Table 1.

Algorithm 1: Training GATE model using gradients.

Input: ${\left\{A_i\right\}}_{i=1}^n$, ${\left\{z_i\right\}}_{i=1}^n$, geometric matrix B, latent space dimension R.

Randomly initialize θ, $\varphi$

while not converged do

Sample a batch of $\left\{A_i\right\}$ with mini-batch size m, denote as ${𝓐}_m$.

for all $A_i\in {𝓐}_m$ do

Sample ${\epsilon }_i\sim N\left(0,I_R\right)$, and compute$z_i={\mu }_{\varphi }\left(A_i\right)+{\epsilon }_i\odot {\text{Σ}}_{\varphi }\left(A_i\right)$.

Compute the gradients ${\nabla }_{\theta }\widetilde{𝓛}\left(A_i;\theta ,\varphi \right)$ and ${\nabla }_{\varphi }\widetilde{𝓛}\left(A_i;\theta ,\varphi \right)$ with zi.

Average the gradients across the batch.

Update θ, $\varphi$ using gradients of θ, $\varphi$.

Return θ, $\varphi$.