IKNO: Infinite-order Kernel Neural Operators

• URL: http://arxiv.org/abs/2605.22182v1
• Date: Thu, 21 May 2026 08:52:36 GMT
• Title: IKNO: Infinite-order Kernel Neural Operators
• Abstract summary: We propose the Infinite-order Kernel Neural Operator (IKNO), which constructs neural operators via infinite-order kernel integrals.<n>We develop two complementary infinite-order neural operator constructions: IKNO-Vanilla, which applies the full- kernel resolvent on the product grid via Kronecker eigendecomposition, and IKNO-TP, an alternative tensor-product operator that composes per-axis resolvents.
• Score: 57.17011066621087
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Neural operators have achieved significant success in modern scientific computing due to their flexibility and strong generalization capabilities. Existing models, however, primarily rely on first-order kernel integral approximations, which severely limit their expressivity. To address this, we propose the Infinite-order Kernel Neural Operator (IKNO), which constructs neural operators via infinite-order kernel integrals and admits an elegant closed-form finite approximation. We develop two complementary infinite-order neural operator constructions: IKNO-Vanilla, which applies the full-kernel resolvent on the product grid via Kronecker eigendecomposition, and IKNO-TP, an alternative tensor-product operator that composes per-axis resolvents. Furthermore, we develop fast computation schemes for both variants of IKNO, which achieve outstanding global information aggregation while maintaining high computational efficiency. Empirically, we evaluate our IKNO on both time-dependent and time-independent benchmarks with arbitrary input shapes, including large-scale industrial datasets. Extensive experiments demonstrate that the IKNO method consistently achieves the SOTA accuracy with significant improvements on nearly all benchmark datasets while maintaining scalability to very large point clouds.

Related papers

• NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers [1.8117099374299037]
  Partial differential equations (PDEs) underpin quantitative descriptions across the physical sciences and engineering.<n>Data-driven surrogates can be strikingly fast but are often unreliable when applied outside their training distribution.<n>Here we introduce Neural Operator Warm Starts (NOWS), a hybrid strategy that harnesses learned solution operators to accelerate classical iterative solvers.
  arXiv  Detail & Related papers  (2025-11-04T11:12:27Z)
• Optimal Convergence Rates for Neural Operators [2.9388890036358104]
  We provide bounds on the number of hidden neurons and the number of second-stage samples necessary for generalization.<n>A key application of neural operators is learning surrogate maps for the solution operators of partial differential equations.
  arXiv  Detail & Related papers  (2024-12-23T12:31:38Z)
• Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning [11.165984223900104]
  This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture.<n>The KNO decouples the choice of kernel from the numerical integration scheme (quadrature)<n> Numerical results demonstrate that on existing benchmarks the training and test accuracy of KNOs is comparable to or higher than popular operator learning techniques.
  arXiv  Detail & Related papers  (2024-06-30T19:28:12Z)
• CoNO: Complex Neural Operator for Continous Dynamical Physical Systems [4.963536645449426]
  We introduce Complex Neural Operator (CoNO) that parameterizes the integral kernel using Fractional Fourier Transform (FrFT) Empirically, CoNO consistently attains state-of-the-art performance, showcasing an average relative gain of 10.9%. CoNO also exhibits the ability to learn from small amounts of data -- giving the same performance as the next best model with just 60% of the training data.
  arXiv  Detail & Related papers  (2024-06-01T14:32:19Z)
• Neural Operators with Localized Integral and Differential Kernels [77.76991758980003]
  We present a principled approach to operator learning that can capture local features under two frameworks. We prove that we obtain differential operators under an appropriate scaling of the kernel values of CNNs. To obtain local integral operators, we utilize suitable basis representations for the kernels based on discrete-continuous convolutions.
  arXiv  Detail & Related papers  (2024-02-26T18:59:31Z)
• Efficient kernel surrogates for neural network-based regression [0.8030359871216615]
  We study the performance of the Conjugate Kernel (CK), an efficient approximation to the Neural Tangent Kernel (NTK) We show that the CK performance is only marginally worse than that of the NTK and, in certain cases, is shown to be superior. In addition to providing a theoretical grounding for using CKs instead of NTKs, our framework suggests a recipe for improving DNN accuracy inexpensively.
  arXiv  Detail & Related papers  (2023-10-28T06:41:47Z)
• Compacting Binary Neural Networks by Sparse Kernel Selection [58.84313343190488]
  This paper is motivated by a previously revealed phenomenon that the binary kernels in successful BNNs are nearly power-law distributed. We develop the Permutation Straight-Through Estimator (PSTE) that is able to not only optimize the selection process end-to-end but also maintain the non-repetitive occupancy of selected codewords. Experiments verify that our method reduces both the model size and bit-wise computational costs, and achieves accuracy improvements compared with state-of-the-art BNNs under comparable budgets.
  arXiv  Detail & Related papers  (2023-03-25T13:53:02Z)
• Efficient Dataset Distillation Using Random Feature Approximation [109.07737733329019]
  We propose a novel algorithm that uses a random feature approximation (RFA) of the Neural Network Gaussian Process (NNGP) kernel. Our algorithm provides at least a 100-fold speedup over KIP and can run on a single GPU. Our new method, termed an RFA Distillation (RFAD), performs competitively with KIP and other dataset condensation algorithms in accuracy over a range of large-scale datasets.
  arXiv  Detail & Related papers  (2022-10-21T15:56:13Z)
• Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks [64.23331120621118]
  We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs) INNs are a class of implicit learning models that use implicit equations as layers. We show that our approach performs at least as well as, and generally better than, applying state-of-the-art interval bound propagation methods to INNs.
  arXiv  Detail & Related papers  (2022-04-01T03:31:27Z)
• Random Features for the Neural Tangent Kernel [57.132634274795066]
  We propose an efficient feature map construction of the Neural Tangent Kernel (NTK) of fully-connected ReLU network. We show that dimension of the resulting features is much smaller than other baseline feature map constructions to achieve comparable error bounds both in theory and practice.
  arXiv  Detail & Related papers  (2021-04-03T09:08:12Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.