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Certainly! Below is the pseudo code for calculating the Earth Mover's Distance (EMD) loss using PyTorch. This is based on the provided description and algorithm. ```python import torch import torch.nn.functional as F def compute_emd_loss(X, Y, vx, vy, lambda_reg=0.01, num_iters=10): """ Compute the EMD loss between two feature maps X and Y. Args: - X: Feature map of shape (1, 1024, 7, 7) - Y: Feature map of shape (1, 1024, 7, 7) - vx: Embedding vector of shape (1024, 1) - vy: Embedding vector of shape (1024, 1) - lambda_reg: Regularization parameter for Sinkhorn-Knopp algorithm - num_iters: Number of iterations for Sinkhorn-Knopp algorithm Returns: - LEMD: EMD loss """ # Flatten the feature maps X = X.view(1, 1024, -1).squeeze(0).T # Shape: (49, 1024) Y = Y.view(1, 1024, -1).squeeze(0).T # Shape: (49, 1024) # Compute the cost matrix M X_norm = X / X.norm(dim=1, keepdim=True) Y_norm = Y / Y.norm(dim=1, keepdim=True) M = 1 - torch.mm(X_norm, Y_norm.T) # Shape: (49, 49) # Compute marginal weights r and c r = torch.clamp(torch.mm(X, vy), min=0).squeeze() # Shape: (49,) c = torch.clamp(torch.mm(Y, vx), min=0).squeeze() # Shape: (49,) # Initialize u and v for Sinkhorn-Knopp iteration u = torch.ones_like(r) v = torch.ones_like(c) # Sinkhorn-Knopp iteration K = torch.exp(-lambda_reg * M) # Shape: (49, 49) for _ in range(num_iters): u = r / (K @ v) v = c / (K.T @ u) # Compute the optimal transport plan pi* pi_star = torch.diag(u) @ K @ torch.diag(v) # Compute the similarity score S S = torch.sum(pi_star * (1 - M)) # Compute the EMD loss LEMD = 2 - 2 * S return LEMD # Example usage: X = torch.rand(1, 1024, 7, 7) # Example feature map Y = torch.rand(1, 1024, 7, 7) # Example feature map vx = torch.rand(1024, 1) # Example embedding vector vy = torch.rand(1024, 1) # Example embedding vector emd_loss = compute_emd_loss(X, Y, vx, vy) print('EMD Loss:', emd_loss.item()) ``` Explanation: 1. **Flatten the feature maps**: The input feature maps `X` and `Y` of shape `(1, 1024, 7, 7)` are flattened into a shape of `(49, 1024)` to obtain local feature vectors. 2. **Compute the cost matrix `M`**: The cosine similarity between each pair of local feature vectors is computed to form the cost matrix `M`. 3. **Compute marginal weights `r` and `c`**: These are calculated using the provided equations. 4. **Sinkhorn-Knopp iteration**: The optimal transport plan `π*` is computed iteratively. 5. **Compute the similarity score `S`**: The dot-product between the optimal transport plan and the similarity matrix `(1 - M)` is calculated. 6. **Compute the EMD loss**: Finally, the EMD loss is computed using the similarity score. This PyTorch implementation should capture the essence of the EMD loss calculation as described in the provided text.

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