Joint Diffusion Processes as an Inductive Bias in Sheaf Neural Networks

The paper introduces RiSNN with update Fu⊳e(t+1)=MLP(xe xu^T), states Proposition 3.5 asserting feature-wise rotation invariance under a global orthogonal rotation X↦XQ, and proves it by induction (Appendix B). The candidate solution proves the same claim directly by showing that S′eu=(x′e)(x′u)^T equals Seu because x′e=xeQ and x′u=xuQ, hence the MLP’s input is unchanged. The paper’s statement and intent are correct (Proposition 3.5; proof sketch in Appendix B), and the candidate provides a cleaner, one-step argument; the only omission in the candidate is the explicit induction across layers (handled in the paper by taking F(0)=Id). Thus, both are correct and essentially consistent, with different proof presentations. See Proposition 3.5 and its appendix proof for the paper’s version .