The Inception Score (IS) is an algorithm used to assess the quality of images created by a generative image model such as a generative adversarial network (GAN).
[1] The score is calculated based on the output of a separate, pretrained Inception v3 image classification model applied to a sample of (typically around 30,000) images generated by the generative model.
The Inception Score is maximized when the following conditions are true: It has been somewhat superseded by the related Fréchet inception distance.
[3] While the Inception Score only evaluates the distribution of generated images, the FID compares the distribution of generated images with the distribution of a set of real images ("ground truth").
and the space of labels
The space of labels is finite.
be a probability distribution over
Let a discriminator be a function of type
is the set of all probability distributions on
be the probability that image
It is usually implemented as an Inception-v3 network trained on ImageNet.
The Inception Score of
{\displaystyle IS(p_{gen},p_{dis}):=\exp \left(\mathbb {E} _{x\sim p_{gen}}\left[D_{KL}\left(p_{dis}(\cdot |x)\|\int p_{dis}(\cdot |x)p_{gen}(x)dx\right)\right]\right)}
Equivalent rewrites include
{\displaystyle \ln IS(p_{gen},p_{dis}):=\mathbb {E} _{x\sim p_{gen}}\left[D_{KL}\left(p_{dis}(\cdot |x)\|\mathbb {E} _{x\sim p_{gen}}[p_{dis}(\cdot |x)]\right)\right]}
is nonnegative by Jensen's inequality.
Pseudocode:INPUT discriminator
INPUT generator
Sample images
, the probability distribution over labels conditional on image
Sum up the results to obtain
{\displaystyle \int p_{dis}(\cdot |x)p_{gen}(x)dx}
from generator, and for each, compute
Average the results, and take its exponential.
RETURN the result.A higher inception score is interpreted as "better", as it means that
is a "sharp and distinct" collection of pictures.
is the total number of possible labels.
, discriminator returns exactly the same label predictions
The highest inception score
is achieved if and only if the two conditions are both true: