**DynaBERT** is a [BERT](https://paperswithcode.com/method/bert)-variant which can flexibly adjust the size and latency by selecting adaptive width and depth. The training process of DynaBERT includes first training a width-adaptive BERT and then allowing both adaptive width and depth, by distilling knowledge from the full-sized model to small sub-networks. Network rewiring is also used to keep the more important attention heads and neurons shared by more sub-networks. 

A two-stage procedure is used to train DynaBERT. First, using knowledge distillation (dashed lines) to transfer the knowledge from a fixed teacher model to student sub-networks with adaptive width in DynaBERTW. Then, using knowledge distillation (dashed lines) to transfer the knowledge from a trained DynaBERTW to student sub-networks with adaptive width and depth in DynaBERT.

**Graph Path Feature Learning** is a probabilistic rule learner optimized to mine instantiated first-order logic rules from knowledge graphs. Instantiated rules contain constants extracted from KGs. Compared to abstract rules that contain no constants, instantiated rules are capable of explaining and expressing concepts in more detail. GPFL utilizes a novel two-stage rule generation mechanism that first generalizes extracted paths into templates that are acyclic abstract rules until a certain degree of template saturation is achieved, then specializes the generated templates into instantiated rules.

GPFL

Towards Learning Instantiated Logical Rules from Knowledge Graphs

DynaBERT

DynaBERT: Dynamic BERT with Adaptive Width and Depth

**Precise RoI Pooling**, or **PrRoI Pooling**, is a region of interest feature extractor that avoids any quantization of coordinates and has a continuous gradient on bounding box coordinates. Given the feature map $\mathcal{F}$ before RoI/PrRoI Pooling (eg from Conv4 in [ResNet](https://paperswithcode.com/method/resnet)-50), let $w_{i,j}$ be the feature at one discrete location $(i,j)$ on the feature map. Using bilinear interpolation, the discrete feature map can be considered continuous at any continuous coordinates $(x,y)$:

$$
f(x,y) = \sum_{i,j}IC(x,y,i,j) \times w_{i,j},
$$

where $IC(x,y,i,j) = max(0,1-|x-i|)\times max(0,1-|y-j|)$ is the interpolation coefficient. Then denote a bin of a RoI as $bin=\{(x_1,y_1),(x_2,y_2)\}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are the continuous coordinates of the top-left and bottom-right points, respectively. We perform pooling (e.g. [average pooling](https://paperswithcode.com/method/average-pooling)) given $bin$ and feature map $\mathcal{F}$ by computing a two-order integral:

Source	DynaBERT: Dynamic BERT with Adaptive Width and Depth
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com