uNet neural network architecture which takes multiple (X) tensors as input and contains [Spatial Transformer](https://paperswithcode.com/method/spatial-transformer) units (ST)

**Spatial Feature Transform**, or **SFT**, is a layer that generates affine transformation parameters for spatial-wise feature modulation, and was originally proposed within the context of image super-resolution. A Spatial Feature Transform (SFT) layer learns a mapping function $\mathcal{M}$ that outputs a modulation parameter pair $(\mathbf{\gamma}, \mathbf{\beta})$ based on some prior condition $\Psi$. The learned parameter pair adaptively influences the outputs by applying an affine transformation spatially to each intermediate feature maps in an SR network. During testing, only a single forward pass is needed to generate the HR image given the LR input and segmentation probability maps.

More precisely, the prior $\Psi$ is modeled by a pair of affine transformation parameters $(\mathbf{\gamma}, \mathbf{\beta})$ through a mapping function $\mathcal{M}: \Psi \mapsto(\mathbf{\gamma}, \mathbf{\beta})$. Consequently,

$$
\hat{\mathbf{y}}=G_{\mathbf{\theta}}(\mathbf{x} \mid \mathbf{\gamma}, \mathbf{\beta}), \quad(\mathbf{\gamma}, \mathbf{\beta})=\mathcal{M}(\Psi)
$$

After obtaining $(\mathbf{\gamma}, \mathbf{\beta})$ from conditions, the transformation is carried out by scaling and shifting feature maps of a specific layer:

$$
\operatorname{SFT}(\mathbf{F} \mid \mathbf{\gamma}, \mathbf{\beta})=\mathbf{\gamma} \odot \mathbf{F}+\mathbf{\beta}
$$

where $\mathbf{F}$ denotes the feature maps, whose dimension is the same as $\gamma$ and $\mathbf{\beta}$, and $\odot$ is referred to element-wise multiplication, i.e., Hadamard product. Since the spatial dimensions are preserved, the SFT layer not only performs feature-wise manipulation but also spatial-wise transformation.

Spatial Feature Transform

Recovering Realistic Texture in Image Super-resolution by Deep Spatial Feature Transform

uNetXST

A Sim2Real Deep Learning Approach for the Transformation of Images from Multiple Vehicle-Mounted Cameras to a Semantically Segmented Image in Bird's Eye View

A **Highway Layer** contains an information highway to other layers that helps with information flow. It is characterised by the use of a gating unit to help this information flow. 

A plain feedforward neural network typically consists of $L$ layers where the $l$th layer ($l \in ${$1, 2, \dots, L$}) applies a nonlinear transform $H$ (parameterized by $\mathbf{W\_{H,l}}$) on its input $\mathbf{x\_{l}}$ to produce its output $\mathbf{y\_{l}}$. Thus, $\mathbf{x\_{1}}$ is the input to the network and $\mathbf{y\_{L}}$ is the network’s output. Omitting the layer index and biases for clarity,

$$ \mathbf{y} = H\left(\mathbf{x},\mathbf{W\_{H}}\right) $$

$H$ is usually an affine transform followed by a non-linear activation function, but in general it may take other forms. 

For a [highway network](https://paperswithcode.com/method/highway-network), we additionally define two nonlinear transforms $T\left(\mathbf{x},\mathbf{W\_{T}}\right)$ and $C\left(\mathbf{x},\mathbf{W\_{C}}\right)$ such that:

$$ \mathbf{y} = H\left(\mathbf{x},\mathbf{W\_{H}}\right)·T\left(\mathbf{x},\mathbf{W\_{T}}\right) + \mathbf{x}·C\left(\mathbf{x},\mathbf{W\_{C}}\right)$$

We refer to T as the transform gate and C as the carry gate, since they express how much of the output is produced by transforming the input and carrying it, respectively. In the original paper, the authors set $C = 1 − T$, giving:

$$ \mathbf{y} = H\left(\mathbf{x},\mathbf{W\_{H}}\right)·T\left(\mathbf{x},\mathbf{W\_{T}}\right) + \mathbf{x}·\left(1-T\left(\mathbf{x},\mathbf{W\_{T}}\right)\right)$$

The authors set:

$$ T\left(x\right) = \sigma\left(\mathbf{W\_{T}}^{T}\mathbf{x} + \mathbf{b\_{T}}\right) $$

Image: [Sik-Ho Tsang](https://towardsdatascience.com/review-highway-networks-gating-function-to-highway-image-classification-5a33833797b5)

Source	A Sim2Real Deep Learning Approach for the Transformation of Images from Multiple Vehicle-Mounted Cameras to a Semantically Segmented Image in Bird's Eye View
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com