## GAN Feature Matching

Introduced by Salimans et al. in Improved Techniques for Training GANs

Feature Matching is a regularizing objective for a generator in generative adversarial networks that prevents it from overtraining on the current discriminator. Instead of directly maximizing the output of the discriminator, the new objective requires the generator to generate data that matches the statistics of the real data, where we use the discriminator only to specify the statistics that we think are worth matching. Specifically, we train the generator to match the expected value of the features on an intermediate layer of the discriminator. This is a natural choice of statistics for the generator to match, since by training the discriminator we ask it to find those features that are most discriminative of real data versus data generated by the current model.

Letting $\mathbf{f}\left(\mathbf{x}\right)$ denote activations on an intermediate layer of the discriminator, our new objective for the generator is defined as: $||\mathbb{E}_{x\sim p_{data} } \mathbf{f}\left(\mathbf{x}\right) − \mathbb{E}_{\mathbf{z}∼p_{\mathbf{z}}\left(\mathbf{z}\right)}\mathbf{f}\left(G\left(\mathbf{z}\right)\right)||^{2}_{2}$. The discriminator, and hence $\mathbf{f}\left(\mathbf{x}\right)$, are trained as with vanilla GANs. As with regular GAN training, the objective has a fixed point where G exactly matches the distribution of training data.

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PAPER DATE
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