HPC-GCM: Hierarchical Predictive Coding with Grid Cell Manifolds

A neuromorphic deep learning framework for motor-imagery brain-computer interface (BCI) decoding, unifying hierarchical predictive coding (the Free Energy Principle) with grid-cell-inspired manifold regularization.

Status: Accepted for publication, ICETEFS 2026 Proceedings, SPIE (Scopus-indexed). Paper archived at Zenodo DOI.

What this is

Most deep learning EEG decoders are "black boxes" that learn static, opaque feature maps. HPC-GCM instead pairs two biologically grounded mechanisms:

• Predictive coding (ventral stream): an iterative internal-state update that minimizes the mismatch between top-down predictions and bottom-up sensory error, mirroring cortical microcircuit theory.
• Grid cell manifolds (dorsal stream): recurrent continuous attractor network (CAN) modules with Mexican-hat lateral connectivity, projecting EEG activity onto a toroidal, hexagonally-tiled coordinate system analogous to entorhinal grid cells.

The two streams are fused before a final classifier. The result is a decoder whose internal state can be directly inspected — you can watch its "belief" settle into a stable attractor for a given motor intention, rather than trusting an opaque softmax.

Key results

Evaluated on Schirrmeister et al.'s (2017) High-Gamma Dataset, 14 subjects, 4-class motor imagery (left hand / right hand / feet / rest):

• 84.61% grand mean accuracy across subjects, exceeding the DeepConvNet baseline (84.0%).
• High-performing subjects reached 89–90% accuracy; the model remained above-chance even on its weakest subject (69.52%).
• 98.01% of representational variance captured in the first two principal components of the fused latent space, with visibly separable per-class clusters.
• Statistically significant hexagonal spatial periodicity emerges in the grid-cell layer's learned activations, consistent with biological grid-cell tiling.
• Graceful degradation under stress testing: accuracy stays well above chance (25%) even at 2.0 SD injected noise and with 70% of electrodes dropped out.

One honest caveat, stated plainly in the paper itself: the accuracy improvement over DeepConvNet was not statistically significant in this run (one-sample t-test, p = 0.34), owing to high inter-subject variance. The interpretability and robustness results are the more decisively established contributions here, not raw accuracy superiority.

Repository structure

• models/ — model architecture code (predictive coding module, grid-cell CAN modules, fusion/classifier head)
• notebooks/ — exploratory and results notebooks
• figures/ — generated figures (loss curves, confusion matrices, PCA projections, grid-manifold heatmaps)
• papers/ — the manuscript and related writeups
• HPCGCM_STATS.md — full statistical results referenced in the paper

(Usage/reproduction instructions to be added — see notebooks/ for the current entry points.)

Citation

If you use this work, please cite:

Gorre, R., King, J., Marquez, C.P., Presado, T.O., Bugtai, N. and Munsayac, F.E.T. Jr (2026). Hierarchical Predictive Coding with Grid Cell Manifolds (HPC-GCM): A Neuromorphic Deep Learning Framework for Motor Imagery Brain-Computer Interface Decoding. ICETEFS 2026 Proceedings, SPIE (Scopus-indexed).

License

CC-BY-4.0 (see Zenodo record).