Appendices This is the supplemental material for Optimization and Generalization Analysis of Transduction through Gradient Boosting and Application to Multi-scale Graph Neural Networks

We give proofs for the theorems and propositions in the order they appeared in the main paper. We prove the more detailed claim. Proposition 1 is a part of the following proposition. The followings are equivalent 1. There exist α,β such that α > β 0 and Z satisfies ( α,β, g)-w.l.c. 2. nullZ, g null > 0 .