Analytical Formulation of LFP Manifold

NeurIPS 2025 Workshop NeurReps Submission133 Authors

Keywords: Neural manifolds, Local Field Potential, Autoregressive Models, Dimensionality, Torus, Systems Neuroscience

TL;DR: We introduce an analytical framework that reveals the manifold geometry of lag-embedded LFP signals via a fixed AR(p) model. Each distinct rhythm adds a phase circle—yielding a K-torus—and the predictions are validated on synthetic LFP-like data

Abstract: Manifold geometry has become a powerful lens for understanding how the brain organizes high-dimensional activity into compact, interpretable structure. Most of these insights, however, come from spiking activity, leaving open the question of whether the same geometrical principles extend to local field potentials (LFPs); the collective signals that reflect the coordination of neural populations. Here we take advantage of the spectral structure of LFPs to derive a closed-form analytical expression for their intrinsic dimensionality. We prove the core geometry of this manifold is a K-torus, where the dimension K is determined by the number of distinct oscillatory rhythms. We validate the computational feasibility and theoretical correctness of our framework using a synthetic benchmark with known chaotic dynamics. This work provides a new, analytically grounded language for interpreting population signals, laying the theoretical foundation for transforming noisy LFPs into reusable geometric abstractions.

Submission Number: 133