The inception score is the most widely used scoring algorithm for GANs. It uses a pre-trained inception V3 network (trained on Imagenet) to extract the features of both generated and real images. It was proposed by Shane Barrat and Rishi Sharma in their paper, A Note on the Inception Score (https://arxiv.org/pdf/1801.01973.pdf). The inception score, or IS for short, measure the quality and the diversity of the generated images. Let's look at the equation for IS:
In the preceding equation, notation x represents a sample, sampled from a distribution. 
and 
represent the same concept. 
is the conditional class distribution, and 
is the marginal class distribution.
To calculate the inception score, perform the following steps:
- Start by sampling N number of images generated by the model, denoted as
- Then, construct the marginal class distribution, using the following equation:
- Then, calculate the KL divergence and the expected improvement, using the following equation:
- Finally, calculate the exponential of the result to give us the inception score.
The quality of the model is good if it has a high inception score. Even though this is an important measure, it has certain problems. For example, it shows a good level of accuracy even when the model generates one image per class, which means the model lacks diversity. To resolve this problem, other performance measures were proposed. We will look at one of these in the following section.