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How to apply linear transformation to the input data in PyTorch?
We can apply a linear transformation to the input data using the torch.nn.Linear() module. It supports input data of type TensorFloat32. This is applied as a layer in the deep neural networks to perform linear transformation. The linear transform used −
y = x * W ^ T + b
Here x is the input data, y is the output data after linear transform. W is the weight matrix and b is biases. The weights W have shape (out_features, in_features) and biases b have shape (out_features). They are initialized randomly and updated during the training of a Neural Network.
Syntax
torch.nn.Linear(in_features, out_features)
Parameters
in_features - It is the size of the input sample.
out_features - It is the size of output sample.
Steps
You could use the following steps to apply linear transformation to input data −
Import the required library. In all the following examples, the required Python library is torch. Make sure you have already installed it.
import torch
Define input tensor and print it.
input = torch.randn(2,3)
print("Input Tensor:
",input)Define the Linear transform using suitable in_features and out_features.
linear = nn.Linear(in_features, out_features)
Apply the above-defined linear transform to the input data. And optionally, assign the output to a new variable.
output = linear(input)
Print the linear transformed tensor.
print("Transformed Tensor:
",output)Example 1
# Import the required library
import torch
import torch.nn as nn
# torch.nn.Linear(in_features, out_features, bias=True,
device=None, dtype=None)
in_features = 3
out_features = 5
linear = nn.Linear(in_features, out_features)
input = torch.randn(2,3)
print("Input Tensor:
",input)
print("Size of Input Tensor:
",input.size())
# Compute the linear transformation
output = linear(input)
print("Transformed Tensor:
",output)
print("Size of Transformed Tensor:
",output.size())Output
Input Tensor: tensor([[-0.0921, 0.1992, -1.4930], [-0.0827, 0.0926, -0.1487]]) Size of Input Tensor: torch.Size([2, 3]) Transformed Tensor: tensor([[-0.5778, -0.3074, -0.5339, -0.3443, -0.1688], [-0.3149, -0.2189, -0.1795, -0.3617, -0.0839]], grad_fn=<AddmmBackward>) Size of Transformed Tensor: torch.Size([2, 5])
Notice that the size has changed after the linear transformation.
Example 2
# Import the required library
import torch
import torch.nn as nn
# torch.nn.Linear(in_features, out_features, bias=True,
device=None, dtype=None)
in_features = 3
out_features = 5
linear = nn.Linear(in_features, out_features, bias=False)
input = torch.randn(2,3)
print("Input Tensor:
",input)
print("Size of Input Tensor:
",input.size())
# Compute the linear transformation
output = linear(input)
print("Transformed Tensor:
",output)
print("Size of Transformed Tensor:
",output.size())Output
Input Tensor: tensor([[-0.6691, -1.6172, -0.9707], [-0.4425, 1.4376, -0.8004]]) Size of Input Tensor: torch.Size([2, 3]) Transformed Tensor: tensor([[ 0.3554, 1.3869, 0.5136, -0.1801, -0.5858], [ 0.3262, 0.2073, -0.8602, -0.0161, 0.5233]], grad_fn=<MmBackward>) Size of Transformed Tensor: torch.Size([2, 5])
Notice how the size changed after the linear transformation.
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