# Spectral Analysis of Representational Similarity with Limited Neurons

arXiv: https://arxiv.org/abs/2502.19648 · HTML: https://mlsanity.com/paper/2502.19648/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 54 references that are in the map.
- First posted on arXiv 27 Feb 2025.

## Builds on (most cited first, 15 of 15)

- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2002.02561/) (2020)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [Convolutional Neural Networks as a Model of the Visual System: Past, Present, and Future](https://mlsanity.com/paper/2001.07092/) (2020)
- [Implicit Regularization of Random Feature Models](https://mlsanity.com/paper/2002.08404/) (2020)
- [Scaling and renormalization in high-dimensional regression](https://mlsanity.com/paper/2405.00592/) (2024)
- [Correcting Biased Centered Kernel Alignment Measures in Biological and Artificial Neural Networks](https://mlsanity.com/paper/2405.01012/) (2024)
- [A Spectral Theory of Neural Prediction and Alignment](https://mlsanity.com/paper/2309.12821/) (2023)
- [Statistical inference on representational geometries](https://mlsanity.com/paper/2112.09200/) (2021)
- [Spectrum Estimation from Samples](https://mlsanity.com/paper/1602.00061/) (2016)
- [Universal scale-free representations in human visual cortex](https://mlsanity.com/paper/2409.06843/) (2024)
- [Estimating Shape Distances on Neural Representations with Limited Samples](https://mlsanity.com/paper/2310.05742/) (2023)
- [Random projections of random manifolds](https://mlsanity.com/paper/1607.04331/) (2016)
- [Estimating the Spectral Moments of the Kernel Integral Operator from Finite Sample Matrices](https://mlsanity.com/paper/2410.17998/) (2024)

## Built on by (most cited first, 2 of 2)

- [AWM: Accurate Weight-Matrix Fingerprint for Large Language Models](https://mlsanity.com/paper/2510.06738/) (2025)
- [Signal-to-Noise Ratio and Sample Size Govern Representational Alignment in Neural Networks](https://mlsanity.com/paper/2605.26973/) (2026)

## Abstract (arXiv)

Understanding representational similarity between neural recordings and computational models is essential for neuroscience, yet remains challenging to measure reliably due to the constraints on the number of neurons that can be recorded simultaneously. In this work, we apply tools from Random Matrix Theory to investigate how such limitations affect similarity measures, focusing on Centered Kernel Alignment (CKA) and Canonical Correlation Analysis (CCA). We propose an analytical framework for representational similarity analysis that relates measured similarities to the spectral properties of the underlying representations. We demonstrate that neural similarities are systematically underestimated under finite neuron sampling, mainly due to eigenvector delocalization. Moreover, for power-law population spectra, we show that the number of localized eigenvectors scales as the square root of the number of recorded neurons, providing a simple rule of thumb for practitioners. To overcome sampling bias, we introduce a denoising method to infer population-level similarity, enabling accurate analysis even with small neuron samples. Theoretical predictions are validated on synthetic and real datasets, offering practical strategies for interpreting neural data under finite sampling constraints.