**Atrous Spatial Pyramid Pooling (ASPP)** is a semantic segmentation module for resampling a given feature layer at multiple rates prior to [convolution](https://paperswithcode.com/method/convolution). This amounts to probing the original image with multiple filters that have complementary effective fields of view, thus capturing objects as well as useful image context at multiple scales. Rather than actually resampling features, the mapping is implemented using multiple parallel atrous convolutional layers with different sampling rates.

**Affine Coupling** is a method for implementing a normalizing flow (where we stack a sequence of invertible bijective transformation functions). Affine coupling is one of these bijective transformation functions. Specifically, it is an example of a reversible transformation where the forward function, the reverse function and the log-determinant are computationally efficient. For the forward function, we split the input dimension into two parts:

$$ \mathbf{x}\_{a}, \mathbf{x}\_{b} = \text{split}\left(\mathbf{x}\right) $$

The second part stays the same $\mathbf{x}\_{b} = \mathbf{y}\_{b}$, while the first part  $\mathbf{x}\_{a}$ undergoes an affine transformation, where the parameters for this transformation are learnt using the second part $\mathbf{x}\_{b}$ being put through a neural network. Together we have:

$$ \left(\log{\mathbf{s}, \mathbf{t}}\right) = \text{NN}\left(\mathbf{x}\_{b}\right) $$

$$ \mathbf{s} = \exp\left(\log{\mathbf{s}}\right) $$

$$ \mathbf{y}\_{a} = \mathbf{s} \odot \mathbf{x}\_{a} + \mathbf{t}  $$

$$ \mathbf{y}\_{b} = \mathbf{x}\_{b} $$

$$ \mathbf{y} = \text{concat}\left(\mathbf{y}\_{a}, \mathbf{y}\_{b}\right) $$

Image: [GLOW](https://paperswithcode.com/method/glow)

Affine Coupling

NICE: Non-linear Independent Components Estimation

ASPP

DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs

A **Boom Layer** is a type of feedforward layer that is closely related to the feedforward layers used in Transformers. The layer takes a vector of the form $v \in \mathbb{R}^{H}$ and uses a matrix
multiplication with a GeLU activation to produce a vector $u \in \mathbb{R}^{N\times{H}}$. We then break $u$ into $N$ vectors and sum those together, producing $w \in \mathbb{R}^{H}$. This minimizes computation and removes an entire matrix of parameters compared to traditional down-projection layers.

The Figure to the right shows the Boom Layer used in the context of [SHA-RNN](https://paperswithcode.com/method/sha-rnn) from the original paper.

Source	DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com