Graph Causal Optimal Transport and Wasserstein Distances

What the math gives to ML

The paper provides a principled way to compare distributions under directed causal-information constraints: each local coupling may depend only on variables available at that node's parents. This is more structured than ordinary Wasserstein alignment, because it prevents an optimizer from matching representations using future, descendant, or otherwise inaccessible variables. The transferable asset is the nodewise dynamic-programming decomposition of a graph-constrained transport objective, which can become a differentiable regularizer or routing mechanism for DAG-structured neural networks. The most promising first test is a conditional representation-alignment loss for graph neural networks or multi-stage models, implemented with small conditional Sinkhorn problems at each node.