Uncovering Trajectory and Topological Signatures in Multimodal Pediatric Sleep Embeddings

Generative models have shown promise in pediatric sleep analysis, but the latent structure of their multimodal embeddings remains poorly understood. We study session-wide diagnostic information contained in sequences of 30-second pediatric polysomnography (PSG) epochs embedded by a multimodal masked autoencoder (PedSleepMAE). We test whether augmenting embeddings with (i) PHATE-derived per-epoch coordinates and whole-night movement descriptors, (ii) persistent-homology summaries of the embedding cloud, and (iii) structured EHR yields task-relevant signals. Simple linear and MLP late-fusion models, chosen for interpretability rather than state-of-the-art performance, show that geometric, topological, and clinical features each provide complementary gains. Across four highly imbalanced binary tasks, AUPRC improves from 0.26$\rightarrow$0.34 (desaturation), 0.31$\rightarrow$0.48 (EEG arousal), 0.09$\rightarrow$0.22 (hypopnea), and 0.05$\rightarrow$0.14 (apnea), and the full fusion model achieves the best calibration (Brier score, ECE). Our results indicate that latent geometry/topology and EHR provide complementary, interpretable signals beyond embeddings and can improve calibration under imbalance.