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Kolmogorov-Arnold Networks: A Critical Assessment of Claims, Performance, and Practical Viability
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Kolmogorov-Arnold Networks (KANs) have gained significant attention as an alternative to traditional multilayer perceptrons, with proponents claiming superior interpretability and performance through learnable univariate activation functions. However, recent systematic evaluations reveal substantial discrepancies between theoretical claims and empirical evidence. This critical assessment examines KANs' actual performance across diverse domains using fair comparison methodologies that control for parameters and computational costs. Our analysis demonstrates that KANs outperform MLPs only in symbolic regression tasks, while consistently underperforming in machine learning, computer vision, and natural language processing benchmarks. The claimed advantages largely stem from B-spline activation functions rather than architectural innovations, and computational overhead (1.36-100x slower) severely limits practical deployment. Furthermore, theoretical claims about breaking the "curse of dimensionality" lack rigorous mathematical foundation. We systematically identify the conditions under which KANs provide value versus traditional approaches, establish evaluation standards for future research, and propose a priority-based roadmap for addressing fundamental limitations. This work provides researchers and practitioners with evidence-based guidance for the rational adoption of KANs while highlighting critical research gaps that must be addressed for broader applicability.
Forward citations
Cited by 13 Pith papers
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A 24-dataset benchmark for inducing schema graphs from raw text, plus an auditable LLM-based pipeline that reports the highest scores on the benchmark's four schema-similarity metrics.
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A Kolmogorov-Arnold Surrogate Model for Chemical Equilibria: Application to Solid Solutions
Kolmogorov-Arnold networks trained on GEM-Selektor output accurately approximate chemical equilibria for cement and radium-sulfate solid-solution systems, outperforming MLPs on the cement benchmark and cutting evaluat...
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Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models
iCKAN combines input-convex Kolmogorov-Arnold networks with a thermodynamic inelasticity framework to turn stress-strain data into symbolic elastic and inelastic potentials.
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QuadKAN: KAN-Enhanced Quadruped Motion Control via End-to-End Reinforcement Learning
A KAN-based spline policy for vision-guided quadruped locomotion improves return, distance, and collision avoidance over MLP baselines in PyBullet simulation.
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Kolmogorov-Arnold Wavefunctions
KAN-based trial wavefunctions reach about 1 percent ground-state energy accuracy for one-dimensional trapped bosons at roughly 10 times lower cost per training step than MLP-based wavefunctions, aided by a transferabl...
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Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum States
SineKAN, a Kolmogorov-Arnold network with sinusoidal activations, accurately represents ground states of 1D spin chains and outperforms RBM, LSTM, and MLP neural quantum states in the J1-J2 model.
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Leveraging KANs for Expedient Training of Multichannel MLPs via Preconditioning and Geometric Refinement
Training in a B-spline KAN basis is equivalent to preconditioned gradient descent on a multichannel ReLU MLP, and geometric refinement plus trainable knots accelerate and improve training.
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Low Tensor-Rank Adaptation of Kolmogorov--Arnold Networks
A low tensor-rank adaptation (LoTRA) method and learning-rate guidance enable efficient fine-tuning of Kolmogorov-Arnold networks, validated on PDE solving and representation tasks.
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SOH-KLSTM: A Hybrid Kolmogorov-Arnold Network and LSTM Model for Enhanced Lithium-Ion Battery Health Monitoring
The paper proposes SOH-KLSTM, a hybrid LSTM model with a KAN-based candidate cell state, reporting a 97.12% reduction in RMSE vs a plain LSTM on the NASA B0005 battery dataset.
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Kolmogorov Arnold Networks (KANs) for Imbalanced Data -- An Empirical Perspective
On ten KEEL datasets, KANs outperform MLPs on raw imbalanced data but resampling and focal loss degrade KANs while MLPs with those techniques match KAN performance at far lower cost.
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Capsule-ConvKAN: A Hybrid Neural Approach to Medical Image Classification
A hybrid Capsule-ConvKAN model reports 91.21% accuracy on histopathological image classification, outperforming CNN, CapsNet, and ConvKAN baselines on a single dataset.
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Taylor expansion-based Kolmogorov-Arnold network for blind image quality assessment
A Taylor-expansion KAN variant outperforms B-spline, orthogonal-polynomial, wavelet, and Fourier KAN variants and MLPs on five authentic BIQA databases, with PCA and shallow layers reducing training cost.
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