kernel-methods

This paper proposes an adaptive spectral bandwidth control method for kernelized graph construction to align kernel spectral properties with intrinsic manifold dimensions, showing improvements in self-supervised learning embedding tasks on CIFAR-100.

This paper develops NTK-KIP, MetaQuill, and MetaQuill-KIP algorithms to improve neural field reconstruction from sparse observations, making NTK-driven neural fields non-linear and meta-learnable for efficient few-shot adaptation.

This paper presents a method combining neural network means with exact Matérn kernel corrections for operator learning in PDEs, achieving competitive or improved performance on public benchmarks like structural mechanics and OCO-2 radiative transfer emulation.

This paper introduces General Coded Computing (GCC), a learning-theoretic framework for mitigating stragglers in distributed computing systems, providing theoretical performance guarantees and experimental validation on deep neural networks.

The paper presents the Frame Kernel Method, a novel multiscale operator learning approach for surrogate modeling of PDEs that uses kernel frame approximations and achieves higher accuracy than popular neural operators while enabling multiscale decomposition.

This paper introduces a deterministic hyperparameter selection method for reservoir computing using free-probability kernels, which eliminates the need for resource-intensive rollouts and achieves performance similar to exhaustive search with significantly lower cost.

This paper proposes a joint-distribution approach to fair representation learning with continuous sensitive attributes, using HSIC as a joint discrepancy to avoid conditional density estimation. It proves statistical efficiency gains over conditional-route methods and introduces the FRHSIC algorithm with comparable fairness-accuracy tradeoffs and faster training.

The paper introduces NysHD, a method that bridges hyperdimensional computing and kernel methods via the Nyström approximation, allowing any positive-semidefinite similarity function to be used as an HDC encoding. It demonstrates improved classification accuracy on graph and string datasets compared to existing HDC encoding methods.

This paper introduces K-Inverse-RFM, a modified Recursive Feature Machine that bridges the performance gap between RFMs and neural networks on mathematical tasks corrupted by label noise, imbalanced data, or alternative data representations.

Introduces Weak-form Kernel Ridge Regression (WKRR) for learning dynamical systems from noisy measurements, combining a weak formulation with kernel ridge regression to filter noise and improve accuracy. The method outperforms baseline methods on chaotic benchmarks up to 64 dimensions and 15,000-dimensional real-world fluid data.

This paper introduces Bernstein–Schur kernels, a class of nonstationary kernels between shift-invariant and dot-product templates, and provides a random feature construction by sketching the finite modulation and randomizing the completely monotone radial factor. The method yields unbiased estimators with operator-norm bounds controlled by intrinsic dimensions, and experiments validate the approach on a biased kernel example.

This paper identifies the geometric mechanism behind boundary-induced acquisition bias in Gaussian processes on bounded domains, showing how kernel truncation inflates posterior variance and distorts acquisition functions independently of the objective function. The authors introduce a function-free diagnostic to quantify this bias across different acquisition classes.

TorchKM is an open-source GPU-accelerated library for kernel machines (SVMs, kernel logistic regression, etc.) with a scikit-learn-style API. It accelerates training and model selection by reusing matrix operations, offering substantial speedups over standard baselines.

This paper introduces KODA (Kernel Optimization for Discrepancy Analysis), a kernel-based framework for comparing and aligning vision-language model representations by identifying sample subsets that are clustered differently across models like CLIP, SigLIP, and BLIP. The method uses contrastive embedding clustering and randomized low-dimensional approximations to scale to large datasets while providing interpretable structural differences between representations.

This paper introduces a distributional generalization of matrix completion where each entry is a probability distribution rather than a scalar, using kernel mean embeddings and Tucker rank to capture low-rank structure. The authors propose a novel estimator with non-asymptotic error bounds and demonstrate effectiveness on synthetic and real-world data.

Researchers from MIT, University of Warwick, and NVIDIA introduce Stein Kernelized Molecular Dynamics (SKMD), an enhanced sampling method that uses interacting particle dynamics to acquire informative training configurations for active learning and fine-tuning of machine learning interatomic potentials (MLIPs). SKMD is a stochastic variant of Stein variational gradient descent adapted for molecular dynamics, preserving the Boltzmann distribution while achieving higher model accuracy in fewer training iterations compared to baselines.

Introduces a perturbative approach for nonparametric instrumental variable estimation that extends kernel ridge methods with higher-order corrections, achieving up to 99% reduction in prediction error in high-dimensional settings.

Proposes Interdomain Attention, a new method that integrates state space models into attention via kernel methods, achieving efficient long-context modeling with a fixed-size state and outperforming SSMs and softmax attention in language modeling experiments up to 1.3B parameters.

This paper decomposes the predictive KL divergence between Gaussian process and latent neural process posteriors into three terms, providing upper bounds that characterize approximation errors and connecting representation dimension to kernel smoothness.

This paper proposes a hybrid quantum-classical workflow for plant phenomics classification under small-data regimes, using supervised latent restructuring (PCA + LDA) to improve geometric separability before quantum kernel alignment. Experiments show improved separability but highlight compression trade-offs and the difficulty of achieving strong quantum performance.