Working of Weighted Softmax Attention Layer

I am trying to understand a graph neural network code which has implemented a weighted attention layer as follows:

class WeightedAttention(nn.Module):
    Weighted softmax attention layer
    def __init__(self, gate_nn, message_nn, num_heads=1):
        gate_nn: Variable(nn.Module)
        super(WeightedAttention, self).__init__()
        self.gate_nn = gate_nn
        self.message_nn = message_nn
        self.pow = torch.nn.Parameter(torch.randn((1)))

    def forward(self, fea, index, weights):
        """ forward pass """

        gate = self.gate_nn(fea)

        gate = gate - scatter_max(gate, index, dim=0)[0][index]

        gate = (weights ** self.pow) * gate.exp()
        # gate = weights * gate.exp()
        # gate = gate.exp()
        gate = gate / (scatter_add(gate, index, dim=0)[index] + 1e-13)
        fea = self.message_nn(fea)
        out = scatter_add(gate * fea, index, dim=0)
        return out

    def __repr__(self):
        return '{}(gate_nn={})'.format(self.__class__.__name__,

I am unable to find anything that explains the working of the weighted attention network. Can someone explain what it is and how the code has implemented it using scatter_max and scatter_add? Also is there any mathematical formulae that can be related to this?