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import torch
import math
device = 'cuda:0' if torch.cuda.is_available() else 'cpu'
dtype = torch.float
lr = 5e-6
class LegendrePolynomial3(torch.autograd.Function):
@staticmethod
def forward(ctx, input):
ctx.save_for_backward(input)
return 0.5*(5*input**3 - 3*input)
@staticmethod
def backward(ctx, grad_output):
input, = ctx.saved_tensors
return grad_output*(7.5*input**2 - 1.5)
def train(X, y):
a = torch.full((), 0, device=device, dtype=dtype, requires_grad=True)
b = torch.full((), -1, device=device, dtype=dtype, requires_grad=True)
c = torch.full((), 0, device=device, dtype=dtype, requires_grad=True)
d = torch.full((), 0.3, device=device, dtype=dtype, requires_grad=True)
for i in range(2000):
P3 = LegendrePolynomial3.apply
# 执行 forward
y_pred = a + b * P3(c + d*X)
loss = (y_pred - y).pow(2).sum()
if i % 100 == 0:
print('{}/{}: {}'.format(i, 2000, loss.item()))
# 执行 backward
loss.backward()
with torch.no_grad():
a -= lr * a.grad
b -= lr * b.grad
c -= lr * c.grad
d -= lr * d.grad
a.grad = None
b.grad = None
c.grad = None
d.grad = None
print('a = {}, b = {}, c = {}, d = {}'.format(a.item(), b.item(), c.item(), d.item()))
if __name__ == '__main__':
X = torch.linspace(-math.pi, math.pi, 2000, dtype=dtype, device=device)
y = torch.sin(X)
train(X, y)
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