Restating the Proof of Linear Convergence for Linear GNNs

We lead the readers through the core proof of a pioneering paper that studies the training dynamics of linear GNNs. First, we reorganize the proof and provide a more concise and reader-friendly version, highlighting several key components. In doing so, we identify a hidden error and correct it, demonstrating that it has no impact on the main result. Additionally, we offer a dialectical discussion on the strengths and an overlooked aspect of the approach.