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Estimating Dimensionality of Neural Representations from Finite Samples

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 7.3Download Report PDF
Dimensionalityestimatorneuroscience
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.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper proposes a bias-corrected estimator for the participation ratio of eigenvalues to measure global dimensionality of neural representation manifolds from finite samples. It resides in the 'Finite-Sample Bias Correction Techniques' leaf, which contains only two papers total (including this one). This places the work in a relatively sparse research direction within the broader taxonomy of 16 papers across 13 leaf nodes. The sibling paper in this leaf also addresses finite-sample correction, suggesting this specific methodological niche—correcting bias in dimensionality measures under limited sampling—is not yet crowded but represents a recognized gap in the field.

The taxonomy tree reveals that neighboring leaves focus on general intrinsic dimension estimation approaches (three papers using nearest-neighbor and correlation-based techniques) and Bayesian nonparametric methods (one paper). These adjacent directions do not explicitly emphasize finite-sample bias correction, instead offering broader algorithmic frameworks. The paper's position bridges methodological development (Intrinsic Dimensionality Estimation Methods branch) with applications to both biological neural recordings and artificial neural networks, connecting to separate branches that examine dimensionality in biological systems (three papers across cortical, hippocampal, and multi-electrode studies) and artificial systems (two papers on deep network representations). This cross-branch applicability distinguishes the work from purely algorithmic or purely empirical studies.

Among 23 candidates examined across three contributions, none were found to clearly refute any contribution. The bias-corrected participation ratio estimator examined 3 candidates with 0 refutable; the noise correction method examined 10 candidates with 0 refutable; and the weighted framework for local dimensionality examined 10 candidates with 0 refutable. This suggests that within the limited search scope—top-K semantic matches plus citation expansion—no prior work was identified that directly anticipates the specific combination of bias correction, noise handling, and weighted local dimensionality estimation proposed here. The noise correction and weighted framework contributions, each examined against 10 candidates, appear particularly distinct from existing approaches in the sampled literature.

Based on the limited search of 23 candidates, the work appears to occupy a methodologically focused niche with modest prior coverage. The taxonomy structure confirms that finite-sample bias correction is an emerging rather than saturated direction, and the contribution-level statistics indicate no substantial overlap with examined prior work. However, this assessment reflects the scope of semantic search and citation expansion, not an exhaustive survey of all dimensionality estimation literature. The cross-applicability to both biological and artificial neural systems, demonstrated empirically, may represent a practical contribution beyond the core methodological novelty.

Taxonomy

Core-task Taxonomy Papers
16
3
Claimed Contributions
23
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: estimating global dimensionality of neural representation manifolds from finite samples. This field addresses a fundamental challenge in neuroscience and machine learning—determining the intrinsic dimensionality of high-dimensional neural activity or learned representations when only limited observations are available. The taxonomy reveals several complementary perspectives: one branch focuses on intrinsic dimensionality estimation methods themselves, developing algorithms that can handle finite-sample biases and adapt to local manifold structure (e.g., Intrinsic Dimension Undersampled Data[4], Manifold Adaptive Dimension Estimation[8]). Other branches examine neural representation dimensionality in biological systems (Dimensionality Manifold Neural Recordings[2], Dimensionality Inferotemporal Cortex[6]) and artificial systems (Intrinsic Dimensionality Image Representations[1], CNN Compression Intrinsic Dimension[13]), while theoretical frameworks (Multineuronal Dimensionality Theory[5], Statistical Neural Representations[9]) provide formal grounding. Additional branches cover manifold learning techniques for reconstruction (Manifold Flattening Reconstruction[7]) and domain-specific applications spanning cognitive maps to chemical reaction coordinates. A central tension across these branches concerns how to reliably estimate dimensionality when sample sizes are modest relative to ambient dimensionality—a ubiquitous constraint in neural recordings and representation analysis. Many studies grapple with finite-sample biases that can systematically overestimate or underestimate true dimensionality, particularly when data lie on curved or variable-density manifolds. Estimating Dimensionality Finite Samples[0] sits squarely within the methodological branch addressing finite-sample bias correction techniques, closely aligned with work like Intrinsic Dimension Undersampled Data[4] that explicitly tackles undersampling challenges. Compared to broader manifold learning approaches (Geometric Nonlinear Manifold Clustering[3]) or domain-specific applications, this work emphasizes rigorous statistical correction to yield accurate global dimensionality estimates despite sampling limitations—a critical step for interpreting neural coding capacity and representational geometry across both biological and artificial systems.

Claimed Contributions

Bias-corrected estimator for participation ratio of eigenvalues

The authors derive an unbiased estimator of the participation ratio (PR) by correcting finite-sample bias in both the numerator and denominator. This estimator addresses the systematic bias that arises when computing global dimensionality from finite data matrices by averaging only over unequal indices, making it resistant to sample size variations.

3 retrieved papers
Noise correction method for dimensionality estimation

The authors present a method to correct bias from additive or multiplicative noise in dimensionality estimation by using two independent trials of the same stimuli and neurons. This approach requires only two trials and achieves bias reduction of O(1/P + 1/Q), more efficient than naive averaging methods.

10 retrieved papers
Weighted dimensionality framework for local dimensionality estimation

The authors extend their framework to measure local (intrinsic) dimensionality by introducing sample weighting schemes. This weighted approach enables estimation of dimensionality in local neighborhoods of a manifold and is resistant to noise, unlike existing popular local dimensionality estimators such as TwoNN.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Bias-corrected estimator for participation ratio of eigenvalues

The authors derive an unbiased estimator of the participation ratio (PR) by correcting finite-sample bias in both the numerator and denominator. This estimator addresses the systematic bias that arises when computing global dimensionality from finite data matrices by averaging only over unequal indices, making it resistant to sample size variations.

Contribution

Noise correction method for dimensionality estimation

The authors present a method to correct bias from additive or multiplicative noise in dimensionality estimation by using two independent trials of the same stimuli and neurons. This approach requires only two trials and achieves bias reduction of O(1/P + 1/Q), more efficient than naive averaging methods.

Contribution

Weighted dimensionality framework for local dimensionality estimation

The authors extend their framework to measure local (intrinsic) dimensionality by introducing sample weighting schemes. This weighted approach enables estimation of dimensionality in local neighborhoods of a manifold and is resistant to noise, unlike existing popular local dimensionality estimators such as TwoNN.

Table of Contents