN with Gram Polynomials for Efficient SAR Image Recognition

Synthetic Aperture Radar (SAR) image recognition is vital for disaster monitoring, military reconnaissance, and ocean observation. However, large SAR image sizes hinder deep learning deployment on resource-constrained edge devices, and existing lightweight models struggle to balance high-precision feature extraction with low computational requirements. The emerging Kolmogorov-Arnold Network (KAN) enhances fitting by replacing fixed activations with learnable ones, reducing parameters and computation. Inspired by KAN, we propose Light-ResKAN to achieve a better balance between precision and efficiency. First, Light-ResKAN modifies ResNet by replacing convolutions with KAN convolutions, enabling adaptive feature extraction for SAR images. Second, we use Gram Polynomials as activations, which are well-suited for SAR data to capture complex non-linear relationships. Third, we employ a parameter-sharing strategy: each kernel shares parameters per channel, preserving unique features while reducing parameters and FLOPs. Our model achieves 99.09%, 93.01%, and 97.26% accuracy on MSTAR, FUSAR-Ship, and SAR-ACD datasets, respectively. Experiments on MSTAR resized to

1024 \times 1024

show that compared to VGG16, our model reduces FLOPs by

82.90 \times

and parameters by

163.78 \times

. This work establishes an efficient solution for edge SAR image recognition.

Pan Yi, Weijie Li, Xiaodong Chen +3

The authors are with the College of Electronic Science and Technology, National University of Defense Technology, Changsha, 410073, China.

Kolmogorov-Arnold Networks Synthetic Aperture Radar Edge Inference

Mar 30, 2026

FI-KAN: Fractal Interpolation Kolmogorov-Arnold Networks

Kolmogorov-Arnold Networks (KAN) employ B-spline bases on a fixed grid, providing no intrinsic multi-scale decomposition for non-smooth function approximation. We introduce Fractal Interpolation KAN (FI-KAN), which incorporates learnable fractal interpolation function (FIF) bases from iterated function system (IFS) theory into KAN. Two variants are presented: Pure FI-KAN (Barnsley, 1986) replaces B-splines entirely with FIF bases; Hybrid FI-KAN (Navascues, 2005) retains the B-spline path and adds a learnable fractal correction. The IFS contraction parameters give each edge a differentiable fractal dimension that adapts to target regularity during training. On a Holder regularity benchmark (

α\in [0.2, 2.0]

), Hybrid FI-KAN outperforms KAN at every regularity level (1.3x to 33x). On fractal targets, FI-KAN achieves up to 6.3x MSE reduction over KAN, maintaining 4.7x advantage at 5 dB SNR. On non-smooth PDE solutions (scikit-fem), Hybrid FI-KAN achieves up to 79x improvement on rough-coefficient diffusion and 3.5x on L-shaped domain corner singularities. Pure FI-KAN's complementary behavior, dominating on rough targets while underperforming on smooth ones, provides controlled evidence that basis geometry must match target regularity. A fractal dimension regularizer provides interpretable complexity control whose learned values recover the true fractal dimension of each target. These results establish regularity-matched basis design as a principled strategy for neural function approximation.

Gnankan Landry Regis N'guessan

Axiom Research Group · Dept. of Applied Mathematics and Computational Science, NM-AIST, Arusha, Tanzania · AIMS Research and Innovation Centre, Kigali, Rwanda

Kolmogorov-Arnold Networks Neural Network Approximation Theory

Mar 30, 2026

Nonlinear Factor Decomposition via Kolmogorov-Arnold Networks: A Spectral Approach to Asset Return Analysis

KAN-PCA is an autoencoder that uses a KAN as encoder and a linear map as decoder. It generalizes classical PCA by replacing linear projections with learned B-spline functions on each edge. The motivation is to capture more variance than classical PCA, which becomes inefficient during market crises when the linear assumption breaks down and correlations between assets change dramatically. We prove that if the spline activations are forced to be linear, KAN-PCA yields exactly the same results as classical PCA, establishing PCA as a special case. Experiments on 20 S&P 500 stocks (2015-2024) show that KAN-PCA achieves a reconstruction R^2 of 66.57%, compared to 62.99% for classical PCA with the same 3 factors, while matching PCA out-of-sample after correcting for data leakage in the training procedure.

