PHINN-EEG: Topological Time-Series Analysis of Dream-State EEG -- Dynamic Betti Curves for Dream Content Classification and Topology-Conditioned Neural Signal Synthesis

Dream detection from EEG has long relied on spectral power features, capping performance around 0.70 AUC. This paper reframes the problem geometrically: by embedding EEG signals in phase space and tracking topological features (Betti curves) across sliding windows, it captures the shape of brain dynamics rather than just energy content. Combined with a topology-conditioned generative model for synthesizing dream-state EEG, the approach targets substantially higher classification accuracy (0.82-0.90 AUC). Potential applications include wearable brain-computer interfaces for sleep and dream monitoring, clinical sleep diagnostics, and generating synthetic EEG data to augment scarce dream-state datasets for future research. Authors: Ren Takahashi, Emre Yusuf, Jayabrata Bhaduri Paper: https://arxiv.org/abs/2607.09662v1