# Learning Generalizable Reconstruction of High-Dimensional Neural Dynamics

arXiv: https://arxiv.org/abs/2608.16569 · HTML: https://mlsanity.com/paper/2608.16569/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 66 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Generalized Teacher Forcing for Learning Chaotic Dynamics](https://mlsanity.com/paper/2306.04406/) (2023)
- [Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems](https://mlsanity.com/paper/2207.02542/) (2022)
- [Sparsity-promoting dynamic mode decomposition](https://mlsanity.com/paper/1309.4165/) (2013)
- [LFADS - Latent Factor Analysis via Dynamical Systems](https://mlsanity.com/paper/1608.06315/) (2016)
- [Adversarial Domain Adaptation for Stable Brain-Machine Interfaces](https://mlsanity.com/paper/1810.00045/) (2018)
- [A scalable generative model for dynamical system reconstruction from neuroimaging data](https://mlsanity.com/paper/2411.02949/) (2024)
- [From univariate to multivariate coupling between continuous signals and point processes: a mathematical framework](https://mlsanity.com/paper/2005.04034/) (2020)
- [Cross-Subject Generalization for EEG Decoding: A Survey of Deep Learning Methods](https://mlsanity.com/paper/2604.27033/) (2026)
- [Zero-Shot Neural Priors for Generalizable Cross-Subject and Cross-Task EEG Decoding](https://mlsanity.com/paper/2606.23706/) (2026)

## Abstract (arXiv)

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. The 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.