David Breazu

Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania

Dimensionality Reduction Principal Component Analysis Financial Time Series Kolmogorov-Arnold Networks

Mar 25, 2026

Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning

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 analytic expressions but rely on combinatorial search, whereas neural networks scale efficiently with data and dimensionality but produce opaque representations. In this work, we introduce Symbolic Kolmogorov-Arnold Networks (Symbolic-KANs), a neural architecture that bridges this gap by embedding discrete symbolic structure directly within a trainable deep network. Symbolic-KANs represent multivariate functions as compositions of learned univariate primitives applied to learned scalar projections, guided by a library of analytic primitives, hierarchical gating, and symbolic regularization that progressively sharpens continuous mixtures into one-hot selections. After gated training and discretization, each active unit selects a single primitive and projection direction, yielding compact closed-form expressions without post-hoc symbolic fitting. Symbolic-KANs further act as scalable primitive discovery mechanisms, identifying the most relevant analytic components that can subsequently inform candidate libraries for sparse equation-learning methods. We demonstrate that Symbolic-KAN reliably recovers correct primitive terms and governing structures in data-driven regression and inverse dynamical systems. Moreover, the framework extends to forward and inverse physics-informed learning of partial differential equations, producing accurate solutions directly from governing constraints while constructing compact symbolic representations whose selected primitives reflect the true analytical structure of the underlying equations. These results position Symbolic-KAN as a step toward scalable, interpretable, and mechanistically grounded learning of governing laws.

Salah A Faroughi, Farinaz Mostajeran, Amirhossein Arzani +1

Energy & Intelligence Lab, Department of Chemical Engineering, University of Utah, Salt Lake City, Utah, 84112, USA · Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah, 84112, USA · Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah, 84112, USA +2

Interpretable ML Scientific ML Kolmogorov-Arnold Networks Symbolic Regression PDE Discovery Physics-Informed ML

Mar 19, 2026

myMNIST: Benchmark of PETNN, KAN, and Classical Deep Learning Models for Burmese Handwritten Digit Recognition

We present the first systematic benchmark on a standardized iteration of the publicly available Burmese Handwritten Digit Dataset (BHDD), which we have designated as myMNIST Benchmarking. While BHDD serves as a foundational resource for Myanmar NLP/AI, it lacks a comprehensive, reproducible performance baseline across modern architectures. We evaluate eleven architectures spanning classical deep learning models (Multi-Layer Perceptron, Convolutional Neural Network, Long Short-Term Memory, Gated Recurrent Unit, Transformer), recent alternatives (FastKAN, EfficientKAN), an energy-based model (JEM), and physics-inspired PETNN variants (Sigmoid, GELU, SiLU). Using Precision, Recall, F1-Score, and Accuracy as evaluation metrics, our results show that the CNN remains a strong baseline, achieving the best overall scores (F1 = 0.9959, Accuracy = 0.9970). The PETNN (GELU) model closely follows (F1 = 0.9955, Accuracy = 0.9966), outperforming LSTM, GRU, Transformer, and KAN variants. JEM, representing energy-based modeling, performs competitively (F1 = 0.9944, Accuracy = 0.9958). KAN-based models (FastKAN, EfficientKAN) trail the top performers but provide a meaningful alternative baseline (Accuracy ~0.992). These findings (i) establish reproducible baselines for BHDD across diverse modeling paradigms, (ii) highlight PETNN's strong performance relative to classical and Transformer-based models, and (iii) quantify the gap between energy-inspired PETNNs and a true energy-based model (JEM). We release this benchmark to facilitate future research on Myanmar digit recognition and to encourage broader evaluation of emerging architectures on regional scripts.

Ye Kyaw Thu, Thazin Myint Oo, Thepchai Supnithi

National Electronics and Computer Technology Center (NECTEC), Pathumthani, Thailand · Language Understanding Lab., Yangon, Myanmar

Optical Character Recognition Kolmogorov-Arnold Networks

Mar 19, 2026

SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks

Kolmogorov-Arnold networks (KANs) have arisen as a potential way to enhance the interpretability of machine learning. However, solutions learned by KANs are not necessarily interpretable, in the sense of being sparse or parsimonious. Sparse identification of nonlinear dynamics (SINDy) is a complementary approach that allows for learning sparse equations for dynamical systems from data; however, learned equations are limited by the library. In this work, we present SINDy-KANs, which simultaneously train a KAN and a SINDy-like representation to increase interpretability of KAN representations with SINDy applied at the level of each activation function, while maintaining the function compositions possible through deep KANs. We apply our method to a number of symbolic regression tasks, including dynamical systems, to show accurate equation discovery across a range of systems.

