Title: Neural network architectures for disentangling the multimodal structure of data ensembles. Abstract: We introduce neural network architectures that model the mechanism that generates data and address the difficult problem of disentangling the multimodal structure of data ensembles. We provide (i) an autoencoder-decoder architecture that implements the $M$-mode SVD and (ii) a generalized autoencoder that employs a kernel activation and implements the doubly nonlinear Kernel-MPCA.  The neural network projection architecture decomposes an unlabeled data given an estimated forward model and a set of observations that constrain the solution set.