# -*- coding: utf-8 -*-
"""
PyTorch: Custom nn Modules
--------------------------
A third order polynomial, trained to predict :math:`y=\sin(x)` from :math:`-\pi`
to :math:`\pi` by minimizing squared Euclidean distance.
This implementation defines the model as a custom Module subclass. Whenever you
want a model more complex than a simple sequence of existing Modules you will
need to define your model this way.
"""
import torch
import math
class Polynomial3(torch.nn.Module):
def __init__(self):
"""
In the constructor we instantiate four parameters and assign them as
member parameters.
"""
super().__init__()
self.a = torch.nn.Parameter(torch.randn(()))
self.b = torch.nn.Parameter(torch.randn(()))
self.c = torch.nn.Parameter(torch.randn(()))
self.d = torch.nn.Parameter(torch.randn(()))
def forward(self, x):
"""
In the forward function we accept a Tensor of input data and we must return
a Tensor of output data. We can use Modules defined in the constructor as
well as arbitrary operators on Tensors.
"""
return self.a + self.b * x + self.c * x ** 2 + self.d * x ** 3
def string(self):
"""
Just like any class in Python, you can also define custom method on PyTorch modules
"""
return f'y = {self.a.item()} + {self.b.item()} x + {self.c.item()} x^2 + {self.d.item()} x^3'
# Create Tensors to hold input and outputs.
x = torch.linspace(-math.pi, math.pi, 2000)
y = torch.sin(x)
# Construct our model by instantiating the class defined above
model = Polynomial3()
# Construct our loss function and an Optimizer. The call to model.parameters()
# in the SGD constructor will contain the learnable parameters (defined
# with torch.nn.Parameter) which are members of the model.
criterion = torch.nn.MSELoss(reduction='sum')
optimizer = torch.optim.SGD(model.parameters(), lr=1e-6)
for t in range(2000):
# Forward pass: Compute predicted y by passing x to the model
y_pred = model(x)
# Compute and print loss
loss = criterion(y_pred, y)
if t % 100 == 99:
print(t, loss.item())
# Zero gradients, perform a backward pass, and update the weights.
optimizer.zero_grad()
loss.backward()
optimizer.step()
print(f'Result: {model.string()}')