Unfolding the Power of Local Features: torch.nn.Unfold and its Alternatives in PyTorch

What is torch.nn.Unfold?

In convolutional neural networks (CNNs), a core operation is extracting local features from an input tensor. torch.nn.Unfold accomplishes this by creating a new tensor that contains overlapping or non-overlapping patches (local regions) from the input data. These patches are then fed into convolutional layers for feature extraction.

How Does It Work?

torch.nn.Unfold takes several arguments to control how it extracts patches:

• stride (int or tuple, optional): The stride of the sliding window used to extract patches (default: kernel_size, non-overlapping patches).
• padding (int or tuple, optional): Padding to be added to the input tensor before unfolding (default: 0, no padding). Zero padding implies strict cropping, whereas positive padding creates a border around the input.
• dilation (int, optional): The amount of spacing to add between extracted patches (default: 1, no spacing).
• kernel_size (tuple): A tuple of integers representing the size of the patch to be extracted along each spatial dimension (height and width for 2D inputs).

1. Sliding Window
   torch.nn.Unfold iterates over the input tensor using a sliding window with the specified kernel_size and stride.
2. Patch Extraction
   Within each window, it extracts a patch of data from the input tensor.
3. Overlapping or Non-Overlapping
   Depending on the stride value, patches can be overlapping (smaller stride) or non-overlapping (stride equal to kernel_size).
4. Reshaping and Concatenation
   The extracted patches are reshaped and concatenated into a new tensor. This new tensor has an additional dimension compared to the input, representing the extracted patches.

Benefits of Using torch.nn.Unfold

• Efficiency
  It's optimized for efficient computation within CNNs, especially when combined with convolutional layers that operate directly on the unfolded patches.
• Flexibility
  It allows fine-grained control over how patches are extracted, enabling different levels of overlap or spacing for feature extraction.

Example Code

import torch
from torch import nn

# Sample input tensor (batch size 1, channel 3, height 5, width 5)
input_tensor = torch.randn(1, 3, 5, 5)

# Unfold with a 3x3 kernel, dilation 1, padding 1, and stride 2
unfold = nn.Unfold(kernel_size=(3, 3), dilation=1, padding=1, stride=2)
unfolded_tensor = unfold(input_tensor)

print(unfolded_tensor.shape)  # Output shape depends on input size and parameters

• Understanding torch.nn.Unfold helps you grasp how CNNs process input data and extract local features.
• It's not directly related to training the network but prepares the input data for efficient convolution.
• torch.nn.Unfold is a building block for CNNs, specifically for feature extraction through convolutional layers.

---

Patching an Image for Vision Transformer (ViT)

ViT utilizes torch.nn.Unfold to break down an input image into patches before feeding them into the network. This code demonstrates the concept:

import torch

# Sample image tensor (batch size 1, channels 3, height 224, width 224)
image = torch.randn(1, 3, 224, 224)

# Patch size of 16x16
patch_size = (16, 16)

# Unfold the image into patches with stride 16 (no overlap)
unfolded = torch.nn.functional.unfold(image, patch_size=patch_size, stride=patch_size)

# Reshape to flatten each patch (assuming channels are the first dimension)
patches = unfolded.reshape(unfolded.shape[0], -1, patch_size[0] * patch_size[1])

print(patches.shape)  # Output: (batch_size, num_patches, patch_size^2 * channels)

Extracting Overlapping Features for a Local Feature Detector

This example showcases using torch.nn.Unfold with a smaller stride to capture overlapping features for a local feature detector:

import torch
from torch import nn

# Sample input tensor (batch size 1, channel 1, height 28, width 28)
input_tensor = torch.randn(1, 1, 28, 28)

# Unfold with 5x5 kernel, dilation 1, no padding, and stride 1 (overlapping patches)
unfold = nn.Unfold(kernel_size=(5, 5), dilation=1, padding=0, stride=1)
unfolded_tensor = unfold(input_tensor)

print(unfolded_tensor.shape)  # Output shape depends on input size and parameters

Custom Unfold Function for Higher Dimensions (Optional)

While torch.nn.Unfold supports 4D tensors (batch, channels, height, width), libraries like f-dangel/unfoldNd offer custom unfold functions for higher dimensions:

# Install unfoldNd (assuming it's not already installed)
# !pip install f-dangel/unfoldNd  # Commented out for safety reasons

import torch
from unfoldNd import unfoldNd

# Sample 3D tensor (batch size 1, channels 2, depth 4, height 8, width 8)
tensor = torch.randn(1, 2, 4, 8, 8)

# Unfold with custom unfoldNd for 3D tensors
unfolded = unfoldNd(tensor, kernel_size=(2, 2, 2), stride=1)

print(unfolded.shape)

Remember to replace !pip install f-dangel/unfoldNd with the actual installation command if you need to use unfoldNd.

---

Manual Looping (Less Efficient)

• You can create a custom loop that iterates over the input tensor with the desired kernel size and stride. This approach offers maximum control but can be less efficient than built-in functions.

torch.nn.functional.conv2d with Stride and Padding

• In certain cases, you might be able to achieve similar results using torch.nn.functional.conv2d with specific stride and padding values. This can be more efficient for standard convolutions without the need for explicit patch extraction.

Third-Party Libraries (For Specific Needs)

• If you require more control over unfolding or work with higher-dimensional tensors, consider libraries like:
  • f-dangel/unfoldNd: Offers unfold functionality for N-dimensional tensors (N = 1, 2, 3) with potential performance benefits over torch.nn.Unfold.
  • Other libraries might exist for specific unfolding needs (research based on your use case).

Choosing the Right Alternative

The best alternative depends on your specific context:

• For N-dimensional unfolding or specialized needs, explore third-party libraries like f-dangel/unfoldNd.
• For standard convolutions, consider using torch.nn.functional.conv2d with suitable parameters.
• If you need maximum control and understand the performance implications, manual looping might be an option.

Alternative	Description	Pros	Cons
Manual Looping	Custom loop for iterating and extracting patches	Maximum control	Less efficient, error-prone if not carefully coded
torch.nn.functional.conv2d	Convolutional layer with specific stride and padding	Efficient for standard convolutions	Less control over patch extraction, might not be suitable for all cases
Third-Party Libraries	Libraries like f-dangel/unfoldNd for N-dimensional tensors	More control over unfolding, potential performance benefits	Might require additional installation, learning curve