Is it possible to replace a 3x3 convolution with two consecutive 3x1 and 1x3 convolutions? What are the advantages and disadvantages?

Yes, a 3x3 convolution can be replaced by two consecutive convolutions of 3x1 and 1x3. This technique is often used to reduce the number of parameters and computational load.

Advantages:

• Fewer parameters: two convolutions of 3x1 and 1x3 have fewer weights combined than a single 3x3.
• Less computation: operations with smaller kernels are simpler and faster.
• Deeper architecture: adding an extra non-linearity layer between the two convolutions can improve the model's expressive power.

Disadvantages:

• Potentially less receptive field per layer, as a 3x3 covers 9 pixels at once, whereas 3x1 and 1x3 cover 3 pixels each.
• Possible loss of information if layers or activations are not properly configured.

Example in PyTorch:

import torch.nn as nn

# Original 3x3 convolution
conv_3x3 = nn.Conv2d(in_channels=64, out_channels=128, kernel_size=3, padding=1)

# Replacement with two convolutions 3x1 and 1x3
conv_3x1 = nn.Conv2d(64, 128, kernel_size=(3,1), padding=(1,0))
conv_1x3 = nn.Conv2d(128, 128, kernel_size=(1,3), padding=(0,1))

# Sequential application of conv_3x1 and conv_1x3 is equivalent to conv_3x3 with fewer parameters