*A paper review summary part of my coursework in IST597: Trustworthy Machine Learning*

## Generative Adversarial Nets

*Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, Yoshua Bengio *

#### Summary

The paper introduces a new framework for estimating generative models via an adversarial process, where two models are simultaneously trained: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1/2 everywhere. The entire system can be trained with backpropagation when G and D are defined by multilayer perceptrons, without the need for Markov chains or unrolled approximate inference networks during either training or generation of samples. The proposed adversarial nets framework can yield specific training algorithms for many kinds of models and optimization algorithms. The document presents theoretical results regarding the global optimality of the proposed framework, showing that the training criterion allows one to recover the data generating distribution as G and D are given enough capacity, i.e., in the non-parametric limit.

#### Results

The proposed adversarial framework involves training two models simultaneously: a generative model G and a discriminative model D. The entire system can be trained with backpropagation when G and D are defined by multilayer perceptrons, without the need for Markov chains or unrolled approximate inference networks during either training or generation of samples. The potential of the framework is demonstrated through qualitative and quantitative evaluation of the generated samples. The experiments show promising results on datasets such as MNIST, the Toronto Face Database (TFD), and CIFAR-10, highlighting the potential of the adversarial framework. The paper also throws light on the differences in training, inference, sampling ang evaluating p(x) among these baselines - Deep Directed Graphical Models, Deep Undirected Graphical Models and Generative Autoencoders.

#### Strengths

The proposed framework appears to use a simplified training process due to the usage of only backpropagation to obtain gradients leading to computational efficiency. A wide variety of functions can be incorporated into the model, providing flexibility in modeling different types of data distributions. Since the generator network is not updated directly with data examples, but only with gradients flowing through the discriminator providing statistical advantage.

#### Possible directions for future work

While the paper stands strong in its claims, an observation is that there is a risk of mode collapse, where the generator collapses to produce limited varieties of samples, reducing the diversity of generated data. The need for well-synchronized training between the generative model G and the discriminative model D is highlighted. If G is trained too much without updating D, it may lead to a scenario where G collapses too many values of z to the same value of x, potentially reducing the diversity needed to model the data distribution.