Factorized Convolutional Layers

It is possible to apply low-rank tensor factorization to convolution kernels to compress the network and reduce the number of parameters.

In TensorLy-Torch, you can easily try factorized convolutions: first, let’s import the library:

import tltorch
import torch

Let’s now create some random data to try our modules: we can choose the size of the convolutions.

device='cpu'
input_channels = 16
output_channels = 32
kernel_size = 3
batch_size = 2
size = 24
order = 2

input_shape = (batch_size, input_channels) + (size, )*order
kernel_shape = (output_channels, input_channels) + (kernel_size, )*order

We can create some random input data:

data = torch.randn(input_shape, dtype=torch.float32, device=device)

Creating Factorized Convolutions

From Random

In PyTorch, you would create a convolution as follows:

conv = torch.nn.Conv2d(input_channels, output_channels, kernel_size)

In TensorLy Torch, it is exactly the same except that factorized convolutions are by default of any order: either you specify the kernel size or your specify the order

conv = tltorch.TuckerConv(input_channels, output_channels, kernel_size, order=2, rank='same')

conv = torch.nn.Conv2d(input_channels, output_channels, kernel_size=3)

In TensorLy-Torch, factorized convolutions can be of any order, so you have to specify the order at creation (in Pytorch, you specify it through the class name, e.g. Conv2d or Conv3d):

fact_conv = tltorch.CPConv(input_channels, output_channels, kernel_size=3, order=2, rank='same')

Or, you can specify the order directly by passing a tuple as kernel_size (in which case, order = len(kernel_size) is used).

fact_conv = tltorch.CPConv(input_channels, output_channels, kernel_size=(3, 3), rank='same')

From an existing Convolution

You can create a Factorized convolution from an existing (PyTorch) convolution:

fact_conv = tltorch.CPConv.from_conv(conv, rank=0.5, decompose_weights=True)

Efficient Convolutional Blocks

If you compress a convolutional kernel, you can get efficient convolutional blocks by applying tensor factorization. For instance, if you apply CP decomposition, you can get a MobileNet-v2 block:

fact_conv = tltorch.CPConv.from_conv(conv, rank=0.5, implementation='mobilenet')

Similarly, if you apply Tucker decomposition, you can get a ResNet BottleNeck block:

fact_conv = tltorch.TuckerConv.from_conv(conv, rank=0.5, implementation='factorized')