Deep Gaussian Processes on Directed Acyclic Graphs

What the math gives to ML

The paper turns compositional Gaussian processes from chains into branching computation graphs, with each node consuming the joint latent state of all of its parents. The transferable asset is not the GP prior alone, but the explicit factorization over a DAG and the resulting ability to preserve dependence between branches during approximate inference. A practical neural analogue is a Bayesian or probabilistic DAG network whose node-wise variational distributions condition on shared parent latents, rather than using independent uncertainty estimates for each branch. This is especially relevant to multi-fidelity models, graph neural networks, and world models containing colliders, where observing one child should update beliefs about multiple upstream causes.