# Enhancing Kernel Flexibility via Learning Asymmetric Locally-Adaptive Kernels

arXiv: https://arxiv.org/abs/2310.05236 · HTML: https://mlsanity.com/paper/2310.05236/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 8 Oct 2023.

## Builds on (most cited first, 18 of 18)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [The Power of Interpolation: Understanding the Effectiveness of SGD in Modern Over-parametrized Learning](https://mlsanity.com/paper/1712.06559/) (2017)
- [When Do Neural Networks Outperform Kernel Methods?](https://mlsanity.com/paper/2006.13409/) (2020)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [FALKON: An Optimal Large Scale Kernel Method](https://mlsanity.com/paper/1705.10958/) (2017)
- [The Interpolation Phase Transition in Neural Networks: Memorization and Generalization under Lazy Training](https://mlsanity.com/paper/2007.12826/) (2020)
- [Information Theory with Kernel Methods](https://mlsanity.com/paper/2202.08545/) (2022)
- [On Reproducing Kernel Banach Spaces: Generic Definitions and Unified Framework of Constructions](https://mlsanity.com/paper/1901.01002/) (2019)
- [Efficient Hyperparameter Tuning for Large Scale Kernel Ridge Regression](https://mlsanity.com/paper/2201.06314/) (2022)
- [Learning with Asymmetric Kernels: Least Squares and Feature Interpretation](https://mlsanity.com/paper/2202.01397/) (2022)
- [Learning Ability of Interpolating Deep Convolutional Neural Networks](https://mlsanity.com/paper/2210.14184/) (2022)
- [Learning Data-adaptive Nonparametric Kernels](https://mlsanity.com/paper/1808.10724/) (2018)
- [MKLpy: a python-based framework for Multiple Kernel Learning](https://mlsanity.com/paper/2007.09982/) (2020)
- [Learning with Hierarchical Gaussian Kernels](https://mlsanity.com/paper/1612.00824/) (2016)
- [Optimal Learning with Anisotropic Gaussian SVMs](https://mlsanity.com/paper/1810.02321/) (2018)

## Built on by (most cited first, 1 of 1)

- [xRFM: Accurate, scalable, and interpretable feature learning models for tabular data](https://mlsanity.com/paper/2508.10053/) (2025)

## Abstract (arXiv)

The lack of sufficient flexibility is the key bottleneck of kernel-based learning that relies on manually designed, pre-given, and non-trainable kernels. To enhance kernel flexibility, this paper introduces the concept of Locally-Adaptive-Bandwidths (LAB) as trainable parameters to enhance the Radial Basis Function (RBF) kernel, giving rise to the LAB RBF kernel. The parameters in LAB RBF kernels are data-dependent, and its number can increase with the dataset, allowing for better adaptation to diverse data patterns and enhancing the flexibility of the learned function. This newfound flexibility also brings challenges, particularly with regards to asymmetry and the need for an efficient learning algorithm. To address these challenges, this paper for the first time establishes an asymmetric kernel ridge regression framework and introduces an iterative kernel learning algorithm. This novel approach not only reduces the demand for extensive support data but also significantly improves generalization by training bandwidths on the available training data. Experimental results on real datasets underscore the remarkable performance of the proposed algorithm, showcasing its superior capability in handling large-scale datasets compared to Nystr"om approximation-based algorithms. Moreover, it demonstrates a significant improvement in regression accuracy over existing kernel-based learning methods and even surpasses residual neural networks.