Reviews: Adversarial Fisher Vectors for Unsupervised Representation Learning

This paper continues along a thread in the literature linking GANs and deep energy-based models, the basic idea being that the discriminator can represent an energy function for the distribution and the generator a sampler for the same; this allows, among other things, a sampling approximation of the negative phase term (the gradient of the partition function) using samples from the generator. Taking this view, the manuscript under consideration proposes to leverage the gradient of the discriminator's parameters to produce both Fisher vectors and a (diagonal approximation to the) Fisher information matrix for the model distribution. This allows for a powerful form of unsupervised representation learning, an induced distance metric (both between points and between sets of points, by applying the distance measure to the means of the sets). Overall, I feel this is a solid piece of generative model research. It proposes a fresh take on well-worn territory, makes several principled contributions as regards training methodology, and empirical demonstrate the method's usefulness, in particular a classification result from unsupervised representation learning that is quite impressive.