Learning Generalizable Reconstruction of High-Dimensional Neural Dynamics

Abstract

Accurate reconstruction of long-duration neural recordings is challenging because local field potentials (LFPs) are high-resolution, multichannel, transient, and variable across subjects. We present PCA-DMD, a scalable operator-theoretic framework that segments LFP recordings into overlapping windows, projects them into a compact PCA space, learns linear Koopman evolution in the latent space, and reconstructs continuous signals through inverse projection and overlap-add aggregation. On 200,000-sample hippocampal recordings, PCA-DMD outperformed Classical DMD, SpDMD, MrDMD, and HODMD, achieving KLD=0.0761 and HD=0.0847. In all-pair cross-subject zero-shot generalization at 300,000 samples, correlations were 0.9504-0.9800, with HD=0.0010-0.0072 and KLD=0.0005-0.0022, without target-subject fine-tuning. Out-of-sample temporal prediction showed close one-step agreement on temporally held-out LFP segments across the unseen interval and multiple channels. Scalability analysis from 400,000 to 900,000 samples showed stable zero-shot reconstruction, with mean correlation remaining about 0.965-0.968 while computational cost increased predictably. External validation on an independent 93-channel Allen Neuropixels recording yielded mean and median channel-wise correlations of 0.7427 and 0.7990, respectively. Koopman spectral and mode analyses revealed dominant eigenvalues concentrated near the unit circle. PCA-DMD therefore provides an interpretable, generalizable, and computationally scalable framework for reconstructing high-dimensional neural dynamics.