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We study the map learned by a family of autoencoders trained on MNIST, andevaluated on ten different data sets created by the random selection of pixelvalues according to ten different distributions. Specifically, we study theeigenvalues of the Jacobians defined by the weight matrices of the autoencoderat each training and evaluation point. For high enough latent dimension, wefind that each autoencoder reconstructs all the evaluation data sets as similar\emph{generalized characters}, but that this reconstructed \emph{generalizedcharacter} changes across autoencoder. Eigenvalue analysis shows that even whenthe reconstructed image appears to be an MNIST character for all out ofdistribution data sets, not all have latent representations that are close tothe latent representation of MNIST characters. All told, the eigenvalueanalysis demonstrated a great deal of geometric instability of the autoencoderboth as a function on out of distribution inputs, and across architectures onthe same set of inputs.

Geometric instability of out of distribution data across autoencoder architecture