layers.py

import math

import torch

import torch.nn as nn
from torch.nn.parameter import Parameter
from torch.nn.modules.module import Module


class GraphConvolution(Module):
    """
    Simple GCN layer, similar to https://arxiv.org/abs/1609.02907
    from https://github.com/tkipf/pygcn/blob/master/pygcn/layers.py
    """

    def __init__(self, in_features, out_features, bias=True):
        super(GraphConvolution, self).__init__()
        self.in_features = in_features
        self.out_features = out_features
        self.weight = Parameter(torch.FloatTensor(in_features, out_features))
        if bias:
            self.bias = Parameter(torch.FloatTensor(out_features))
        else:
            self.register_parameter('bias', None)
        self.reset_parameters()

    def reset_parameters(self):
        stdv = 1. / math.sqrt(self.weight.size(1))
        self.weight.data.uniform_(-stdv, stdv)
        if self.bias is not None:
            self.bias.data.uniform_(-stdv, stdv)

    def forward(self, input, adj):
        support = torch.mm(input, self.weight)
        output = torch.spmm(adj, support)
        if self.bias is not None:
            return output + self.bias
        else:
            return output

    def __repr__(self):
        return self.__class__.__name__ + ' (' \
               + str(self.in_features) + ' -> ' \
               + str(self.out_features) + ')'



# Adapted from https://github.com/gpeyre/SinkhornAutoDiff
class SinkhornDistance(nn.Module):
    r"""
    Given two empirical measures with n points each with locations x and y,
    outputs an approximation of the regularized OT cost for point clouds.
    Args:
        eps (float): regularization coefficient
        max_iter (int): maximum number of Sinkhorn iterations
        reduction (string, optional): Specifies the reduction to apply to the output:
            'none' | 'mean' | 'sum'. 'none': no reduction will be applied,
            'mean': the sum of the output will be divided by the number of
            elements in the output, 'sum': the output will be summed. Default: 'mean'
    Shape:
        - Input: :math:`(N, \text{in\_features})`, :math:`(N, \text{in\_features})`
        - Output: :math:`(N)` or :math:`()`, depending on `reduction`
    """
    def __init__(self, eps, max_iter, reduction='mean'):
        super(SinkhornDistance, self).__init__()
        self.eps = eps
        self.max_iter = max_iter
        self.reduction = reduction

    def forward(self, x, y):
        # The Sinkhorn algorithm takes as input three variables :
        C = self._cost_matrix(x, y)  # Wasserstein cost function
        n_points = x.shape[-2]
        if x.dim() == 2:
            batch_size = 1
        else:
            batch_size = x.shape[0]

        # both marginals are fixed with equal weights
        mu = torch.empty(batch_size, n_points, dtype=torch.float,
                         requires_grad=False).fill_(1.0 / n_points).squeeze()
        nu = torch.empty(batch_size, n_points, dtype=torch.float,
                         requires_grad=False).fill_(1.0 / n_points).squeeze()

        u = torch.zeros_like(mu)
        v = torch.zeros_like(nu)
        # To check if algorithm terminates because of threshold
        # or max iterations reached
        actual_nits = 0
        # Stopping criterion
        thresh = 1e-1

        # Sinkhorn iterations
        for i in range(self.max_iter):
            u1 = u  # useful to check the update
            u = self.eps * (torch.log(mu+1e-8) - self.lse(self.M(C, u, v))) + u
            v = self.eps * (torch.log(nu+1e-8) - self.lse(self.M(C, u, v).transpose(-2, -1))) + v
            err = (u - u1).abs().sum(-1).mean()

            actual_nits += 1
            if err.item() < thresh:
                break

        U, V = u, v
        # Transport plan pi = diag(a)*K*diag(b)
        pi = torch.exp(self.M(C, U, V))
        # Sinkhorn distance
        cost = torch.sum(pi * C, dim=(-2, -1))

        if self.reduction == 'mean':
            cost = cost.mean()
        elif self.reduction == 'sum':
            cost = cost.sum()

        return cost, pi, C

    def M(self, C, u, v):
        "Modified cost for logarithmic updates"
        "$M_{ij} = (-c_{ij} + u_i + v_j) / \epsilon$"
        return (-C + u.unsqueeze(-1) + v.unsqueeze(-2)) / self.eps

    @staticmethod
    def _cost_matrix(x, y, p=2):
        "Returns the matrix of $|x_i-y_j|^p$."
        x_col = x.unsqueeze(-2)
        y_lin = y.unsqueeze(-3)
        C = torch.sum((torch.abs(x_col - y_lin)) ** p, -1)
        return C

    @staticmethod
    def lse(A):
        "log-sum-exp"
        # add 10^-6 to prevent NaN
        result = torch.log(torch.exp(A).sum(-1) + 1e-6)
        return result

    @staticmethod
    def ave(u, u1, tau):
        "Barycenter subroutine, used by kinetic acceleration through extrapolation."
        return tau * u + (1 - tau) * u1


class AddCoords(nn.Module):

    def __init__(self, with_r=False):
        super().__init__()
        self.with_r = with_r

    def forward(self, input_tensor):
        """
        Args:
            input_tensor: shape(batch, channel, x_dim, y_dim)
        """
        batch_size, _, x_dim, y_dim = input_tensor.size()

        xx_channel = torch.arange(x_dim).repeat(1, y_dim, 1)
        yy_channel = torch.arange(y_dim).repeat(1, x_dim, 1).transpose(1, 2)

        xx_channel = xx_channel.float() / (x_dim - 1)
        yy_channel = yy_channel.float() / (y_dim - 1)

        xx_channel = xx_channel * 2 - 1
        yy_channel = yy_channel * 2 - 1

        xx_channel = xx_channel.repeat(batch_size, 1, 1, 1).transpose(2, 3)
        yy_channel = yy_channel.repeat(batch_size, 1, 1, 1).transpose(2, 3)

        ret = torch.cat([
            input_tensor,
            xx_channel.type_as(input_tensor),
            yy_channel.type_as(input_tensor)], dim=1)

        if self.with_r:
            rr = torch.sqrt(torch.pow(xx_channel.type_as(input_tensor) - 0.5, 2) + torch.pow(yy_channel.type_as(input_tensor) - 0.5, 2))
            ret = torch.cat([ret, rr], dim=1)

        return ret


class CoordConv(nn.Module):

    def __init__(self, in_channels, out_channels, with_r=False, **kwargs):
        super().__init__()
        self.addcoords = AddCoords(with_r=with_r)
        in_size = in_channels+2
        if with_r:
            in_size += 1
        self.conv = nn.Conv2d(in_size, out_channels, **kwargs)

    def forward(self, x):
        ret = self.addcoords(x)
        ret = self.conv(ret)
        return ret