SETSe is a deterministic physics based graph embedding algorithm. It embeds weighted feature rich networks. It treats each edge as a spring and each node as a bead whose movement is constrained by the graph adjacency matrix so that the nodes move in parallel planes enforcing a minimum distance between neighboring nodes. The node features act as forces moving the nodes up and down. The network converges to the embedded state when the force produced by each node is equal and opposite to the sum of the forces exerted by its edges, creating a net force of 0.

SETSe has no conventional loss function and does not attempt to place similar nodes close to each other.

**BigGAN-deep** is a deeper version (4x) of [BigGAN](https://paperswithcode.com/method/biggan).  The main difference is a slightly differently designed [residual block](https://paperswithcode.com/method/residual-block). Here the $z$ vector is concatenated with the conditional vector without splitting it into chunks.  It is also based on residual blocks with bottlenecks. BigGAN-deep uses a different strategy than BigGAN aimed at preserving identity throughout the skip connections. In G, where the number of channels needs to be reduced, BigGAN-deep simply retains the first group of channels and drop the rest to produce the required number of channels. In D, where the number of channels should be increased, BigGAN-deep passes the input channels unperturbed, and concatenates them with the remaining channels produced by a 1 × 1 [convolution](https://paperswithcode.com/method/convolution). As far as the
network configuration is concerned, the discriminator is an exact reflection of the generator. 

There are two blocks at each resolution (BigGAN uses one), and as a result BigGAN-deep is four times
deeper than BigGAN. Despite their increased depth, the BigGAN-deep models have significantly
fewer parameters mainly due to the bottleneck structure of their residual blocks.

BigGAN-deep

Large Scale GAN Training for High Fidelity Natural Image Synthesis

SETSe

**Normalizing Flows** are a method for constructing complex distributions by transforming a
probability density through a series of invertible mappings. By repeatedly applying the rule for change of variables, the initial density ‘flows’ through the sequence of invertible mappings. At the end of this sequence we obtain a valid probability distribution and hence this type of flow is referred to as a normalizing flow.

In the case of finite flows, the basic rule for the transformation of densities considers an invertible, smooth mapping $f : \mathbb{R}^{d} \rightarrow \mathbb{R}^{d}$ with inverse $f^{-1} = g$, i.e. the composition $g \cdot f\left(z\right) = z$. If we use this mapping to transform a random variable $z$ with distribution $q\left(z\right)$, the resulting random variable $z' = f\left(z\right)$ has a distribution:

$$ q\left(\mathbf{z}'\right) = q\left(\mathbf{z}\right)\bigl\vert{\text{det}}\frac{\delta{f}^{-1}}{\delta{\mathbf{z'}}}\bigr\vert = q\left(\mathbf{z}\right)\bigl\vert{\text{det}}\frac{\delta{f}}{\delta{\mathbf{z}}}\bigr\vert ^{-1} $$

where the last equality can be seen by applying the chain rule (inverse function theorem) and is a property of Jacobians of invertible functions. We can construct arbitrarily complex densities by composing several simple maps and successively applying the above equation. The density $q\_{K}\left(\mathbf{z}\right)$ obtained by successively transforming a random variable $z\_{0}$ with distribution $q\_{0}$ through a chain of $K$ transformations $f\_{k}$ is:

$$ z\_{K} = f\_{K} \cdot \dots \cdot f\_{2} \cdot f\_{1}\left(z\_{0}\right) $$

$$ \ln{q}\_{K}\left(z\_{K}\right) = \ln{q}\_{0}\left(z\_{0}\right) − \sum^{K}\_{k=1}\ln\vert\det\frac{\delta{f\_{k}}}{\delta{\mathbf{z\_{k-1}}}}\vert $$

The path traversed by the random variables $z\_{k} = f\_{k}\left(z\_{k-1}\right)$ with initial distribution $q\_{0}\left(z\_{0}\right)$ is called the flow and the path formed by the successive distributions $q\_{k}$ is a normalizing flow.

Year	2000
Data Source	CC BY-SA - https://paperswithcode.com