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Learning Generalizable Reconstruction of High-Dimensional Neural Dynamics

Anima Kujur, Zahra Monfared

arXiv:2608.16569v1cs.LG

TL;DR

Long-duration multichannel neural recordings are difficult to reconstruct while preserving dynamics across subjects and unseen time intervals. PCA-DMD learns latent Koopman dynamics from PCA-compressed recording windows and achieves strong reconstruction, zero-shot cross-subject generalization, temporal prediction, scalability, and external validation.

  • Problem

    Reconstructing long, multichannel neural recordings remains difficult, especially when dynamical representations must generalize across unseen subjects.

  • Method

    PCA-DMD projects overlapping multichannel recording windows into PCA space, learns latent linear Koopman evolution, and reconstructs continuous signals through inverse projection and overlap-add aggregation.

  • Results

    PCA-DMD showed strong reconstruction, zero-shot cross-subject generalization, temporal prediction, scalability, and external validation across hippocampal and independent Neuropixels recordings.

  • Takeaways & Limitations

    PCA-DMD provides a scalable, generalizable, and interpretable framework for reconstructing high-dimensional neural time series.

  • Takeaways & Limitations

    Primary cross-subject experiments used four subjects, so larger and more heterogeneous cohorts are needed to establish population-level generalization.

Abstract

from arXiv · show

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.

1 Introduction

Long-duration multichannel LFP reconstruction is difficult because neural recordings are high-resolution, transient, nonstationary, heterogeneous, and subject-dependent. PCA-DMD addresses these challenges by combining PCA compression, latent Koopman evolution, inverse projection, and overlap-add reconstruction, with benchmarks spanning fidelity, cross-subject transfer, prediction, scalability, external validation, and spectral analysis.

  • Motivation: High-resolution multichannel neural recordings combine transient, nonlinear, heterogeneous dynamics with long observation horizons, making accurate reconstruction a stringent test of learned dynamical structure.The challenge is especially pronounced when recordings contain millions of samples and vary across subjects, sessions, electrodes, and acquisition systems.
  • Method: PCA-DMD explicitly compresses vectorized multichannel windows with PCA, learns Koopman evolution in latent space, and reconstructs recordings through inverse projection and overlap-add aggregation.This computational organization distinguishes PCA-DMD from related Hankel-DMD, delay-coordinate DMD, and HAVOK-type formulations.
  • Evaluation: At 200,000 samples, PCA-DMD achieves the lowest Hellinger distance (HD) and Kullback–Leibler divergence (KLD) among the evaluated DMD variants.The benchmark compares Classical DMD, SpDMD, MrDMD, HODMD, and Hankel-DMD.
  • Generalization: 0.9504-0.9800 correlations in the 300,000-sample all-pair experiment demonstrate cross-subject zero-shot generalization without target-specific fine-tuning.The protocol transfers the learned PCA representation and latent Koopman dynamics across four subjects and evaluates unseen targets.
  • Additional analyses: The study further evaluates one-step prediction on held-out LFP segments, scalability from 400,000 to 900,000 samples, external validation on an independent 93-channel Allen Neuropixels recording, and Koopman spectral and mode analyses.These analyses assess unseen temporal regions, long-horizon reconstruction and computational cost, applicability under different acquisition characteristics, and learned latent-dynamics organization.

2 Related Work

Prior work models neural activity with low-dimensional latent dynamics and increasingly sophisticated Koopman/DMD formulations, but long, multichannel recordings remain difficult to reconstruct. Cross-subject transfer of learned Koopman representations is also comparatively underexplored, motivating the present PCA-DMD extensions.

  • Neural-signal modeling context: Hippocampal SWRs combine fast oscillations with synchronized CA1 firing, while their brief duration, high-frequency content, and channel variability complicate faithful long-duration reconstruction.SWRs are linked to memory consolidation, replay, retrieval, and planning, and suppressing post-learning ripple activity impairs hippocampus-dependent memory.
  • Neural-signal modeling context: Most computational studies detect or classify individual SWR events rather than reconstructing continuous multichannel signals.Existing approaches include convolutional and recurrent detectors, consensus and spatiotemporal classifiers, and topological methods.
  • Latent dynamical representations: Latent state-space, recurrent, variational, and structured dynamical models recover informative trajectories, but recurrent optimization and memory demands worsen for very long, full-resolution recordings.These limitations motivate non-recurrent formulations that retain compact latent representations while supporting direct and interpretable dynamical evolution.
  • Koopman and DMD methods: Koopman theory enables spectral analysis of nonlinear dynamics through linear evolution in observable space, while DMD and its extensions target finite-dimensional, sparse, delayed, higher-order, multiresolution, and streaming representations.Named variants include Extended DMD, HAVOK, SpDMD, HODMD, MrDMD, and streaming or low-storage formulations.
  • Open challenges: Direct DMD remains challenging for long multichannel neural recordings because sliding-window regressions can be high-dimensional and ill-conditioned, rank truncation can remove transient high-frequency components, and operators are usually fit per recording.Prior scalability work primarily addresses storage and incremental computation within a single data stream, leaving cross-subject operator transfer comparatively underexplored.
  • Present work: The present work evaluates PCA-DMD cross-subject generalization through ordered source–target pairs at 300,000 samples, without target-specific fine-tuning, alongside held-out temporal prediction and scalability analyses.These evaluations extend PCA-DMD beyond its original within-subject reconstruction setting.

