democratic_pooling.py

    def forward(self, x):
        x = self.features(x)
        [bs, ch, h, w] = x.shape
        x = x.view(bs, ch, -1).transpose(2, 1)
        # x.register_hook(self.save_grad('x'))

        # Gram Matrix NxN for the N input features "x"
        K = x.bmm(x.transpose(2, 1))
        K = x * x;   # < --- IS THIS CORRECT for 1st order features????

        alpha = torch.autograd.Variable(torch.ones(bs, h*w, 1)).cuda()
        Ci = torch.sum(K, 2, keepdim=True)
        mask = Ci < 1e-10
        mask = mask.detach()
        Ci = torch.pow(Ci, self.gamma)
        Ci[mask] = 0
        Ci = Ci.detach()

        # Sinkhorn iterations
        for _ in range(10):
            alpha = torch.pow(alpha + 1e-10, 1-self.sinkhorn_t) / \
                    (torch.pow(K.bmm(alpha) + 1e-10, self.sinkhorn_t) + 1e-10)

        # x = x * torch.pow(alpha, 0.5)
        # x = x.transpose(1, 2).bmm(x).view(bs, -1)  # EDIT THIS OUT FOR FIRST ORDER ????
        x = x * alpha 

        x = torch.sqrt(x + 1e-8)
        x = torch.nn.functional.normalize(x)

        x = self.fc(x)

        return x