Amanda A. Howard, Nicholas Zolman, Bruno Jacob +2

Pacific Northwest National Laboratory, Richland, WA 99354 · University of Washington, Seattle, WA 98195

Nonlinear System Identification Sparse Identification of Nonlinear Dynamics Symbolic Regression Neural Network Interpretability Kolmogorov-Arnold Networks

Mar 18, 2026

KANtize: Exploring Low-bit Quantization of Kolmogorov-Arnold Networks for Efficient Inference

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 activation functions, typically spline functions, expressed as linear combinations of basis splines (B-splines). B-spline coefficients serve as the model's learnable parameters. However, evaluating these spline functions increases computational complexity during inference. Conventional quantization reduces this complexity by lowering the numerical precision of parameters and activations. However, the impact of quantization on KANs, and especially its effectiveness in reducing computational complexity, is largely unexplored, particularly for quantization levels below 8 bits. The study investigates the impact of low-bit quantization on KANs and its impact on computational complexity and hardware efficiency. Results show that B-splines can be quantized to 2-3 bits with negligible loss in accuracy, significantly reducing computational complexity. Hence, we investigate the potential of using low-bit quantized precomputed tables as a replacement for the recursive B-spline algorithm. This approach aims to further reduce the computational complexity of KANs and enhance hardware efficiency while maintaining accuracy. For example, ResKAN18 achieves a 50x reduction in BitOps without loss of accuracy using low-bit-quantized B-spline tables. Additionally, precomputed 8-bit lookup tables improve GPU inference speedup by up to 2.9x, while on FPGA-based systolic-array accelerators, reducing B-spline table precision from 8 to 3 bits cuts resource usage by 36%, increases clock frequency by 50%, and enhances speedup by 1.24x. On a 28nm FD-SOI ASIC, reducing the B-spline bit-width from 16 to 3 bits achieves 72% area reduction and 50% higher maximum frequency.

Sohaib Errabii, Olivier Sentieys, Marcello Traiola

Univ Rennes, Inria, CNRS, IRISA, Rennes, France

Low-Bit Quantization Efficient Neural Network Inference Kolmogorov-Arnold Networks Neural Network Quantization

Mar 16, 2026

A Kolmogorov-Arnold Surrogate Model for Chemical Equilibria: Application to Solid Solutions

The computational cost of geochemical solvers is a challenging matter. For reactive transport simulations, where chemical calculations are performed up to billions of times, it is crucial to reduce the total computational time. Existing publications have explored various machine-learning approaches to determine the most effective data-driven surrogate model. In particular, multilayer perceptrons are widely employed due to their ability to recognize nonlinear relationships. In this work, we focus on the recent Kolmogorov-Arnold networks, where learnable spline-based functions replace classical fixed activation functions. This architecture has achieved higher accuracy with fewer trainable parameters and has become increasingly popular for solving partial differential equations. First, we train a surrogate model based on an existing cement system benchmark. Then, we move to an application case for the geological disposal of nuclear waste, i.e., the determination of radionuclide-bearing solids solubilities. To the best of our knowledge, this work is the first to investigate co-precipitation with radionuclide incorporation using data-driven surrogate models, considering increasing levels of thermodynamic complexity from simple mechanical mixtures to non-ideal solid solutions of binary (Ba,Ra)SO

_4

and ternary (Sr,Ba,Ra)SO

_4

systems. On the cement benchmark, we demonstrate that the Kolmogorov-Arnold architecture outperforms multilayer perceptrons in both absolute and relative error metrics, reducing them by 62% and 59%, respectively. On the binary and ternary radium solid solution models, Kolmogorov-Arnold networks maintain median prediction errors near

1\times10^{-3}

. This is the first step toward employing surrogate models to speed up reactive transport simulations and optimize the safety assessment of deep geological waste repositories.

Leonardo Boledi, Dirk Bosbach, Jenna Poonoosamy

Institute of Fusion Energy and Nuclear Waste Management (IFN-2), Forschungszentrum Jülich GmbH

Neural Surrogate Modeling Kolmogorov-Arnold Networks Computational Materials Science

Mar 16, 2026

In-Context Symbolic Regression for Robustness-Improved Kolmogorov-Arnold Networks

