Given the task definition and input, reply with output. In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

We introduce a neural architecture to perform amortized approximate Bayesian inference over latent random permutations of two sets of objects. The method involves approximating permanents of matrices of pairwise probabilities using recent ideas on functions defined over sets. Each sampled permutation comes with a probability estimate, a quantity unavailable in MCMC approaches. We illustrate the method in sets of 2D points and MNIST images.
A novel neural architecture for efficient amortized inference over latent permutations