Python Programming

Remember the way we defined our model ModelNumberQuestions ?

import torch

class ModelNumberQuestions(torch.nn.Module):
    def __init__(self):
        super().__init__()
        initial_theta_0 = torch.Tensor([1])
        initial_theta_1 = torch.Tensor([2])
        self.theta_0 = torch.nn.Parameter(initial_theta_0)
        self.theta_1 = torch.nn.Parameter(initial_theta_1)

    def forward(self, tensor_number_tasks):
        return self.theta_1 * tensor_number_tasks + self.theta_0

You can see that the model above performs a linear operation:

$f_\theta(n_T) = \theta_1 n_T + \theta_0$

PyTorch already provides an implementation of that operation (and the name is quite straightforward): torch.nn.Linear

Such linear operation takes two necessary arguments:

• in_features: Number of features as input to the linear operation. In our case, the input has only one feature: $n_T$. So we set in_features=1
• out_features: Number of features as outputted by the linear operation. In our case, the output has only one feature: $\widehat{n_Q}$. So we set out_features=1

In the end, our class ModelNumberQuestions becomes way simpler!

import torch

class ModelNumberQuestions(torch.nn.Module):
    def __init__(self):
        super().__init__()
        self.linear = torch.nn.Linear(in_features=1,
                                      out_features=1)
        # self.linear is automatically initialised

    def forward(self, tensor_number_tasks):
        return self.linear(tensor_number_tasks)

You can see all the parameters of ModelNumberQuestions by printing the named_parameters():

net = ModelNumberQuestions()
print(list(net.named_parameters()))

You should get something like this:

[('linear.weight', Parameter containing:
tensor([[0.1731]], requires_grad=True)), ('linear.bias', Parameter containing:
tensor([0.7059], requires_grad=True))]

You can notice that we still have two parameters:

• linear.weight corresponding to our former theta_1
• linear.bias corresponding to our former theta_0

Exercise:

Try your implementation of train_parameters_linear_regression with our new implementation of ModelNumberQuestions.

The results should remain unchanged! :D