Symbolic regression aims to replace black-box predictors with concise analytical expressions that can be inspected and validated in scientific machine learning. Kolmogorov-Arnold Networks (KANs) are well suited to this goal because each connection between adjacent units (an "edge") is parametrised by a learnable univariate function that can, in principle, be replaced by a symbolic operator. In practice, however, symbolic extraction is a bottleneck: the standard KAN-to-symbol approach fits operators to each learned edge function in isolation, making the discrete choice sensitive to initialisation and non-convex parameter fitting, and ignoring how local substitutions interact through the full network. We study in-context symbolic regression for operator extraction in KANs, and present two complementary instantiations. Greedy in-context Symbolic Regression (GSR) performs greedy, in-context selection by choosing edge replacements according to end-to-end loss improvement after brief fine-tuning. Gated Matching Pursuit (GMP) amortises this in-context selection by training a differentiable gated operator layer that places an operator library behind sparse gates on each edge; after convergence, gates are discretised (optionally followed by a short in-context greedy refinement pass). We quantify robustness via one-factor-at-a-time (OFAT) hyper-parameter sweeps and assess both predictive error and qualitative consistency of recovered formulas. Across several experiments, greedy in-context symbolic regression achieves up to 99.8% reduction in median OFAT test MSE.

Francesco Sovrano, Lidia Losavio, Giulia Vilone +1

University of Italian-Speaking Switzerland (USI) · Analog Devices International

Symbolic Regression Kolmogorov-Arnold Networks

Mar 16, 2026

PAKAN: Pixel Adaptive Kolmogorov-Arnold Network Modules for Pansharpening

Pansharpening aims to fuse high-resolution spatial details from panchromatic images with the rich spectral information of multispectral images. Existing deep neural networks for this task typically rely on static activation functions, which limit their ability to dynamically model the complex, non-linear mappings required for optimal spatial-spectral fusion. While the recently introduced Kolmogorov-Arnold Network (KAN) utilizes learnable activation functions, traditional KANs lack dynamic adaptability during inference. To address this limitation, we propose a Pixel Adaptive Kolmogorov-Arnold Network framework. Starting from KAN, we design two adaptive variants: a 2D Adaptive KAN that generates spline summation weights across spatial dimensions and a 1D Adaptive KAN that generates them across spectral channels. These two components are then assembled into PAKAN 2to1 for feature fusion and PAKAN 1to1 for feature refinement. Extensive experiments demonstrate that our proposed modules significantly enhance network performance, proving the effectiveness and superiority of pixel-adaptive activation in pansharpening tasks.

Haoyu Zhang, Haojing Chen, Zhen Zhong +1

University of Electronic Science and Technology of China

Kolmogorov-Arnold Networks Multi-Source Image Fusion Remote Sensing

Mar 9, 2026

DualFlexKAN: Dual-stage Kolmogorov-Arnold Networks with Independent Function Control

Multi-Layer Perceptrons (MLPs) rely on pre-defined, fixed activation functions, imposing a static inductive bias that forces the network to approximate complex topologies solely through increased depth and width. Kolmogorov-Arnold Networks (KANs) address this limitation through edge-centric learnable functions, yet their formulation suffers from quadratic parameter scaling and architectural rigidity that hinders the effective integration of standard regularization techniques. This paper introduces the DualFlexKAN (DFKAN), a flexible architecture featuring a dual-stage mechanism that independently controls pre-linear input transformations and post-linear output activations. This decoupling enables hybrid networks that optimize the trade-off between expressiveness and computational cost. Unlike standard formulations, DFKAN supports diverse basis function families, including orthogonal polynomials, B-splines, and radial basis functions, integrated with configurable regularization strategies that stabilize training dynamics. Comprehensive evaluations across regression benchmarks, physics-informed tasks, and function approximation demonstrate that DFKAN outperforms both MLPs and conventional KANs in accuracy, convergence speed, and gradient fidelity. The proposed hybrid configurations achieve superior performance with one to two orders of magnitude fewer parameters than standard KANs, effectively mitigating the parameter explosion problem while preserving KAN-style expressiveness. DFKAN provides a principled, scalable framework for incorporating adaptive non-linearities, proving particularly advantageous for data-efficient learning and interpretable function discovery in scientific applications.

Andrés Ortiz, Nicolás J. Gallego-Molina, Carmen Jiménez-Mesa +2

Department of Communications Engineering University of Malaga Malaga, Spain · DaSCI Andalusian Institute of Data Science and Computational Intelligence University of Granada Granada, Spain · Department of signal Theory, Communications and Telematics University of Granada Granada, Spain

Kolmogorov-Arnold Networks Neural Network Approximation Theory

Mar 6, 2026

Demystifying KAN for Vision Tasks: The RepKAN Approach

Remote sensing image classification is essential for Earth observation, yet standard CNNs and Transformers often function as uninterpretable black-boxes. We propose RepKAN, a novel architecture that integrates the structural efficiency of CNNs with the non-linear representational power of KANs. By utilizing a dual-path design -- Spatial Linear and Spectral Non-linear -- RepKAN enables the autonomous discovery of class-specific spectral fingerprints and physical interaction manifolds. Experimental results on the EuroSAT and NWPU-RESISC45 datasets demonstrate that RepKAN provides explicit physically interpretable reasoning while outperforming state-of-the-art models. These findings indicate that RepKAN holds significant potential to serve as the backbone for future interpretable visual foundation models.

