Differentiable Kernel Ridge Regression for Deep Learning Pipelines

• URL: http://arxiv.org/abs/2605.02313v1
• Date: Mon, 04 May 2026 08:13:08 GMT
• Title: Differentiable Kernel Ridge Regression for Deep Learning Pipelines
• Abstract summary: We introduce emphSparse Kernels (SKs), a differentiable, localized, and lazy variant of kernel ridge regression (KRR)<n>SKs expose three distinct sets of parameters -- feature representations, target values, and evaluation points -- each of which can be fixed or learned.<n>Our results suggest that kernel methods, once made scalable and differentiable, can be readily integrated with deep learning.
• Score: 2.1485350418225244
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deep neural networks dominate modern machine learning, while alternative function approximators remain comparatively underexplored at scale. In this work, we revisit kernel methods as drop-in components for standard deep learning pipelines. We introduce \emph{Sparse Kernels} (SKs), a differentiable, localized, and lazy variant of kernel ridge regression (KRR) that defers training to inference time and reduces to the solution of small local systems. We integrate SKs into PyTorch as modular layers that preserve end-to-end trainability, and we show that they expose three distinct sets of parameters -- feature representations, target values, and evaluation points -- each of which can be fixed or learned. This decomposition broadens the design space available to practitioners, enabling, in particular, training-free transfer, nonlinear probing, and hybrid kernel-neural models. Across convolutional networks, vision transformers, and reinforcement learning, SK-based modules serve two complementary roles: in some settings, they match the performance of trained neural readouts with substantially less training; in others, they augment existing models and improve their performance when used as additional components. Our results suggest that kernel methods, once made scalable and differentiable, can be readily integrated with deep learning rather than treated as a separate paradigm.

Related papers

• Simplifying Neural Networks During Training [1.7966001353008778]
  We propose an NC-inspired training framework for simplifying deep networks during training.<n>Our method monitors representation dynamics through the Inverse Fisher Criterion.<n>We then replace the trailing proxy layers with a lightweight classification head and continue training the reduced model.
  arXiv  Detail & Related papers  (2026-07-30T08:32:40Z)
• KVNN: Learnable Multi-Kernel Volterra Neural Networks [6.550684951976901]
  kernelized Volterra Neural Network (kVNN)<n>Experiments on two representative tasks: video action recognition and image denoising.<n>Results are maintained even when trained from scratch without large-scale pretraining.
  arXiv  Detail & Related papers  (2026-04-16T15:18:48Z)
• Function Spaces Without Kernels: Learning Compact Hilbert Space Representations [17.20282687120807]
  We show that function encoders provide a principled connection to feature learning and kernel methods.<n>We develop two training algorithms that learn compact bases.<n>This work suggests a path toward neural predictors with kernel-level guarantees.
  arXiv  Detail & Related papers  (2025-09-24T22:55:52Z)
• Deep Hierarchical Learning with Nested Subspace Networks [53.71337604556311]
  We propose Nested Subspace Networks (NSNs) for large neural networks.<n>NSNs enable a single model to be dynamically and granularly adjusted across a continuous spectrum of compute budgets.<n>We show that NSNs can be surgically applied to pre-trained LLMs and unlock a smooth and predictable compute-performance frontier.
  arXiv  Detail & Related papers  (2025-09-22T15:13:14Z)
• Manifold meta-learning for reduced-complexity neural system identification [1.0276024900942875]
  We propose a meta-learning framework that discovers a low-dimensional manifold.<n>This manifold is learned from a meta-dataset of input-output sequences generated by a class of related dynamical systems.<n>Unlike bilevel meta-learning approaches, our method employs an auxiliary neural network to map datasets directly onto the learned manifold.
  arXiv  Detail & Related papers  (2025-04-16T06:49:56Z)
• 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)
• Robust Learning with Progressive Data Expansion Against Spurious Correlation [65.83104529677234]
  We study the learning process of a two-layer nonlinear convolutional neural network in the presence of spurious features. Our analysis suggests that imbalanced data groups and easily learnable spurious features can lead to the dominance of spurious features during the learning process. We propose a new training algorithm called PDE that efficiently enhances the model's robustness for a better worst-group performance.
  arXiv  Detail & Related papers  (2023-06-08T05:44:06Z)
• Local Learning with Neuron Groups [15.578925277062657]
  Local learning is an approach to model-parallelism that removes the standard end-to-end learning setup. We study how local learning can be applied at the level of splitting layers or modules into sub-components.
  arXiv  Detail & Related papers  (2023-01-18T16:25:10Z)
• Inducing Gaussian Process Networks [80.40892394020797]
  We propose inducing Gaussian process networks (IGN), a simple framework for simultaneously learning the feature space as well as the inducing points. The inducing points, in particular, are learned directly in the feature space, enabling a seamless representation of complex structured domains. We report on experimental results for real-world data sets showing that IGNs provide significant advances over state-of-the-art methods.
  arXiv  Detail & Related papers  (2022-04-21T05:27:09Z)
• TorchDyn: A Neural Differential Equations Library [16.43439140464003]
  We introduce TorchDyn, a PyTorch library dedicated to continuous-depth learning. It is designed to elevate neural differential equations to be as accessible as regular plug-and-play deep learning primitives.
  arXiv  Detail & Related papers  (2020-09-20T03:45:49Z)
• Learning to Learn Kernels with Variational Random Features [118.09565227041844]
  We introduce kernels with random Fourier features in the meta-learning framework to leverage their strong few-shot learning ability. We formulate the optimization of MetaVRF as a variational inference problem. We show that MetaVRF delivers much better, or at least competitive, performance compared to existing meta-learning alternatives.
  arXiv  Detail & Related papers  (2020-06-11T18:05:29Z)
• Kernel and Rich Regimes in Overparametrized Models [69.40899443842443]
  We show that gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. We also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.
  arXiv  Detail & Related papers  (2020-02-20T15:43:02Z)

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.