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:
- The entropy of the distribution of labels predicted by the Inceptionv3 model for the generated images is minimized. In other words, the classification model confidently predicts a single label for each image. Intuitively, this corresponds to the desideratum of generated images being "sharp" or "distinct".
- The predictions of the classification model are evenly distributed across all possible labels. This corresponds to the desideratum that the output of the generative model is "diverse".[2]
It has been somewhat superseded by the related Fréchet inception distance.[3] While the Inception Score only evaluates the distribution of generated images, the FID compares the distribution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").
Definition
Let there be two spaces, the space of images and the space of labels . The space of labels is finite.
Let be a probability distribution over that we wish to judge.
Let a discriminator be a function of type where is the set of all probability distributions on . For any image , and any label , let be the probability that image has label , according to the discriminator. It is usually implemented as an Inception-v3 network trained on ImageNet.
The Inception Score of relative to isEquivalent rewrites include is nonnegative by Jensen's inequality.
![{\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)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/36af3ef23e143b66488e00217429a4632314e90c)
![{\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]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5908f9f470b7e2ca1cb788db1bac335e9ac4b72)
![{\displaystyle \ln IS(p_{gen},p_{dis}):=H[\mathbb {E} _{x\sim p_{gen}}[p_{dis}(\cdot |x)]]-\mathbb {E} _{x\sim p_{gen}}[H[p_{dis}(\cdot |x)]]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/57d5b19df57ab5b6f0ab1810141a316929812266)
Pseudocode:
References
- ↑ Salimans, Tim; Goodfellow, Ian; Zaremba, Wojciech; Cheung, Vicki; Radford, Alec; Chen, Xi; Chen, Xi (2016). "Improved Techniques for Training GANs". Advances in Neural Information Processing Systems. 29. Curran Associates, Inc. arXiv:1606.03498.
- ↑ Frolov, Stanislav; Hinz, Tobias; Raue, Federico; Hees, Jörn; Dengel, Andreas (December 2021). "Adversarial text-to-image synthesis: A review". Neural Networks. 144: 187–209. arXiv:2101.09983. doi:10.1016/j.neunet.2021.07.019. PMID 34500257. S2CID 231698782.
- ↑ Borji, Ali (2022). "Pros and cons of GAN evaluation measures: New developments". Computer Vision and Image Understanding. 215 103329. arXiv:2103.09396. doi:10.1016/j.cviu.2021.103329. S2CID 232257836.