# Gaussian RBF Centered Kernel Alignment (CKA) in the Large Bandwidth Limit

arXiv: https://arxiv.org/abs/2112.09305 · HTML: https://mlsanity.com/paper/2112.09305/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 17 Dec 2021.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [Emerging Cross-lingual Structure in Pretrained Language Models](https://mlsanity.com/paper/1911.01464/) (2019)
- [Entangled Watermarks as a Defense against Model Extraction](https://mlsanity.com/paper/2002.12200/) (2020)
- [Universality and individuality in neural dynamics across large populations of recurrent networks](https://mlsanity.com/paper/1907.08549/) (2019)

## Built on by (most cited first, 6 of 6)

- [Objective drives the consistency of representational similarity across datasets](https://mlsanity.com/paper/2411.05561/) (2024)
- [Lie Detector: Unified Backdoor Detection via Cross-Examination Framework](https://mlsanity.com/paper/2503.16872/) (2025)
- [Internal Cross-layer Gradients for Extending Homogeneity to Heterogeneity in Federated Learning](https://mlsanity.com/paper/2308.11464/) (2023)
- [Seeing Through the Brain: New Insights from Decoding Visual Stimuli with fMRI](https://mlsanity.com/paper/2510.16196/) (2025)
- [Data eccentricity, asymptotics of Gaussian RBF reproducing kernel Hilbert space, and kernel PCA](https://mlsanity.com/paper/2607.21823/) (2026)
- [DCRL: Decoupling and Coupling Reinforcement Learning via Policy-Reward Manifold Alignment](https://mlsanity.com/paper/2609.27572/) (2026)

## Abstract (arXiv)

We prove that Centered Kernel Alignment (CKA) based on a Gaussian RBF kernel converges to linear CKA in the large-bandwidth limit. We show that convergence onset is sensitive to the geometry of the feature representations, and that representation eccentricity bounds the range of bandwidths for which Gaussian CKA behaves nonlinearly.