**Concatenation Affinity** is a type of affinity or self-similarity function between two points $\mathbb{x\_{i}}$ and $\mathbb{x\_{j}}$ that uses a concatenation function:

$$ f\left(\mathbb{x\_{i}}, \mathbb{x\_{j}}\right) = \text{ReLU}\left(\mathbb{w}^{T}\_{f}\left[\theta\left(\mathbb{x}\_{i}\right), \phi\left(\mathbb{x}\_{j}\right)\right]\right)$$

Here $\left[·, ·\right]$ denotes concatenation and $\mathbb{w}\_{f}$ is a weight vector that projects the concatenated vector to a scalar.

A **Multiplicative LSTM (mLSTM)** is a  recurrent neural network architecture for sequence modelling that combines the long short-term memory ([LSTM](https://paperswithcode.com/method/lstm)) and multiplicative recurrent neural network ([mRNN](https://paperswithcode.com/method/mrnn)) architectures. The mRNN and LSTM architectures can be combined by adding connections from the mRNN’s intermediate state $m\_{t}$ to each gating units in the LSTM.

mLSTM

Multiplicative LSTM for sequence modelling

Concatenation Affinity

Non-local Neural Networks

**Grid Sensitive** is a trick for object detection introduced by [YOLOv4](https://paperswithcode.com/method/yolov4). When we decode the coordinate of the bounding box center $x$ and $y$, in original [YOLOv3](https://paperswithcode.com/method/yolov3), we can get them by

$$
\begin{aligned}
&x=s \cdot\left(g\_{x}+\sigma\left(p\_{x}\right)\right) \\
&y=s \cdot\left(g\_{y}+\sigma\left(p\_{y}\right)\right)
\end{aligned}
$$

where $\sigma$ is the sigmoid function, $g\_{x}$ and $g\_{y}$ are integers and $s$ is a scale factor. Obviously, $x$ and $y$ cannot be exactly equal to $s \cdot g\_{x}$ or $s \cdot\left(g\_{x}+1\right)$. This makes it difficult to predict the centres of bounding boxes that just located on the grid boundary. We can address this problem, by changing the equation to

$$
\begin{aligned}
&x=s \cdot\left(g\_{x}+\alpha \cdot \sigma\left(p\_{x}\right)-(\alpha-1) / 2\right) \\
&y=s \cdot\left(g\_{y}+\alpha \cdot \sigma\left(p\_{y}\right)-(\alpha-1) / 2\right)
\end{aligned}
$$

This makes it easier for the model to predict bounding box center exactly located on the grid boundary. The FLOPs added by Grid Sensitive are really small, and can be totally ignored.

Source	Non-local Neural Networks
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com