Abstract: Existing methods for inferring latent relational structures struggle to integrate partial prior knowledge, such as known edges, node-degree constraints, and global sparsity, without destabilizing training or conflicting with probabilistic assumptions. We propose Soft-Gated Structural Inference (SGSI), a VAE framework that seamlessly incorporates domain constraints via (1) soft gating with learnable edge masks to preserve gradients, (2) cloning-clamping of deterministic edges to avoid distributional conflicts, and (3) adaptive regularization to balance data-driven learning with domain constraints. By excluding known edges from stochastic inference, SGSI reallocates capacity to uncertain interactions, optimizing the information bottleneck trade-off. Experiments on 16 datasets show SGSI improves edge recovery by up to $9$\% AUROC over baselines, scales to larger graphs ($94.2$\% AUROC), and maintains stable training. SGSI bridges domain expertise with data-driven learning, enabling interpretable and robust structural discovery in dynamical systems.

Lay Summary:

Understanding how components in complex systems interact, such as cells in biology or agents in robotics, is crucial for making accurate predictions. However, discovering these interactions from data is often challenging because existing methods struggle to integrate known relationships provided by experts. To tackle this issue, we developed a new approach called Soft-Gated Structural Inference (SGSI).SGSI enhances existing machine learning techniques by smoothly incorporating partial knowledge, such as known connections or expected sparsity, into the learning process. Instead of rigidly enforcing these constraints, SGSI uses a flexible “soft-gating” mechanism that carefully guides the learning without compromising its stability or predictive power.Our extensive experiments showed that SGSI not only improves the accuracy of identifying interactions, up to 9% better than current methods, but also works effectively on larger and more complex datasets. This capability makes SGSI especially valuable for domains like biology, physics, and robotics, where combining expert knowledge with data-driven insights can significantly enhance our understanding of complex systems.