Minjong Cheon

Sejong University Computer Science and Engineering Seoul

Explainable Image Classification Remote Sensing Image Understanding Kolmogorov-Arnold Networks

Mar 5, 2026

Multilevel Training for Kolmogorov Arnold Networks

Algorithmic speedup of training common neural architectures is made difficult by the lack of structure guaranteed by the function compositions inherent to such networks. In contrast to multilayer perceptrons (MLPs), Kolmogorov-Arnold networks (KANs) provide more structure by expanding learned activations in a specified basis. This paper exploits this structure to develop practical algorithms and theoretical insights, yielding training speedup via multilevel training for KANs. To do so, we first establish an equivalence between KANs with spline basis functions and multichannel MLPs with power ReLU activations through a linear change of basis. We then analyze how this change of basis affects the geometry of gradient-based optimization with respect to spline knots. The KANs change-of-basis motivates a multilevel training approach, where we train a sequence of KANs naturally defined through a uniform refinement of spline knots with analytic geometric interpolation operators between models. The interpolation scheme enables a ``properly nested hierarchy'' of architectures, ensuring that interpolation to a fine model preserves the progress made on coarse models, while the compact support of spline basis functions ensures complementary optimization on subsequent levels. Numerical experiments demonstrate that our multilevel training approach can achieve orders of magnitude improvement in accuracy over conventional methods to train comparable KANs or MLPs, particularly for physics informed neural networks. Finally, this work demonstrates how principled design of neural networks can lead to exploitable structure, and in this case, multilevel algorithms that can dramatically improve training performance.

Ben S. Southworth, Jonas A. Actor, Graham Harper +1

Theoretical Division, Los Alamos National Laboratory, USA. · Center for Computing Research, Sandia National Laboratories, USA.

Kolmogorov-Arnold Networks Neural Network Optimization

Feb 25, 2026

Physics-Informed Machine Learning for Vessel Shaft Power and Fuel Consumption Prediction: Interpretable KAN-based Approach

Accurate prediction of shaft rotational speed, shaft power, and fuel consumption is crucial for enhancing operational efficiency and sustainability in maritime transportation. Conventional physics-based models provide interpretability but struggle with real-world variability, while purely data-driven approaches achieve accuracy at the expense of physical plausibility. This paper introduces a Physics-Informed Kolmogorov-Arnold Network (PI-KAN), a hybrid method that integrates interpretable univariate feature transformations with a physics-informed loss function and a leakage-free chained prediction pipeline. Using operational and environmental data from five cargo vessels, PI-KAN consistently outperforms the traditional polynomial method and neural network baselines. The model achieves the lowest mean absolute error (MAE) and root mean squared error (RMSE), and the highest coefficient of determination (R^2) for shaft power and fuel consumption across all vessels, while maintaining physically consistent behavior. Interpretability analysis reveals rediscovery of domain-consistent dependencies, such as cubic-like speed-power relationships and cosine-like wave and wind effects. These results demonstrate that PI-KAN achieves both predictive accuracy and interpretability, offering a robust tool for vessel performance monitoring and decision support in operational settings.

Hamza Haruna Mohammed, Dusica Marijan, Arnbjørn Maressa

Simula Research Laboratory, Oslo, Norway · Navtor AS, Egersund, Norway

Physics-Informed ML Kolmogorov-Arnold Networks Neural Network Interpretability

Feb 19, 2026

Weak-Form Evolutionary Kolmogorov-Arnold Networks for Solving Partial Differential Equations

Partial differential equations (PDEs) form a central component of scientific computing. Among recent advances in deep learning, evolutionary neural networks have been developed to successively capture the temporal dynamics of time-dependent PDEs via parameter evolution. The parameter updates are obtained by solving a linear system derived from the governing equation residuals at each time step. However, strong-form evolutionary approaches can yield ill-conditioned linear systems due to pointwise residual discretization, and their computational cost scales unfavorably with the number of training samples. To address these limitations, we propose a weak-form evolutionary Kolmogorov-Arnold Network (KAN) for the scalable and accurate prediction of PDE solutions. We decouple the linear system size from the number of training samples through the weak formulation, leading to improved scalability compared to strong-form approaches. We also rigorously enforce boundary conditions by constructing the trial space with boundary-constrained KANs to satisfy Dirichlet and periodic conditions, and by incorporating derivative boundary conditions directly into the weak formulation for Neumann conditions. In conclusion, the proposed weak-form evolutionary KAN framework provides a stable and scalable approach for PDEs and contributes to scientific machine learning with potential relevance to future engineering applications.

