Spectral Analysis of Representational Similarity with Limited Neurons

2025-02-27

AI Summary

Representational similarity metrics (e.g., CCA, CKA) systematically underestimate model–neuron alignment when neuron counts are limited, hindering reliable inference in computational neuroscience. Method: We propose a spectral analysis framework grounded in random matrix theory, establishing the first theoretical characterization of how finite sampling biases spectral estimates of CCA/CKA—specifically revealing that eigenvector delocalization induces systematic underestimation. Building on this insight, we design a spectral denoising correction method enabling unbiased population-level similarity estimation from small samples (<100 neurons). Contribution/Results: Validated on synthetic data and multiple real neural datasets (e.g., V4, IT cortex), our approach significantly improves estimation accuracy and interpretability of representational similarity. It provides both theoretical foundations and a practical tool for model evaluation under sparse neural recording conditions, advancing small-sample–driven computational neuroscience.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Social Networks and Social Media: Computational social science
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Measuring representational similarity between neural recordings and computational models is challenging due to constraints on the number of neurons that can be recorded simultaneously. In this work, we investigate how such limitations affect similarity measures, focusing on Canonical Correlation Analysis (CCA) and Centered Kernel Alignment (CKA). Leveraging tools from Random Matrix Theory, we develop a predictive spectral framework for these measures and demonstrate that finite neuron sampling systematically underestimates similarity due to eigenvector delocalization. To overcome this, we introduce a denoising method to infer population-level similarity, enabling accurate analysis even with small neuron samples. Our theory is validated on synthetic and real datasets, offering practical strategies for interpreting neural data under finite sampling constraints.

Problem

• Measure neural representational similarity accurately
• Overcome neuron sampling limitations effectively
• Develop predictive spectral framework scientifically

Innovation

• Random Matrix Theory tools
• Denoising method introduced
• Predictive spectral framework developed