Interpret the non-monotonic dependence of the optimal diffusion time on signal strength

Explain and characterize the non-monotonic dependence of the optimal diffusion time t* (the diffusion time that maximizes test accuracy) on the graph signal strength λ in the continuous graph convolutional network trained on the contextual stochastic block model, by providing a theoretical mechanism or analytical description of t*(λ).

Background

Within the continuous-depth GCN analysis, the diffusion time t controls how features propagate over the graph. The authors find an optimal diffusion time t* that maximizes test accuracy and observe that t* depends on the graph signal strength λ.

While limits for small and large t are analytically tractable and show that some diffusion is beneficial but excessive diffusion leads to oversmoothing, the observed non-monotonic dependence of t* on λ lacks a theoretical explanation, prompting a need for an interpretation or underlying mechanism.