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Exploring the Enigma of Neural Dynamics Through A Scattering-Transform Mixer Landscape for Riemannian Manifold
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Proposes DeepHoloBrain, a physics-informed MLP-Mixer-style model on the SPD Riemannian manifold whose mapping is constrained by graph-harmonic scattering transforms built from the structural connectome, and applies it to fMRI/DWI classification of task, AD diagnosis.
Problem
Existing SPD-manifold deep networks learn unconstrained mapping matrices that lack interpretability, need large data, and transfer poorly; the paper also seeks to understand how static structural connectivity shapes dynamic functional connectivity.
Approach
Replace free mapping matrices with graph-harmonic scattering-transform wavelets derived from the SC Laplacian, applied row-wise and column-wise in an MLP-Mixer structure with block max-pooling to keep outputs SPD, yielding an interpretable SC-FC coupling model.
Key results
- On HCP-Aging task recognition, OURS reaches 0.995 accuracy vs 0.984 for SPDNet (best baseline).
- On OASIS AD risk forecasting, OURS reaches 0.885 accuracy vs 0.871 for SPDNet.
- With HCP-A pre-training and ADNI fine-tuning, OURS+ reaches 0.740 accuracy, versus 0.712 for SPDNet+.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DeepHoloBrain instead of SPDNet | HCP-A task recognition · HCP-A | accuracy: 0.984$\pm$ 0.003 -> 0.995$\pm$ 0.003* | Helped |
| Use DeepHoloBrain instead of SPDNet | OASIS AD risk diagnosis · OASIS | accuracy: 0.871$\pm$ 0.018 -> 0.885$\pm$0.017* | Helped |
| Use DeepHoloBrain instead of SPDNet | ADNI AD risk diagnosis · ADNI | accuracy: 0.800$\pm$0.085 -> 0.820$\pm$ 0.071* | Helped |
| Use DeepHoloBrain with SC and FC rather than FC-only BolT | HCP-A task recognition · HCP-A | accuracy: 0.863 vs. 0.995 | Helped |
| Use DeepHoloBrain with SC and FC rather than FC-only BolT | ADNI AD risk diagnosis · ADNI | accuracy: 0.812 vs. 0.820 | Helped |
| Pretrain on HCP-A, then fine-tune on ADNI | DeepHoloBrain · ADNI AD risk diagnosis | accuracy: 0.7400* | Mixed |
Surprising findings
- GCN-based methods that use SC topology perform poorly on HCP-A task recognition, which the authors attribute to weak correlation between topology and task-driven functional fluctuations.
Limitations
- Proof-of-concept scope; the physics/holography interpretation is largely analogical.
- Small ADNI/OASIS cohorts with high variance across folds (e.g., CDL std 0.623 on OASIS).
- Several reported gains are within overlapping standard deviations, and the claimed significance tests are weakly specified.
Experimental setup
Datasets: HCP-Aging ADNI OASIS
Benchmarks: HCP-Aging task recognition ADNI AD risk classification OASIS AD risk classification
Metrics: accuracy recall F1-score precision AUC
Baselines: SPDNet CDL LEML SPDML AIM RSR DeepO2P GCN GAT GIN BrainNetCNN GraphT
Builds on: SPDNet MLP-Mixer graph wavelet scattering transform holography
Closest papers by meaning
- Riemannian Flow Matching for Brain Connectivity Matrices via Pullback Geometry (NeurIPS 2025 · similarity 0.88)
- MAGNET: Manifold-Aware Graph Diffusion Network for Connectome Generation (NeurIPS 2026 · similarity 0.88)
- $\textit{NeuroPath}$: A Neural Pathway Transformer for Joining the Dots of Human Connectomes (NeurIPS 2024 · similarity 0.87)
- Geometry-Aware Similarity Metrics for Neural Representations on Riemannian and Statistical Manifolds (NeurIPS 2026 · similarity 0.87)
- Functional Connectomes of Neural Networks (AAAI 2025 · similarity 0.86)
- Spiking Graph Neural Network on Riemannian Manifolds (NeurIPS 2024 · similarity 0.86)
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