1. The document presents a method for deep learning using variational autoencoders that model the relationship between pairs of data points (x1, x2). 2. It introduces variables to represent latent vectors z and z~ that are used to generate x1 and x2, as well as a subset S of dimensions that relate x1 and x2. 3. The method works by training an encoder qφ(z|x) to approximate a prior p(z) and maximiz