3 Materials and Data

The study uses multichannel hippocampal LFP recordings from four rodent subjects, with complementary reconstruction, generalization, prediction, and scalability evaluations. An independent 93-channel Allen Neuropixels recording provides external validation under a distinct acquisition configuration.

  • Primary dataset: The primary dataset contains four subjects, S = {S1, S2, S3, S4}, each with C = 8 simultaneously recorded LFP channels.Recordings were collected for sharp wave-ripple analysis from a publicly available repository with expert SWR annotations.
  • Primary dataset: fs = 30,000 Hz supports resolving ripple activity in the 100–250 Hz range, with approximately 22,326,272 samples per channel and roughly 744 seconds of recording.The recordings are continuous and high resolution across channels.
  • Experimental settings: The primary dataset supports within-subject reconstruction, cross-subject zero-shot generalization, out-of-sample temporal prediction, and scalability analysis.Cross-subject evaluation uses ordered source–target pairs without target-specific fine-tuning, while scalability uses source subject S1 and unseen targets S2, S3, and S4.
  • External validation: The independent Allen Neuropixels recording contains 93 channels and approximately 300,000 samples acquired at approximately 1,250 Hz, corresponding to roughly 240 seconds.It comes from the Allen Brain Observatory Visual Coding dataset and is used to assess robustness beyond the primary hippocampal data.
  • External validation: External validation evaluates full-length reconstruction, channel-wise performance, multichannel structure, PCA explained variance, and Koopman spectral properties under a distinct acquisition configuration.The Allen recording differs from the primary dataset in channel dimensionality, sampling rate, recording duration, and acquisition setting.

4 Methods

PCA-DMD reconstructs multichannel LFP recordings by learning linear Koopman evolution in a PCA-compressed latent space from overlapping windows, then inverse-projecting and overlap-adding predicted windows. The methods evaluate within-subject reconstruction, cross-subject zero-shot generalization, temporal prediction, scalability, external validity, and latent spectral structure.

  • PCA-DMD framework: PCA-DMD segments multichannel LFP recordings into overlapping windows, vectorizes them, projects them into a compact PCA space, and learns a linear Koopman operator for latent evolution.Windows are reconstructed through inverse PCA projection and stitched with overlap-add aggregation, optionally using tapering to reduce boundary artifacts.
  • Datasets: The primary dataset contains four hippocampal subjects with eight channels sampled at 30 kHz and recordings ranging from 200,000 to 900,000 samples; an independent Allen Neuropixels recording provides 93-channel external validation.The external recording contains approximately 300,000 samples.
  • PCA-DMD framework: The recordings use windows of length w = 3000 samples and step size δ = 30, with rank-d PCA reducing the window dimension to d ≪ wm.Each vectorized window has dimension wm, where m is the channel count.
  • Evaluation design: Evaluation covers within-subject reconstruction against Classical DMD, SpDMD, MrDMD, and HODMD; all ordered cross-subject pairs without target fine-tuning; held-out temporal prediction; scalability; and external validation.Scalability fits on S1 and applies the model without fine-tuning to S2–S4 across 400,000 to 900,000 samples.
  • Spectral analysis: Koopman eigenvalues and eigenvectors are analyzed to characterize latent stability, persistence, oscillatory behavior, and the spatiotemporal structures represented by the learned dynamics.PCA-induced low-rank compression retains dominant variance while reducing dimensionality for Koopman regression and long-horizon reconstruction.

5 Results

PCA-DMD produced the most accurate reconstructions among evaluated methods and generalized across unseen subjects, longer recordings, and held-out temporal intervals. Its performance remained stable as signal length increased, while computational cost scaled predictably and out-of-sample predictions tracked unseen neural dynamics across channels.