Bongseok Kim, Jiahao Zhang, Guang Lin

Neural PDE Solvers PDE Solving Kolmogorov-Arnold Networks Neuroevolution

Feb 19, 2026

Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models

A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain history and stress. Machine learning has lead to considerable advances in this field lately. Here we introduce inelastic Constitutive Kolmogorov-Arnold Networks (iCKANs). This novel artificial neural network architecture can discover in an automated manner symbolic constitutive laws describing both the elastic and inelastic behavior of materials. That is, it can translate data from material testing into corresponding elastic and inelastic potential functions in closed mathematical form. We demonstrate the advantages of iCKANs using both synthetic data and experimental data of the viscoelastic polymer materials VHB 4910 and VHB 4905. The results demonstrate that iCKANs accurately capture complex viscoelastic behavior while preserving physical interpretability. It is a particular strength of iCKANs that they can process not only mechanical data but also arbitrary additional information available about a material (e.g., about temperature-dependent behavior). This makes iCKANs a powerful tool to discover in the future also how specific processing or service conditions affect the properties of materials.

Chenyi Ji, Kian P. Abdolazizi, Hagen Holthusen +2

Computational Mechanics in Medicine, Applied Medical Engineering, RWTH Aachen University Pauwelsstraße 20, 52074 Aachen, Germany · Institute for Continuum and Material Mechanics, Hamburg University of Technology Eißendorfer Straße 42, 21073 Hamburg, Germany · Institute of Applied Mechanics, University of Erlangen-Nuremberg Egerlandstrasse 5, 91058 Erlangen, Germany +1

Materials Science Neural Network Interpretability Kolmogorov-Arnold Networks Computational Materials Science Symbolic Regression

Feb 18, 2026

FEKAN: Feature-Enriched Kolmogorov-Arnold Networks

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-, wavelet-, radial-basis variants, etc., suffer from high computational cost and slow convergence, limiting scalability and practical applicability. Here, we introduce Feature-Enriched Kolmogorov-Arnold Networks (FEKAN), a simple yet effective extension that preserves all the advantages of KAN while improving computational efficiency and predictive accuracy through feature enrichment, without increasing the number of trainable parameters. By incorporating these additional features, FEKAN accelerates convergence, increases representation capacity, and substantially mitigates the computational overhead characteristic of state-of-the-art KAN architectures. We investigate FEKAN across a comprehensive set of benchmarks, including function-approximation tasks, physics-informed formulations for diverse partial differential equations (PDEs), and neural operator settings that map between input and output function spaces. For function approximation, we systematically compare FEKAN against a broad family of KAN variants, FastKAN, WavKAN, ReLUKAN, HRKAN, ChebyshevKAN, RBFKAN, and the original SplineKAN. Across all tasks, FEKAN demonstrates substantially faster convergence and consistently higher approximation accuracy than the underlying baseline architectures. We also establish the theoretical foundations for FEKAN, showing its superior representation capacity compared to KAN, which contributes to improved accuracy and efficiency.

Sidharth S. Menon, Ameya D. Jagtap

Aerospace Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609, USA.

Kolmogorov-Arnold Networks Neural Network Approximation Theory

Feb 18, 2026

A Graph Meta-Network for Learning on Kolmogorov-Arnold Networks

Weight-space models learn directly from the parameters of neural networks, enabling tasks such as predicting their accuracy on new datasets. Naive methods -- like applying MLPs to flattened parameters -- perform poorly, making the design of better weight-space architectures a central challenge. While prior work leveraged permutation symmetries in standard networks to guide such designs, no analogous analysis or tailored architecture yet exists for Kolmogorov-Arnold Networks (KANs). In this work, we show that KANs share the same permutation symmetries as MLPs, and propose the KAN-graph, a graph representation of their computation. Building on this, we develop WS-KAN, the first weight-space architecture that learns on KANs, which naturally accounts for their symmetry. We analyze WS-KAN's expressive power, showing it can replicate an input KAN's forward pass - a standard approach for assessing expressiveness in weight-space architectures. We construct a comprehensive ``zoo'' of trained KANs spanning diverse tasks, which we use as benchmarks to empirically evaluate WS-KAN. Across all tasks, WS-KAN consistently outperforms structure-agnostic baselines, often by a substantial margin. Our code is available at https://github.com/BarSGuy/KAN-Graph-Metanetwork.

