Calling Information In Message Diffusion Process of Class MessagePassing()

[WYClen]

Hello,
I want to realize convolution given below by using torch_geometric.nn.MessagePassing class:

Given current event $e = (v_i,v_j,t,r)$, where $v_i,v_j,t,r$ denotes the source nodes、target nodes、continuous timestamp and event type respectively.
I want to caculate this function:
$\lambda(e) = \sum_{p\in \mathcal{N}_i,<t} \alpha(p,e)z(v_p,v_j)\kappa_i(t-t_p)$
Where $\alpha(.)$ is the evolved attention mechanism function,$z(.)$ is the node distance measure, and $\kappa_i(.)$ is the time decay function with a learnable personalized
parameter $\delta_i$ .

Now I am puzzled by two problems below:

1.Calling Information In Message Diffusion Process of Class MessagePassing()

The tutorial in the pyg documentation only gives out an resolution by rewriting the method MessagePassing.forward and MessagePassing.message, which only diffuses the message from node j to node i and calls information from node i and j like this:

from torch_geometric.nn import MessagePassing
import torch
class HHP(MessagePassing):
    ...
    def message(self,x_i,x_j,...):
        ...
        return x_i - x_j
    def forward(self,x,...):
        ...
        out = self.propagate(x,...)
        ...

I want to know how to diffuse message from node p to event e,so that I can call information from node i,j,neighborp of node i and event e at the same time. It is great if there is an example or else I can refer to.

2.Parameter $\delta_i$ In $\kappa_i(.)$

Due to the $\delta_i$ is taged with node i, I want to claim a parameter like this:

class HHP(MessagePassing):
    def __init__(self,...):
        self.delta = torch.empty(1,1)
        ...
    def message(self,timestamps_i,timestamps_j):
        return torch.exp(-self.delta*(timestamps_i-timestamps_j))
    def forward(self,timestamp,...):
        out = self.propagate(timestamp,...)
        ...

I want to know if using torch.empty is correctly claim a parameter taged with node i. Should I adopt other method?
Thanks for your attention to my question.