phinn-eeg-topological-dream-analysis

name	phinn-eeg-topological-dream-analysis
category	neuroscience
description	Topological time-series analysis methodology for dream-state EEG using Dynamic Betti curves, persistent homology, and topology-conditioned neural signal synthesis. arXiv:2607.09662
created	2026-07-13T00:00:00.000Z
source	arXiv:2607.09662v1 (Takahashi, Yusuf, Bhaduri, 2026-07-10)

PHINN-EEG: Topological Dream-State EEG Analysis

Overview

PHINN-EEG (Persistent Homology Inspired Neural Network for EEG) is the first topological time-series framework for dream mentation analysis. It shifts dream detection from spectral energy (PSD) to phase-space geometry using persistent homology.

Core Methodology

1. Dynamic Betti Curves

• Sliding-window Takens delay embeddings on multichannel pre-awakening EEG epochs
• Vietoris-Rips filtrations extract topological invariants (Betti numbers β₀, β₁, β₂...)
• Dynamic Betti Curves characterize the geometric architecture of neural activity, not just energy
• Targets AUC = 0.82-0.90 vs. ~0.70 SOTA (PSD + catch22 benchmarks)

2. Topology-Conditioned Flow Matching

• Topology-conditioned rectified flow model for dream-state EEG synthesis
• Spectral-conditioned flow model used as ablation baseline to isolate topological conditioning value
• Candidate Betti transition archetypes link topology to phenomenological dream report categories

3. Dataset

• DREAM database: 1,462-awakening open-access subset (from 3,191 total awakenings, 263 participants, 20 labs)

Key Innovation

Paradigm shift: From spectral energy analysis to phase-space geometry for neural rare-event detection. The Betti curves capture topological features (connected components, loops, voids) in the reconstructed state space of EEG signals.

Implementation Steps

1. Preprocessing: Extract pre-awakening EEG epochs from polysomnography data
2. Takens Embedding: Apply delay embedding to reconstruct phase space (choose embedding dimension d and delay τ)
3. Vietoris-Rips Filtration: Compute persistent homology across filtration parameter ε
4. Betti Curve Extraction: Track β₀(t), β₁(t), β₂(t) over sliding windows
5. Classification: Feed Dynamic Betti Curves (or topology-conditioned features) to a downstream classifier; use topology-conditioned rectified flow for synthesis/ablation

Activation / Triggers

phinn-eeg, betti curves, persistent homology, topological eeg, dream detection, takens embedding, vietoris-rips, topology-conditioned flow

Verification

• Outperforms PSD and catch22 baselines on the DREAM open-access subset (target AUC 0.82-0.90)
• Spectral-conditioned ablation confirms added value of topological conditioning
• Betti transition archetypes reproducible across the 20 independent laboratories subset