**L2M** is a learning algorithm that can work for most cross-domain distribution matching tasks. It automatically learns the cross-domain distribution matching without relying on hand-crafted priors on the matching loss. Instead, L2M reduces the inductive bias by using a meta-network to learn the distribution matching loss in a data-driven way.

**Pixel2Style2Pixel**, or **pSp**, is an image-to-image translation framework that is based on a novel encoder that directly generates a series of style vectors which are fed into a pretrained [StyleGAN](https://paperswithcode.com/method/stylegan) generator, forming the extended $\mathcal{W+}$ latent space. Feature maps are first extracted using a standard feature pyramid over a [ResNet](https://paperswithcode.com/method/resnet) backbone. Then, for each of $18$ target styles, a small mapping network is trained to extract the learned styles from the corresponding feature map, where styles $(0-2)$ are generated from the small feature map, $(3-6)$ from the medium feature map, and $(7-18)$ from the largest feature map. The mapping network, map2style, is a small fully convolutional network, which gradually reduces spatial size using a set of 2-strided convolutions followed by [LeakyReLU](https://paperswithcode.com/method/leaky-relu) activations. Each generated 512 vector, is fed into [StyleGAN](https://paperswithcode.com/method/stylegan), starting from its matching affine transformation, $A$.

pixel2style2pixel

Encoding in Style: a StyleGAN Encoder for Image-to-Image Translation

Learning to Match Distributions for Domain Adaptation

The **Introspective Adversarial Network (IAN)** is a hybridization of [GANs](https://paperswithcode.com/method/gan) and [VAEs](https://paperswithcode.com/method/vae) that leverages the power of the adversarial objective while maintaining the VAE’s efficient inference mechanism. It uses the discriminator of the GAN, $D$, as a feature extractor for an inference subnetwork, $E$, which is implemented as a fully-connected layer on top of the final convolutional layer of the discriminator. We infer latent values $Z \sim E\left(X\right) = q\left(Z\mid{X}\right)$ for reconstruction and sample random values $Z \sim p\left(Z\right)$ from a standard normal for random image generation using the generator network, $G$.

Three distinct loss functions are used:

- $\mathcal{L}\_{img}$, the L1 pixel-wise reconstruction loss, which is preferred to the L2 reconstruction loss for its higher average gradient.
- $\mathcal{L\_{feature}}$, the feature-wise reconstruction loss, evaluated as the L2 difference between the original and reconstruction in the space of the hidden layers of the discriminator.
- $\mathcal{L}\_{adv}$, the ternary adversarial loss, a modification of the adversarial loss that forces the discriminator to label a sample as real, generated, or reconstructed (as opposed to a binary
real vs. generated label).

Including the VAE’s KL divergence between the inferred latents $E\left(X\right)$ and the prior $p\left(Z\right)$, the loss function for the generator and encoder network is thus:

$$\mathcal{L}\_{E, G} = \lambda\_{adv}\mathcal{L}\_{G\_{adv}} + \lambda\_{img}\mathcal{L}\_{img}  + \lambda\_{feature}\mathcal{L}\_{feature}  + D\_{KL}\left(E\left(X\right) || p\left(Z\right)\right) $$

Where the $\lambda$ terms weight the relative importance of each loss. We set $\lambda\_{img}$ to 3 and leave the other terms at 1. The discriminator is updated solely using the ternary adversarial loss. During each training step, the generator produces reconstructions $G\left(E\left(X\right)\right)$ (using the standard VAE reparameterization trick) from data $X$ and random samples $G\left(Z\right)$, while the discriminator observes $X$ as well as the reconstructions and random samples, and both networks are simultaneously updated.

Source	Learning to Match Distributions for Domain Adaptation
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com