Paper List

期刊: ArXiv Preprint
发布日期: 2026-03-11
Computational NeuroscienceTheoretical Neuroscience

Linear Readout of Neural Manifolds with Continuous Variables

Department of Physics and Kempner Institute, Harvard University | Center for Computational Neuroscience, Flatiron Institute

Will Slatton, Chi-Ning Chou, SueYeon Chung
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30秒速读

IN SHORT: This paper addresses the core challenge of quantifying how the geometric structure of high-dimensional neural population activity (neural manifolds) determines the efficiency of linearly decoding continuous variables, amidst complex neural variability.

核心创新

  • Theory Develops the first statistical-mechanical theory of 'regression capacity,' extending manifold capacity theory from discrete classification to continuous regression problems.
  • Methodology Derives closed-form analytical formulas for regression capacity in synthetic models (e.g., spherical manifolds) and provides an instance-based estimator applicable to finite, real-world datasets.
  • Biology Applies the framework to primate visual cortex data, quantitatively demonstrating a monotonic increase in linear decodability for object pose parameters (size, position) along the ventral stream (pixels → V4 → IT).

主要结论

  • For synthetic spherical manifold models, regression capacity α decreases with increasing manifold dimensionality D and equivalent radius R_equiv (e.g., capacity drops as D increases for fixed R_equiv).
  • In the mean-field model for point-like manifolds, capacity depends solely on the asymptotically equivalent tolerance ε_equiv = ε/(σ√(1-ρ)), where σ scales labels and ρ controls label correlations.
  • Application to macaque ventral stream data shows regression capacity for object size and position increases (critical dimension N_crit decreases) from early (pixels) to late (IT) processing stages, indicating more efficient geometric organization for linear readout.
研究空白： While manifold capacity theory successfully linked manifold geometry to classification performance, a general theoretical framework connecting manifold geometry to regression (continuous variable decoding) performance was lacking, with existing machine learning approaches offering limited geometric insight.

摘要: Brains and artificial neural networks compute with continuous variables such as object position or stimulus orientation. However, the complex variability in neural responses makes it difficult to link internal representational structure to task performance. We develop a statistical-mechanical theory of regression capacity that relates linear decoding efficiency of continuous variables to geometric properties of neural manifolds. Our theory handles complex neural variability and applies to real data, revealing increasing capacity for decoding object position and size along the monkey visual stream.