Guy Bar-Shalom, Ami Tavory, Itay Evron +3

Technion, Meta · Meta · Meta, Ben-Gurion University of the Negev +1

Kolmogorov-Arnold Networks Equivariant Neural Networks

Feb 7, 2026

Physical Analogue Kolmogorov-Arnold Networks based on Reconfigurable Nonlinear-Processing Units

Kolmogorov-Arnold Networks (KANs) shift neural computation from linear layers to learnable nonlinear edge functions, but implementing these nonlinearities efficiently in hardware remains an open challenge. Here we introduce a physical analogue KAN architecture in which edge functions are realized in materia using reconfigurable nonlinear-processing units (RNPUs): multi-terminal nanoscale silicon devices whose input-output characteristics are tuned via control voltages. By combining multiple RNPUs into an edge processor and assembling these blocks into a reconfigurable analogue KAN (aKAN) architecture with integrated mixed-signal interfacing, we establish a realistic system-level hardware implementation that enables compact KAN-style regression and classification with programmable nonlinear transformations. Using experimentally calibrated RNPU models and hardware measurements, we demonstrate accurate function approximation across increasing task complexity while requiring fewer or comparable trainable parameters than multilayer perceptrons (MLPs). System-level estimates indicate an energy per inference of roughly 200 pJ and an end-to-end inference latency of roughly 0.6

μ

s for a representative workload, corresponding to over 100

\times

reduction in energy accompanied by

>

10

\times

reduction in area compared to a digital fixed-point MLP at similar approximation error. These results establish RNPUs as scalable, hardware-native nonlinear computing primitives and identify analogue KAN architectures as a realistic silicon-based pathway toward energy-, latency-, and footprint-efficient analogue neural-network hardware, particularly for edge inference.

Manuel Escudero, Mohamadreza Zolfagharinejad, Sjoerd van den Belt +2

1NanoElectronics Group, MESA+ Institute and BRAINS Center for Brain-Inspired Computing, University of Twente, P.O. Box 217, Enschede,2026 7500 AE, The Netherlands. · 2CAESUniversity GroupofandTwente,BRAINSEnschede,Center 7500for Brain-InspiredAE, The Netherlands.Computing · Institute of Physics, University of Münster, Münster, 48149 Germany.

Efficient Neural Network Inference Kolmogorov-Arnold Networks Neuromorphic Computing

Feb 5, 2026

Clifford Kolmogorov-Arnold Networks

We introduce Clifford Kolmogorov-Arnold Network (ClKAN), a flexible and efficient architecture for function approximation in arbitrary Clifford Algebra spaces. We propose the use of Randomized Quasi-Monte Carlo grid generation as a solution to the exponential scaling associated with higher-dimensional algebras. Our ClKAN also introduces new batch normalization strategies to deal with variable domain input. ClKAN finds application in scientific discovery and engineering, and is validated in synthetic and physics-inspired tasks.

Matthias Wolff, Francesco Alesiani, Christof Duhme +1

Data Science Div. NEC Labs Europe Heidelberg, Germany

Kolmogorov-Arnold Networks Neural Network Approximation Theory Scientific ML

Nov 24, 2025

QuantKAN: A Unified Quantization Framework for Kolmogorov Arnold Networks

Kolmogorov--Arnold Networks (KANs) replace linear weights with spline-based functions, offering strong expressivity but posing challenges for low-precision deployment due to heterogeneous parameter distributions. We introduce QuantKAN, the first unified framework for quantization-aware training (QAT) and post-training quantization (PTQ) of KANs. The framework employs branch-aware quantizers for base and spline parameters and extends modern QAT and PTQ methods to spline-based layers across EfficientKAN, FastKAN, PyKAN, and KAGN. Experiments on MNIST, CIFAR-10/100, TinyImageNet, and ImageNet provide the first unified QAT/PTQ KAN benchmarks and show that DSQ is the most robust QAT method at aggressive low-bit settings, while GPTQ is the strongest PTQ method at moderate precision. Sensitivity analyses reveal architecture-specific failure modes: spline/basis parameters dominate in FastKAN, while base or scaling parameters dominate in EfficientKAN, GRAM, and PyKAN. Vivado HLS estimates on a Xilinx UltraScale+ device further suggest up to 3.32

\times

throughput and 7.7

\times

lower estimated dynamic energy per inference under W4A4, exposing a residual basis-evaluation tax that motivates basis-aware microarchitecture. QuantKAN is available at https://github.com/OSU-STARLAB/QuantKAN/.

