Historical Constraints on Neural State Space: Measuring Assembly Depth via Eigenvalue Distribution Structure

A tractable measure called Participation Ratio (PR), derived from the distribution of eigenvalues in neural activity covariance matrices, can distinguish biological from artificial information processing without computationally expensive methods. Simulations show that biological systems with history-dependent gain actively reduce the effective dimensionality of their state space in a way that resists input variability, whereas artificial systems with fixed gain passively reflect input diversity as high-dimensional spread. This active low-dimensionalization is explained by the Maximum Entropy principle, where history-dependent gain imposes structured constraints that converge toward a low-PR attractor state regardless of environmental changes. The measure offers a practical, neurobiologically grounded index for comparing biological and artificial systems.

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Abstract

A central unresolved question in computational consciousness research concerns whether meaningful differences between biological and artificial systems can be quantified without recourse to computationally intractable measures such as Integrated Information Theory (IIT). We propose Participation Ratio (PR) — derived from the eigenvalue distribution of neural trajectory covariance matrices — as a tractable proxy for the effective dimensionality of state-space usage. We show through simulation that history-dependent (biological) gain formation and fixed (AI-style) gain produce qualitatively distinct PR signatures: biological gain actively low-dimensionalizes the state space in a manner robust to input diversity, while AI fixed gain passively reflects input diversity as high-dimensional spread. This active low-dimensionalization is interpreted via the Maximum Entropy principle (Savin & Tkacik, 2017): history-dependent gain formation imposes structured constraints on eigenvalue distributions, converging toward a low-PR attractor state regardless of environmental variability. The result connects to Shine et al. (2018) on gain-mediated segregation/integration transitions, Claudi et al. (2025) MADE framework for attractor manifold topology, and Ferguson & Cardin (2020) on cortical gain modulation mechanisms. We propose PR as a practically computable, neurobiologically grounded index for comparing the structural organization of biological and artificial information processing