**MultiGrain** is a type of image model that learns a single embedding for classes, instances and copies.  In other words, it is a convolutional neural network that is suitable for both image classification and instance retrieval. We learn MultiGrain by jointly training an image embedding for multiple tasks. The resulting representation is compact and can outperform narrowly-trained embeddings. The learned embedding output incorporates different levels of granularity.

A **Projection Discriminator** is a type of discriminator for generative adversarial networks. It is motivated by a probabilistic model in which the distribution of the conditional variable $\textbf{y}$ given $\textbf{x}$ is discrete or uni-modal continuous distributions.

If we look at the original solution for the loss function $\mathcal{L}\_{D}$ in the vanilla GANs, we can decompose it into the sum of two log-likelihood ratios:

$$ f^{*}\left(\mathbf{x}, \mathbf{y}\right) = \log\frac{q\left(\mathbf{x}\mid{\mathbf{y}}\right)q\left(\mathbf{y}\right)}{p\left(\mathbf{x}\mid{\mathbf{y}}\right)p\left(\mathbf{y}\right)} = \log\frac{q\left(\mathbf{y}\mid{\mathbf{x}}\right)}{p\left(\mathbf{y}\mid{\mathbf{x}}\right)} + \log\frac{q\left(\mathbf{x}\right)}{p\left(\mathbf{x}\right)}  = r\left(\mathbf{y\mid{x}}\right) + r\left(\mathbf{x}\right) $$

We can model the log likelihood ratio $r\left(\mathbf{y\mid{x}}\right)$ and  $r\left(\mathbf{x}\right)$ by some parametric functions $f\_{1}$ and $f\_{2}$ respectively. If we make a standing assumption that $p\left(y\mid{x}\right)$ and $q\left(y\mid{x}\right)$ are simple distributions like those that are Gaussian or discrete log linear on the feature space, then the parametrization of the following form becomes natural:

$$ f\left(\mathbf{x}, \mathbf{y}; \theta\right) = f\_{1}\left(\mathbf{x}, \mathbf{y}; \theta\right) + f\_{2}\left(\mathbf{x}; \theta\right) = \mathbf{y}^{T}V\phi\left(\mathbf{x}; \theta\_{\phi}\right) + \psi\left(\phi(\mathbf{x}; \theta\_{\phi}); \theta\_{\psi}\right) $$

where $V$ is the embedding matrix of $y$, $\phi\left(·, \theta\_{\phi}\right)$ is a vector output function of $x$, and $\psi\left(·, \theta\_{\psi}\right)$ is a scalar function of the same $\phi\left(\mathbf{x}; \theta\_{\phi}\right)$ that appears in $f\_{1}$. The learned parameters $\theta = ${$V, \theta\_{\phi}, \theta\_{\psi}$} are trained to optimize the adversarial loss. This model of the discriminator is the projection.

Projection Discriminator

cGANs with Projection Discriminator

MultiGrain

MultiGrain: a unified image embedding for classes and instances

**Revision Network** is a style transfer module that aims to revise the rough stylized image via generating residual details image $r_{c s}$, while the final stylized image is generated by combining $r\_{c s}$ and rough stylized image $\bar{x}\_{c s}$. This procedure ensures that the distribution of global style pattern in $\bar{x}\_{c s}$ is properly kept. Meanwhile, learning to revise local style patterns with residual details image is easier for the Revision Network.

As shown in the Figure, the Revision Network is designed as a simple yet effective encoder-decoder architecture, with only one down-sampling and one up-sampling layer. Further, a [patch discriminator](https://paperswithcode.com/method/patchgan) is used to help Revision Network to capture fine patch textures under adversarial learning setting. The patch discriminator $D$ is defined following SinGAN, where $D$ owns 5 convolution layers and 32 hidden channels. A relatively shallow $D$ is chosen to (1) avoid overfitting since we only have one style image and (2) control the receptive field to ensure D can only capture local patterns.

Source	MultiGrain: a unified image embedding for classes and instances
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com