Post-Hoc Wasserstein Certificates for Autoencoder Reconstructions

Abstract

Assessment of autoencoders is frequently constrained to average empirical losses, which lack principled and distributional guarantees. Existing methods incorporating optimal transport are training-centric and fail to provide post-hoc certificates for a trained model. In this paper, we derive a high-probability, data-dependent upper bound on the Wasserstein-1 distance between the input and reconstruction distributions. The bound is computed directly from the empirical mean absolute error on a hold-out set, requiring neither retraining nor the use of an optimal transport solver. We provide an explicit finite-sample deviation radius scaling. Moreover, we introduce an analytic attribution framework based on a joint-Gaussian surrogate, which provides interpretable insight into the structure of the reconstruction error. This framework decomposes the expected reconstruction loss into bias, variance, and alignment components in closed form. This enables an auditable procedure for both certifying and diagnosing autoencoder reconstructions.