Emergent Language Symbolic Autoencoder (ELSA) with weak supervision to model hierarchical brain networks

Brain networks display hierarchical organization, a complexity that is challenging for deep learning models that are often flat classifiers and lack interpretability. To address this, we propose a novel architecture called the Emergent Language Symbolic Autoencoder (ELSA), a hierarchical symbolic autoencoder informed by weak supervision and an Emergent Language framework that learns to represent brain networks as interpretable symbolic sentences while simultaneously reconstructing the original data. Our framework's primary innovations are a set of hierarchically-aware loss functions and their application to modeling resting-state fMRI networks. By combining weak supervision from Independent Component Analysis (ICA) order with novel Progressive, Strict, and Containing Bias losses, we explicitly enforce a coarse-to-fine structure on the emergent language without requiring extensive manual labeling. We evaluated ELSA on data from the publicly available 1000 Functional Connectomes Project. The model generated sentences with clear hierarchical organization, where early symbols corresponded to broad parent networks and later symbols specified finer sub-networks. With the use of our proposed Progressive Strict loss function and containing bias penalty, the model's hierarchical consistency drastically improves compared to baseline, achieving near-perfect consistency at higher ICA orders and 43.5% at the challenging lowest order. The model also produces qualitatively superior visual progressions of the network reconstructions. By replacing opaque feature vectors with an interpretable symbolic language, ELSA provides a transparent, multi-level description of functional brain organization and offers a general framework for studying other hierarchically structured biomedical data.