Learning Interpretable Dynamical Representations from Health Time-Series using Spectrogram Cellular Automata

Modern speech models learn powerful latent representations, but these embeddings provide limited insight into how signal structure evolves over time. We introduce Spectrogram Cellular Automata (SCA), a representation that converts speech spectrograms into evolving cellular-automaton states and summarizes their trajectories using interpretable dynamical descriptors of entropy, stability, recurrence, occupancy, fractal complexity, and propagation. We evaluate SCA for depression detection on E-DAIC using subject-disjoint splits and strict training-only fitting of normalization, SMOTE, and PCA to control information leakage. Ablation experiments further isolate the contribution of CA evolution beyond static spectrogram statistics. SCA provides competitive standalone performance and improves several conventional and pretrained representations when fused with them. Preliminary zero-shot evaluation on MODMA provides additional evidence of transfer.