Implementation of the Dense Synthesizer

I’m trying to understand the Synthesizer paper (https://arxiv.org/pdf/2005.00743.pdf 1) and there’s a description of the dense synthesizer mechanism that should replace the traditional attention model as described in the Transformer architecture.

The Dense Synthesizer is described as such:

So I tried to implement the layer and it looks like this but I’m not sure whether I’m getting it right:

class DenseSynthesizer(nn.Module):
    def __init__(self, l, d):
        super(DenseSynthesizer, self).__init__()
        self.linear1 = nn.Linear(d, l)
        self.linear2 = nn.Linear(l, l)

    def forward(self, x, v):
        # Equation (1) and (2)
        # Shape: l x l
        b = self.linear2(F.relu(self.linear1(x)))   
        # Equation (3)
        # [l x l] x [l x d] -> [l x d]
        return torch.matmul(F.softmax(b), v) 

Usage:

l, d = 4, 5

x, v =  torch.rand(l, d), torch.rand(l, d)

synthesis = DenseSynthesizer(l, d)
synthesis(x, v) 

Example:

x and v are tensors:

x = tensor([[0.0844, 0.2683, 0.4299, 0.1827, 0.1188],
         [0.2793, 0.0389, 0.3834, 0.9897, 0.4197],
         [0.1420, 0.8051, 0.1601, 0.3299, 0.3340],
         [0.8908, 0.1066, 0.1140, 0.7145, 0.3619]])

v = tensor([[0.3806, 0.1775, 0.5457, 0.6746, 0.4505],
         [0.6309, 0.2790, 0.7215, 0.4283, 0.5853],
         [0.7548, 0.6887, 0.0426, 0.1057, 0.7895],
         [0.1881, 0.5334, 0.6834, 0.4845, 0.1960]])

And passing through a forward pass through the dense synthesis, it returns:

>>> synthesis = DenseSynthesizer(l, d)
>>> synthesis(x, v) 

tensor([[0.5371, 0.4528, 0.4560, 0.3735, 0.5492],
        [0.5426, 0.4434, 0.4625, 0.3770, 0.5536],
        [0.5362, 0.4477, 0.4658, 0.3769, 0.5468],
        [0.5430, 0.4461, 0.4559, 0.3755, 0.5551]], grad_fn=<MmBackward>)

Is the implementation and understanding of the dense synthesizer correct?

Theoretically, how is that different from a multi-layered perceptron that takes in two different inputs and makes uses of it at different point in the forward propagation?

from Implementation of the Dense Synthesizer