2639ba2137371773aa1e64e7735cdb30-Supplemental.pdf

Supplementary information for "Limiting fluctuation and trajectorial stability of multilayer neural networks with mean field training": Appendix A introduces several preliminaries: new notations and known results from [ 17 ]. Appendix B studies the Gaussian component G and proves Theorem 2 . Appendix C presents the proof of Theorem 3 for well-posedness of R . Appendix D proves Theorem 5 that connects the neural network with the second-order MF limit at the fluctuation level. Appendix E proves Theorem 6 that establishes a central limit theorem for the output fluctuation.