Multimodal Teacher Forcing for Reconstructing Nonlinear Dynamical Systems

The candidate solution derives exactly the same consistency loss and total MVAE-TF objective as the paper: starting from the MVAE negative ELBO (Eq. 5), instantiating the prior with timewise Gaussians centered at z_{1:K,t}, noting the t=1 term vanishes because z1 is initialized from \tilde z1, and arriving at L_cons in Eq. 8; then combining with the dendPLRNN likelihood to get L_total in Eq. 9 . The only minor notational mismatch is that the paper’s L_MVAE in Eq. 9 refers to the reconstruction plus entropy terms (first and third terms of Eq. 5), whereas the model first wrote L_MVAE as the full negative ELBO before replacing the prior term with L_cons; the final expression still matches the paper’s Eq. 9 .