What is Inception Score?

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Inception Score (IS)

The Inception Score is a metric used to evaluate the quality of images generated by models like GANs. It was one of the earliest and most popular metrics before FID became standard.

How It Works

1. Image Classification

   • Generated images are fed into a pre-trained Inception-v3 network (trained on ImageNet).

   • For each image, the network outputs a probability distribution over object classes.

2. Two Key Ideas:

   • Image Quality: A good image should look like a clear example of a real object, not blurry or ambiguous.

     • This means the probability distribution (p(y|x)) for a single image should be sharp/peaked (low entropy).

   • Diversity: A good set of generated images should cover many object classes.

     • This means the marginal distribution (p(y)) across all generated images should be spread out/uniform.

3. Mathematical Formula

$$IS = \exp\left( \mathbb{E}_x \left[ KL(p(y|x) \, || \, p(y)) \right] \right)$$

Where:

• $p(y|x)$ = conditional label distribution for image $x$.

• $p(y)$ = marginal distribution across all generated images.

• KL divergence measures how different the two distributions are.

Interpretation

• High IS → good images that are both:

  • Sharp and meaningful (high confidence).

  • Diverse across many categories.

• Low IS → blurry, repetitive, or unrealistic images.

👉 Example:

• If all images are of cats → sharp but not diverse → low IS.

• If all images are random noise → diverse but not sharp → low IS.

• Good GANs strike a balance → high IS.

Limitations of IS

• Only measures what the classifier (Inception-v3) sees → can be biased.

• Does not directly compare generated images to real ones (unlike FID).

• Can be fooled if a model generates images that exploit classifier weaknesses.

✅ In summary:
The Inception Score (IS) evaluates generated images based on how clear (low entropy per image) and diverse (high entropy across dataset) they are, using a pre-trained Inception network.

Read more :

What is perplexity in LLM evaluation?

What is FID (Fréchet Inception Distance)?

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