Deep Gaussian Processes on Directed Acyclic Graphs (arXiv:2607.09645)

Summary

This paper introduces deep Gaussian processes (DGPs) defined over directed acyclic graphs (DAGs), enabling the modeling of real-world processes that naturally decompose into compositions of functions along a DAG. The authors — Federico L. Perlino, Oliver Hamelijnck, Adam M. Johansen, and Theodoros Damoulas — provide theoretical analysis of prior collapse behavior in these models and study how graph topology and intermediate observations affect information retention across layers. They derive an almost-sure lower bound on the depth up to which input distinctiveness is preserved. On the inference side, they propose a structured variational approximation that retains graph dependencies, composes uncertainty in a principled way, and captures the explanatory cancellation behavior of collider structures. Empirically, the method achieves state-of-the-art performance on protein signaling networks and multi-fidelity heavy-ion collision simulation tasks. The work bridges deep learning structure and Gaussian process uncertainty quantification for graph-structured compositional modeling.