  • Within-subject reconstruction: PCA-DMD achieved the lowest reconstruction errors, with KLD=0.0761 and HD=0.0847, outperforming Classical DMD, HODMD, MrDMD, and SpDMD.It retained slowly varying structure, faster amplitude fluctuations, and multichannel temporal organization more faithfully than the comparison methods.
  • Cross-subject generalization: 0.9504–0.9800 correlations, HD=0.0010–0.0072, and KLD=0.0005–0.0022 demonstrated cross-subject zero-shot reconstruction without target-subject fine-tuning.Classical DMD, HODMD, and HankelDMD produced correlations close to 0.10, while SpDMD reached approximately 0.15–0.27.
  • Scalability: 0.96527 to 0.96812 mean correlation across 400k–900k samples showed stable reconstruction agreement as sequence length more than doubled.Mean HD decreased from 1.360×10−3 to 9.377×10−4, and mean KLD decreased from 9.033×10−4 to 4.223×10−4.
  • Scalability: 31.56 seconds at 400k samples and 47.39 seconds at 900k samples quantified predictable runtime growth, with source fitting dominating the computational cost.At 900k samples, model fitting required 42.23 seconds, whereas target reconstruction required 4.73–6.00 seconds.
  • Out-of-sample temporal prediction: One-step predictions closely tracked unseen LFP temporal structure and amplitude variations across the complete held-out interval and multiple channels.Zoomed regions from the beginning, middle, and end of validation reproduced dominant waveform morphology, including the late interval farthest from the training boundary.

6 Limitations and Future Work

PCA-DMD remains limited by its linear latent representation, narrow validation scope, signal-level metrics, and one-step prediction setup. Future work targets richer nonlinear representations, scalable streaming implementations, broader datasets, downstream neuroscience tasks, and uncertainty quantification.

  • Current limitations: PCA-DMD’s linear PCA basis and finite-dimensional latent operator may miss strongly nonlinear or highly localized neural events.Richer observables may be required, and reconstruction performance also depends on windowing choices.
  • Current limitations: Four-subject cross-subject experiments and an S1-fixed scalability analysis do not establish population-level generalization across subjects, sessions, laboratories, states, or species.The Allen experiment demonstrates external reconstruction robustness, not cross-dataset zero-shot generalization, because the model was fitted directly to that recording.
  • Current limitations: Signal-level metrics do not fully establish preservation of biologically important transient events, motivating event-level analyses of SWR timing, duration, ripple-band power, phase relationships, and propagation.Scalability has been demonstrated up to 900,000 samples, but biological event preservation remains insufficiently validated.
  • Current limitations: One-step prediction from observed states does not demonstrate autonomous long-horizon forecasting, requiring multi-step recursive evaluation and measurement of error accumulation across horizons.The current experiment uses a temporally held-out interval but does not recursively propagate model outputs.
  • Future work: Future work will pursue nonlinear latent models, adaptive windowing, streaming computation, larger multi-institutional datasets, neuroscience applications, and uncertainty quantification.Proposed methods include kernel approaches, autoencoders, incremental PCA, online operator estimation, GPU acceleration, distributed reconstruction, bootstrap analysis, spectral confidence intervals, and ensemble Koopman models.

7 Conclusion

PCA-DMD is presented as a scalable, generalizable, and interpretable framework for reconstructing long-duration, high-dimensional neural recordings. Its evaluation combines latent Koopman modeling with within-subject reconstruction, zero-shot generalization, temporal prediction, scalability testing, external validation, and spectral analysis.

  • Framework: PCA-DMD combines overlapping windows, PCA latent compression, linear Koopman evolution, inverse projection, and overlap-add aggregation for continuous neural-recording reconstruction.The framework also retains an interpretable spectral representation.
  • Empirical evaluation: 0.0761 KLD and 0.0847 HD were achieved on 200,000-sample hippocampal LFP recordings, outperforming the evaluated conventional DMD variants.At 300,000 samples, latent dynamics also demonstrated cross-subject zero-shot generalization across ordered source–target pairs without target-specific fine-tuning.
  • Scalability and validation: 0.965–0.968 mean correlation remained stable as S1-based zero-shot evaluation expanded from 400,000 to 900,000 samples, while HD and KLD decreased and runtime increased predictably.The evaluation covered S2, S3, and S4.
  • Scalability and validation: 0.7427 mean and 0.7990 median channel-wise correlations were obtained on an independent 93-channel Allen Neuropixels recording.This provided external validation beyond the primary hippocampal recordings.
  • Interpretability: Dominant Koopman eigenvalues concentrated near the unit circle, while representative modes revealed structured temporal and channel-wise patterns.These analyses characterize the learned latent dynamics beyond signal-level reconstruction metrics.

Appendix · A Koopman Operator

The Koopman operator analyzes nonlinear dynamical systems through the evolution of observables, yielding a linear but typically infinite-dimensional representation. Koopman mode decomposition expresses these dynamics as linearly evolving modes and underpins data-driven methods such as DMD.

