**Non Maximum Suppression** is a computer vision method that selects a single entity out of many overlapping entities (for example bounding boxes in object detection). The criteria is usually discarding entities that are below a given probability bound. With remaining entities we repeatedly pick the entity with the highest probability, output that as the prediction, and discard any remaining box where a $\text{IoU} \geq 0.5$ with the box output in the previous step.

Image Credit: [Martin Kersner](https://github.com/martinkersner/non-maximum-suppression-cpp)

CP with N3 Regularizer and Relation Prediction

CP-N3-RP

Relation Prediction as an Auxiliary Training Objective for Improving Multi-Relational Graph Representations

Non Maximum Suppression

**AMSBound** is a variant of the [AMSGrad](https://paperswithcode.com/method/amsgrad) stochastic optimizer which is designed to be more robust to extreme learning rates. Dynamic bounds are employed on learning rates, where the lower and upper bound are initialized as zero and infinity respectively, and they both smoothly converge to a constant final step size. AMSBound can be regarded as an adaptive method at the beginning of training, and it gradually and smoothly transforms to [SGD](https://paperswithcode.com/method/sgd) (or with momentum) as time step increases. 

$$ g\_{t} = \nabla{f}\_{t}\left(x\_{t}\right) $$

$$ m\_{t} = \beta\_{1t}m\_{t-1} + \left(1-\beta\_{1t}\right)g\_{t} $$

$$ v\_{t} = \beta\_{2}v\_{t-1} + \left(1-\beta\_{2}\right)g\_{t}^{2}$$

$$ \hat{v}\_{t} = \max\left(\hat{v}\_{t-1}, v\_{t}\right) \text{ and } V\_{t} = \text{diag}\left(\hat{v}\_{t}\right) $$

$$ \eta = \text{Clip}\left(\alpha/\sqrt{V\_{t}}, \eta\_{l}\left(t\right), \eta\_{u}\left(t\right)\right) \text{ and } \eta\_{t} = \eta/\sqrt{t} $$

$$ x\_{t+1} = \Pi\_{\mathcal{F}, \text{diag}\left(\eta\_{t}^{-1}\right)}\left(x\_{t} - \eta\_{t} \odot m\_{t} \right) $$

Where $\alpha$ is the initial step size, and $\eta_{l}$ and $\eta_{u}$ are the lower and upper bound functions respectively.

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