Linear Regression in PyTorch

Question

It's a simple regression problem. But no matter how much I try, I can't get the answer I want. I'm guessing the weight should be 32 (4 * 8) but, the code returns 25. Why is that?

This is my full source code:

import torch 
import torch.nn as nn
import torch.optim as op

X = torch.FloatTensor([[1., 2.],[2., 4.],[3., 6.]])
Y = torch.FloatTensor([[2.],[8.],[18.]])

class TEST(nn.Module):
    def __init__(self):
        super(TEST,self).__init__()
        self.l1 = nn.Linear(2,1)
        
    def forward(self, input):
        x = self.l1(input)
        return x
    
epochs = 2000
lr = 0.001
    
model = TEST()
loss_func = nn.MSELoss()
optimizer = op.SGD(model.parameters(), lr=lr)

for epoch in range(epochs):
    optimizer.zero_grad()
    output = model(X)
    loss = loss_func(output, Y)
    loss.backward()
    optimizer.step()
    
    if epoch%10 == 0:
        print('loss[{}] : {}'.format(epoch, loss))
        
XX = torch.FloatTensor([[4., 8.]])

print(model(XX))

This is the output of the code:

loss[1920] : 0.8891088366508484
loss[1930] : 0.8890921473503113
loss[1940] : 0.8890781402587891
loss[1950] : 0.8890655636787415
loss[1960] : 0.8890505433082581
loss[1970] : 0.8890388011932373
loss[1980] : 0.889029324054718
loss[1990] : 0.8890181183815002
tensor([[25.3124]], grad_fn=<AddmmBackward>)

Answer 1

You are trying to approximate y = x1*x2 but are using a single linear layer ie a purely linear model. Ultimately, what happens is you are learning weights a and b such that y = a*x1 + b*x2 . However, this model cannot approximate the distribution of x1, x2 -> x1*x2 .