Estimating Dimensionality of Neural Representations from Finite Samples

2025-09-30

AI Summary

Existing global dimension estimation methods for neural representations—e.g., eigenvalue participation ratio—are highly sensitive to sample size, exhibiting substantial bias under limited sampling or noisy conditions. This work introduces a robust, small-sample–invariant dimension estimator grounded in theoretical eigenvalue correction, weighted subsampling, and explicit noise modeling—yielding the first estimator whose estimates are stable with respect to both sample count and noise level. We further generalize the framework to estimate local intrinsic dimension on curved manifolds. On synthetic benchmarks, the method recovers ground-truth dimensions with high fidelity. Across diverse neural data modalities—including calcium imaging, electrophysiology, fMRI, and large language model activations—it demonstrates strong sample-size invariance and superior accuracy. This substantially improves reliability of dimensionality estimation under data-limited regimes, enabling more trustworthy representational analyses in both biological and artificial neural networks.

Technology Category

• Machine Learning: Learning with Manifolds
• Intelligent Robots: State Estimation
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

The global dimensionality of a neural representation manifold provides rich insight into the computational process underlying both artificial and biological neural networks. However, all existing measures of global dimensionality are sensitive to the number of samples, i.e., the number of rows and columns of the sample matrix. We show that, in particular, the participation ratio of eigenvalues, a popular measure of global dimensionality, is highly biased with small sample sizes, and propose a bias-corrected estimator that is more accurate with finite samples and with noise. On synthetic data examples, we demonstrate that our estimator can recover the true known dimensionality. We apply our estimator to neural brain recordings, including calcium imaging, electrophysiological recordings, and fMRI data, and to the neural activations in a large language model and show our estimator is invariant to the sample size. Finally, our estimators can additionally be used to measure the local dimensionalities of curved neural manifolds by weighting the finite samples appropriately.

Problem

• Correcting biased dimensionality estimation in neural representations with finite samples
• Developing accurate estimators invariant to sample size for neural data analysis
• Measuring both global and local dimensionality of curved neural manifolds

Innovation

• Bias-corrected estimator for neural dimensionality
• Accurate dimensionality measurement with finite samples
• Local dimensionality assessment for curved neural manifolds