Unfold the Power of Patches: Exploring PyTorch's Functionality for Deep Learning

Unfold

• Purpose: Extracts patches (local regions) from a tensor in a sliding window fashion, similar to pooling operations (max pooling, average pooling) but with more control over the extraction process. This is commonly used in deep learning architectures like Vision Transformer (ViT).
• Functionality:
  • It iterates over the input tensor, creating blocks (patches) of a specified size (defined by the kernel_size parameter).
  • The stride (defined by the dilation parameter) determines the movement between extracting patches. With a stride equal to the kernel size, there's no overlap between patches. Smaller strides create overlapping patches.
  • The extracted patches are flattened and concatenated into a new tensor.

Fold

• Purpose: The inverse operation of unfold. It takes a tensor of patches and arranges them back into the original format, potentially with overlapping regions.
• Functionality:
  • The input tensor is reshaped into blocks based on the original input dimensions and patch size.
  • Overlapping regions are summed together (unlike convolution, which uses a dot product).

Key Points and Considerations:

• Both fold and unfold are memory-efficient as they don't create actual copies of data, but rather manipulate views of the existing tensor.
• Changes made to the unfolded tensor will be reflected in the original tensor (and vice versa).
• unfold is typically used before feeding data into a deep learning model, while fold is used after processing to reconstruct the output.

Example (Image Patching with Unfold):

import torch

# Sample image tensor (assuming batch size 1 and 3 channels)
img = torch.randn(1, 3, 28, 28)  # Batch size, channels, height, width

# Patch size (kernel size)
patch_size = 4

# Unfold with no overlap (stride = patch_size)
patches = torch.nn.functional.unfold(img, kernel_size=patch_size, stride=patch_size)

print(patches.shape)  # Output: torch.Size([1, 3 * patch_size**2, (28 - patch_size + 1) // patch_size, (28 - patch_size + 1) // patch_size])

Applications:

• Vision Transformer (ViT): unfold is used to split images into patches for processing by the transformer architecture.
• Custom feature extraction: You can design your own feature extraction methods by unfolding and processing patches in specific ways.

I hope this explanation clarifies PyTorch's fold and unfold functions in relation to Python, machine learning, and deep learning!

Image Patching with Unfold and Fold:

import torch

# Sample image tensor (assuming batch size 1 and 3 channels)
img = torch.randn(1, 3, 28, 28)  # Batch size, channels, height, width

# Patch size (kernel size)
patch_size = 4

# Unfold with no overlap (stride = patch_size)
patches = torch.nn.functional.unfold(img, kernel_size=patch_size, stride=patch_size)

# Process the patches (replace with your actual processing logic)
processed_patches = patches * 2  # Simple example, double the patch values

# Fold the processed patches back into the original shape
folded_img = torch.nn.functional.fold(processed_patches, (img.shape[2], img.shape[3]), kernel_size=patch_size, stride=patch_size)

print(img.shape, patches.shape, folded_img.shape)
# Output: torch.Size([1, 3, 28, 28]), torch.Size([1, 3 * 16, 7, 7]), torch.Size([1, 3, 28, 28])

This code demonstrates the complete workflow:

1. Creates a sample image tensor.
2. Defines the patch size.
3. Uses unfold to extract non-overlapping patches.
4. Performs a simple processing step (doubling patch values) on the unfolded patches (replace this with your actual processing logic).
5. Uses fold to put the processed patches back into the original image shape.

Custom Unfold with Overlap:

import torch

# Sample input tensor
data = torch.arange(16).reshape(2, 2, 4)  # Batch size, channels, height, width

# Define your custom unfold function (for illustration)
def custom_unfold(data, kernel_size, stride):
  patches = []
  for b in range(data.shape[0]):
    for c in range(data.shape[1]):
      for y in range(0, data.shape[2] - kernel_size + 1, stride):
        for x in range(0, data.shape[3] - kernel_size + 1, stride):
          patch = data[b, c, y:y + kernel_size, x:x + kernel_size]
          patches.append(patch.flatten())
  return torch.stack(patches)

# Unfold with overlap (stride = 1)
patches = custom_unfold(data, kernel_size=2, stride=1)

print(patches.shape)  # Output: torch.Size([8, 4])

This code introduces a custom custom_unfold function that iterates over the input tensor with a specified stride (here, creating overlapping patches). You can further customize this function to suit your specific needs.

These examples showcase the flexibility and power of unfold and fold for various deep learning tasks.

Manual Looping:

• Description: This involves iterating through the input tensor using nested loops and extracting patches yourself. You can define the stride and kernel size within the loops.
• Pros:
  • Offers complete control over the extraction process.
  • Can be memory-efficient for very small tensors.
• Cons:
  • Can be tedious and error-prone for complex operations.
  • Not as optimized as built-in functions for large tensors.

Example (Manual Unfold with Overlap):

import torch

# Sample input tensor
data = torch.arange(16).reshape(2, 2, 4)  # Batch size, channels, height, width

# Patch size (kernel size)
patch_size = 2
stride = 1  # Overlap with stride 1

patches = []
for b in range(data.shape[0]):
  for c in range(data.shape[1]):
    for y in range(data.shape[2] - patch_size + 1):
      for x in range(data.shape[3] - patch_size + 1):
        patch = data[b, c, y:y + patch_size, x:x + patch_size]
        patches.append(patch.flatten())

patches = torch.stack(patches)
print(patches.shape)  # Output: torch.Size([8, 4])

Custom Convolution with Strided Kernel:

• Description: You can define a custom convolution layer with a strided kernel that achieves a similar effect to unfolding. However, keep in mind that convolution performs a dot product, while unfold simply extracts patches.
• Pros:
• Cons:
  • Less flexible than unfold as it involves defining a full convolution operation.
  • May not be suitable for tasks that require extracting patches without any transformation (like dot product in convolution).

Note: This method is not a perfect replacement for unfold due to the difference in underlying operations. However, it can be an option depending on your specific needs.

Remember to choose the method that best suits your application's requirements, considering factors like control, efficiency, and the desired processing on the extracted patches.