  • A Koopman Operator: The Koopman operator provides a linear perspective on nonlinear dynamical systems by analyzing observables rather than states.
  • A Koopman Operator: For an observable ϕ : H →C, the Koopman operator K is defined through the observable’s evolution.
  • A Koopman Operator: Although the underlying map f may be nonlinear, the Koopman operator K is always linear.
  • A Koopman Operator: The Koopman operator is typically infinite-dimensional, enabling spectral methods for nonlinear dynamics.
  • A Koopman Operator: Koopman eigenfunctions φk and eigenvalues λk characterize the operator’s spectral structure.
  • A Koopman Operator: Under suitable assumptions, the state can be expanded in terms of Koopman eigenfunctions.
  • A Koopman Operator: Koopman mode decomposition expresses nonlinear dynamics as a superposition of modes evolving linearly in time.
  • A Koopman Operator: This decomposition forms the theoretical foundation for data-driven methods such as dynamic mode decomposition (DMD).

B SOTA Methods and their Results on LFP Reconstruction … B.4 MrDMD

The SOTA methods reconstruct LFP recordings by fitting DMD variants to overlapping windows and aggregating predicted snapshots. Classical DMD and SpDMD use rank-8 decompositions, while HODMD and MrDMD add scaling with delay or multiscale decomposition, respectively.

  • B.1 Classical DMD: Classical DMD segments LFP signals into overlapping windows of w = 3000 with step δ = 30 and applies PyDMD using SVD rank r = 8.The transposed snapshot matrix is decomposed, and predictions use the real part of the DMD-reconstructed data.
  • B.1 Classical DMD: Classical DMD reconstructs the full signal by averaging overlapping predicted windows and trimming the output to t ∈[δ, min(N, T −δ)].The overlap count c(t) weights the window aggregation.
  • B.2 SpDMD: SpDMD uses the same w = 3000 and δ = 30 overlapping-window scheme with SVD rank r = 8 and sparsity parameter ρ = 10−6.It fits PyDMD’s SpDMD directly on the transposed window matrix and forms predictions from the real part of reconstructed data.
  • B.2 SpDMD: SpDMD forms the full reconstruction by averaging overlapping windows, counting coverage with c(t), and trimming to t ∈[δ, min(N, T −δ)].Predicted snapshots use Xpred = Re(ΦΛb), with b derived from the initial snapshot projection.
  • B.3 HODMD: HODMD reconstructs the signal through overlapping-window averaging, using c(t) for coverage and trimming the output to t ∈[δ, min(N, T −δ)].Predictions are generated from shifted windows after StandardScaler transformation.
  • B.4 MrDMD: MrDMD standardizes w = 3000, δ = 30 overlapping windows and applies a base DMD with SVD rank r = 8, maximum level L = 2, and maximum cycles C = 1.The method fits scaled transposed matrices for multiscale decomposition.
  • B.4 MrDMD: MrDMD inverse-scales reconstructed snapshots and assembles the full signal through overlapping averages, with output trimmed to t ∈[δ, min(N, T −δ)].Predictions use Xpred = Re(MrDMD(StandardScaler(X))T ).

C (Hyper)parameters

This section lists parameter abbreviations and the parameters used across PCA-DMD and four comparison methods.

  • Table 5 presents short forms of parameters.
  • Table 6 reports parameters for PCA-DMD, Classical DMD, SpDMD, HODMD, and MrDMD.

D Evaluation Measures · D.1 Kullback-Leibler divergence (KLD) · D.2 Hellinger Distance

The evaluation measures quantify geometric agreement between true and reconstructed LFP trajectories using KLD and temporal agreement using Hellinger distance. Both measures are computed channel-wise across eight LFP channels from histogram- or spectrum-based representations.

  • D Evaluation Measures: KLD evaluates geometrical agreement between true and reconstructed LFP signals for PCA-DMD and four DMD-based methods.The compared methods are Classical DMD, SpDMD, MrDMD, and HODMD.
  • D.1 Kullback-Leibler divergence (KLD): For each of eight LFP channels, KLD compares probability distributions p(x) and q(x) estimated from true and reconstructed trajectories.The distributions are estimated in the observation space.
  • D.1 Kullback-Leibler divergence (KLD): 100 bins are used to estimate the KLD distributions over trimmed signal segments.The histogram-based computation is applied to the true and reconstructed trajectories.
  • D.2 Hellinger Distance: HD assesses temporal agreement between ground-truth and reconstructed LFP signals and is averaged across eight dynamical variables.HD is bounded between 0 and 1.
  • D.2 Hellinger Distance: 100 bins approximate each channel’s true and reconstructed power spectra over trimmed signal segments for HD computation.The spectra are normalized as part of the histogram-based approximation.
  • D.2 Hellinger Distance: ϵ = 10^-10 regularizes HD for numerical stability, which ranges from 0 for perfect agreement to 1.HD is calculated per channel and then averaged.
  • D.2 Hellinger Distance: For channel i, HD uses normalized power spectra f_i(ω) and g_i(ω) from the true and reconstructed signals.These spectra correspond to the i-th channel.
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