NeuralFieldManifold: Uncovering the Manifold Geometry of Local Field Potentials

Lag-embedded local field potential dynamics lie on a low-dimensional K-torus, where K matches sustained oscillatory modes, with topology preserved under nonstationary neuronal processes.

• Why it matters: Neural manifold methods have largely targeted spiking, leaving the geometric rules for LFP population signals—central to clinical and brain-computer interface work—unclear.
• What they did: The authors model LFPs as bounded autoregressive processes and introduce DeepLagField, a physics-informed network that estimates time-varying AR structure and effective model order while preserving toroidal geometry.
• The result: Persistent homology on primate V1 LFP, rodent hippocampal LFP, and mouse cortical EEG shows torus-consistent Betti-number signatures, and decoding uses these structures to rival conventional spectral features.

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