mlsanityData to 7 Oct 2026

ExSpliNet: An interpretable and expressive spline-based neural network

arXiv 2205.01510 ↗First posted 3 May 2022cs.LG cs.NA math.NAcited by 33

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Abstract (arXiv)

In this paper we present ExSpliNet, an interpretable and expressive neural network model. The model combines ideas of Kolmogorov neural networks, ensembles of probabilistic trees, and multivariate B-spline representations. We give a probabilistic interpretation of the model and show its universal approximation properties. We also discuss how it can be efficiently encoded by exploiting B-spline properties. Finally, we test the effectiveness of the proposed model on synthetic approximation problems and classical machine learning benchmark datasets.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). Builds on 21 of its 69 references that are in the map. First posted on arXiv 3 May 2022.

Builds on

21 of 69 references.

References · 21

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9 more
  1. 2018Deep Neural Decision Treescited by 72
  2. 2018Mad Max: Affine Spline Insights into Deep Learningcited by 54
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 13; 2025: 12; 2026: 8.

33 papers.

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  1. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  2. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 118
  3. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
  4. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 60
  5. 2024Physics Informed Kolmogorov-Arnold Neural Networks for Dynamical Analysis via Efficent-KAN and WAV-KANcited by 25
  6. 2025AuroRA: Breaking Low-Rank Bottleneck of LoRA with Nonlinear Mappingcited by 22
  7. 2024FC-KAN: Function Combinations in Kolmogorov-Arnold Networkscited by 18
  8. 2025A Practitioner's Guide to Kolmogorov-Arnold Networkscited by 16
  9. 2024Leveraging KANs For Enhanced Deep Koopman Operator Discoverycited by 9
  10. 2025Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNscited by 9
  11. 2025Fast and Accurate Gigapixel Pathological Image Classification with Hierarchical Distillation Multi-Instance Learningcited by 5
  12. 2024KAN we improve on HEP classification tasks? Kolmogorov-Arnold Networks applied to an LHC physics examplecited by 4
21 more
  1. 2024Nonparametric Automatic Differentiation Variational Inference with Spline Approximationcited by 3
  2. 2026Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learningcited by 3
  3. 2025Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertaintycited by 2
  4. 2026InKAN: B-Spline KANs via Truncated Power Formcited by 2
  5. 2024Learning Expressive Random Feature Models via Parametrized Activationscited by 1
  6. 2025Physics-Informed Deep B-Spline Networkscited by 1
  7. 2025A Kolmogorov-Arnold Neural Model for Cascading Extremescited by 1
  8. 2025BEKAN: Boundary condition-guaranteed evolutionary Kolmogorov-Arnold networks with radial basis functions for solving PDE problemscited by 1
  9. 2025On the Generalization Properties of Learning the Random Feature Models with Learnable Activation Functionscited by 1
  10. 2026SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functionscited by 1
  11. 2024SL2A-INR: Single-Layer Learnable Activation for Implicit Neural Representationcited by 0
  12. 2024Model Comparisons: XNet Outperforms KANcited by 0
  13. 2024Hybrid deep additive neural networkscited by 0
  14. 2025Local Control Networks (LCNs): Optimizing Flexibility in Neural Network Data Pattern Capturecited by 0
  15. 2025Enhancing Neural Function Approximation: The XNet Outperforming KANcited by 0
  16. 2025Polynomial, trigonometric, and tropical activationscited by 0
  17. 2026Fully Kolmogorov-Arnold Deep Model in Medical Image Segmentationcited by 0
  18. 2026Weak-Form Evolutionary Kolmogorov-Arnold Networks for Solving Partial Differential Equationscited by 0
  19. 2026Geometric Kolmogorov--Arnold Network (GeoKAN)cited by 0
  20. 2026Twincher: Bijective Representation Learning for Robust Inversion of Continuous Systemscited by 0
  21. 2026Structured Nonparametric Variational Inference for Dependent Latent Modelingcited by 0