Questions about prediction of SGNP

Hi @jereliu ,

I have a few questions about the inference stage of SGNP:
1. According to the Eq 9) and Algorithrm 1) in the paper, shouldn't there be K precision matrix for each dimension of the output, where K is the number of class? And the dimension of each one is [ batch_size, batch_size], but the total matrix should be [K, batch_size, batch_size], am I understanding something wrong? And in the codes, I can just find the a single covariance matrix with size of [batch_size, batch_size].
2. After searching the codes for a while, I couldn't find the sampling step which is the 5th step in Algorithm 2). Without this sampling step, the prediction is similar to MAP prediction except for the difference during training. This way to make prediction should be essential in this method, right?

I would appreciate if you can explain more to me.

Best,
Jianxiang