The Truncation Trick is a technique used in generative adversarial networks (GANs) to sample from a truncated normal distribution. This procedure was first introduced in a paper called Megapixel Size Image Creation with GAN and has since been used in other GAN models such as BigGAN.

What is a Generative Adversarial Network?

Before discussing the Truncation Trick, it is helpful to know what a GAN is. A GAN is a type of artificial intelligence that learns to generate new data after being trained on a set of existing data. It consists of two parts: a generator and a discriminator.

The generator creates new data that is similar to the existing data. The discriminator determines whether the data is real (from the training set) or fake (generated by the generator). The two parts work together in a game-like scenario where the generator tries to fool the discriminator, and the discriminator tries to distinguish real data from fake data. As the two parts play this game, the generator gets better and better at creating new data that is indistinguishable from the real data.

What is the Truncated Normal Distribution?

Now, let's talk about the Truncation Trick. To understand this technique, we must first understand the truncated normal distribution. The normal distribution is a probability distribution that represents how likely it is that a certain variable falls within a range of values. The truncated normal distribution is a modification of the normal distribution where any values that fall outside of a certain range are "truncated" or cut off, and then resampled to fall within that range.

In the case of GANs, the truncated normal distribution is used to sample values for a random vector called $z$. This vector is fed into the generator and is used to create new data. By truncating the normal distribution, the values of $z$ are limited to a certain range of values, which can help improve the quality of the generated data.

The Benefits of the Truncation Trick

So, why use the Truncation Trick? According to the authors of the BigGAN paper, using the Truncation Trick provides a boost to the Inception Score and FID. The Inception Score is a metric that measures the diversity and quality of the generated data. The FID (Fréchet Inception Distance) measures the similarity between the generated data and the real data. Both of these metrics are used to evaluate the performance of GANs.

The Truncation Trick can help improve these metrics by limiting the range of values that are sampled for $z$. This, in turn, can help the generator produce higher-quality data that is more similar to the real data.

The Truncation Trick is a useful technique for improving the performance of generative adversarial networks. By limiting the range of values that are sampled for $z$, the generator can produce higher-quality data that is more similar to the real data. This technique is particularly useful for models such as BigGAN, where the goal is to generate high-resolution images with a high level of detail.

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