Animated monkey and mouse LFP delay trajectories

Neural Field Manifold#

Recover low-dimensional manifold geometry from noisy, autocorrelated time series

Overview#

Neural Field Manifold connects local signal dynamics to the geometry of delay embeddings. Use it to process neural recordings, fit autoregressive models, reconstruct delay-coordinate trajectories, and quantify ring and torus geometry.

The framework models local signals as autoregressive processes and relates their oscillatory modes to delay-embedding geometry. Under the paper’s assumptions, K sustained oscillatory modes correspond to a K-torus. The tutorials examine how noise, nonstationarity, and source mixing affect that reconstruction, and compare intrinsic dynamics with PCA dimensionality.

The package includes DeepLagField, a PyTorch model that jointly estimates autoregressive order and time-varying coefficients. NumPy and SciPy tools support classical AR models, synthetic dynamical systems, and geometric fits.

Oscillatory dynamics and delay-coordinate geometry

Installation#

Requires Python 3.10 or later. Install from GitHub while the PyPI release is being prepared:

python -m pip install "neuralfieldmanifold @ git+https://github.com/erfanzabeh/NeuralFieldManifold.git@main"

See Installation for plotting, notebook dependencies, and editable installs.

Quick Start#

Load a bundled recording, process it, and measure its delay geometry:

import neuralfieldmanifold as nfm

recording = nfm.datasets.load("monkey_lfp")
processed = nfm.preprocessing.process(
    recording.signal,
    sampling_rate_hz=recording.sampling_rate_hz,
    config=nfm.preprocessing.PreprocessConfig(
        notch_hz=50,
        band_hz=(1, 50),
        envelope_band_hz=(1, 80),
        envelope_lowpass_hz=3,
    ),
)
cloud = nfm.embedding.delay(processed.signal, dimension=3, tau_samples=30)
fit = nfm.geometry.fit_torus(cloud)
print(f"Torus score: {fit.score:.3f}; error: {fit.error:.3f}")

Use your own one-dimensional signal and sampling rate in place of the sample. Choose filtering bands and delays appropriate to that recording. Continue with Getting Started or browse the API Reference.

Foundations#

Explore intrinsic and embedding dimensions, oscillatory dynamics, and synthetic manifold reconstruction in the tutorial library.

Demonstrations#

The tutorial library includes monkey V1 LFP, mice hippocampus EEG and LFP, and DeepLagField training examples, with saved figures and complete analysis code.

Contributors#

Citation#

If you use Neural Field Manifold in your research, please cite:

@inproceedings{fallah2026neuralfieldmanifold,
  title     = {{NeuralFieldManifold}: Reconstruction of {LFP} Manifold with Lag Embedding},
  author    = {Fallah, Kasra and Chen, Haoyu Novak and Singha, Rudramani and Kong, Eunji and Turi, Gergely and Losonczy, Attila and Zabeh, Erfan},
  booktitle = {Advances in Neural Information Processing Systems},
  year      = {2026},
}