cubic went through several 3D convolutional layers to finally predict its amino acid category and coordinates.

### Aspect-ratio Preserved RoI Layer

In natural images, objects generally have completely different aspect ratios and conventional RoI pooling resizes the regions and abandons the original aspect ratio of the object. It can be seen as aspect-ratio augmentation, which is usually beneficial for the generalization ability of the deep model. However, aspect ratios of different amino acids should be maintained as they actually reflect different categories. We thus proposed an APRoI layer, which first crops the input at the RoI location, and then pads it with zero to a defined size of $W_T \times H_T \times L_T$. Despite its simplicity, the APRoI layer preserved the aspect ratio of the objects and proved to be vital for our amino acid classification.

The back-propagation passes derivatives through the APRoI layer. Let $x_{ijk} \in \mathbb{R}^3$ be the input of the APRoI layer, and $y_{rijk}$ be the layer’s output at voxel index $i,j,k$ from the $r$-th RoI. The APRoI layers back-propagate partial derivative of the loss with respect to each input $x_{ijk}$ as Eqn \[eqn:aproi2\]: $$\begin{aligned}
\begin{split}
   & \frac{\partial L}{\partial x_{ijk}} = \sum_r [i_s\le i < i_e, j_s\le 