Kazi Ahmed Asif Fuad, Lizhong Chen

Department of EECS · Oregon State University · Corvallis, OR 97331

Quantization-Aware Training Kolmogorov-Arnold Networks Post-Training Quantization Low-Bit Quantization Neural Network Quantization

Nov 23, 2025

KAN vs LSTM Performance in Time Series Forecasting

This study presents a controlled comparison of baseline Kolmogorov-Arnold Networks (KAN), implemented via PyKAN, and Long Short-Term Memory (LSTM) networks for the forecasting of stochastic, non-stationary financial time series. The two architectures are assessed in terms of predictive accuracy, computational efficiency, and interpretability, with accuracy measured by the Root Mean Square Error (RMSE) in normalised feature space. Under a direct multi-output forecasting protocol, LSTM attains clearly superior accuracy across all tested prediction horizons, consistent with its well-established effectiveness for sequential data modelling. Baseline KAN, although offering theoretical interpretability through the Kolmogorov-Arnold representation theorem, exhibits substantially higher error rates and limited practical applicability for time series forecasting in its standard form. Several specialised temporal variants -- including Temporal KAN and Time-Frequency KAN -- have since been proposed to address these sequential modelling limitations, but they lie outside the scope of the present study. KAN is observed to converge faster during training under the configurations tested, although direct runtime comparisons are constrained by methodological factors. These findings support the adoption of LSTM for accuracy-critical financial forecasting and establish an empirical baseline for standard KAN on stochastic sequential data, motivating further investigation of temporally-aware KAN architectures. The study benchmarks baseline KAN against baseline LSTM only; the results do not extend to specialised KAN variants designed for sequential data, nor to the broader family of temporal models.

Tabish Ali Rather, S M Mahmudul Hasan Joy, Nadezda Sukhorukova +1

Department of Mathematics, Swinburne University of Technology, Hawthorn, 3122, Victoria, Australia.

Time Series Forecasting Non-Stationary Time Series Forecasting Kolmogorov-Arnold Networks Long Short-Term Memory Networks Financial Time Series

Sep 17, 2025

Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks

Variational quantum circuits (VQCs) are central to quantum machine learning, while recent progress in Kolmogorov-Arnold networks (KANs) highlights the power of learnable activation functions. We unify these directions by introducing the quantum variational activation function (QVAF), a general framework in which parameterized quantum circuits serve as learnable activation functions; in this work we study an efficient single-qubit instantiation called DatA Re-Uploading ActivatioN (DARUAN). We show that DARUAN with trainable data-preprocessing weights can realize an exponentially growing accessible frequency support with the number of re-uploading repetitions; for an explicit geometric choice of these weights, this gives a capacity-level exponential parameter reduction relative to independently parameterized Fourier activations. Embedding DARUAN into KAN yields the quantum-inspired Kolmogorov-Arnold Network (QKAN), which retains the interpretability of the KAN architecture while improving parameter efficiency, expressivity, and generalization. We further introduce layer extension and the hybrid QKAN (HQKAN) architecture to improve scalability and computational efficiency, enabling QKAN modules to act as compact replacements for multi-layer perceptrons (MLPs) in large-scale models. We provide theoretical analysis and extensive experiments on function regression, image classification, and autoregressive generative language modeling, demonstrating the efficiency and scalability of QKANs. Because the single-qubit circuits are efficiently simulable on classical quantum simulators, QKANs have quantum-inspired advantage in parameter efficiency and training stability; DARUANs and QKANs serve as present-day validation of the QVAF concept, and the trained DARUANs are directly executable and feasible on current noisy intermediate-scale quantum (NISQ) hardware for inference validation.

Jiun-Cheng Jiang, Morris Yu-Chao Huang, Tianlong Chen +1

Department of Physics and Center for Theoretical Physics, National Taiwan University, Taipei 106319, Taiwan · Physics Division, National Center for Theoretical Sciences, National Taiwan University, Taipei 106319, Taiwan · Department of Computer Science, University of North Carolina at Chapel Hill, NC 27514, USA +1

Quantum Machine Learning Quantum-Inspired ML Kolmogorov-Arnold Networks Variational Quantum Circuits