Using autograd to confirm answers to CSC321 Winter 2018, Hw2, Q3

autograd_vs_h2_q3.md

Using autograd to confirm answers to CSC321 Winter 2018, Hw2, Q3

import torch
from torch.autograd import Variable

torch.manual_seed(0)

<torch._C.Generator at 0x7f997494de10>

# X, is the training examples
X = Variable(torch.rand(10,4), requires_grad=True)
X

tensor([[0.4963, 0.7682, 0.0885, 0.1320],
        [0.3074, 0.6341, 0.4901, 0.8964],
        [0.4556, 0.6323, 0.3489, 0.4017],
        [0.0223, 0.1689, 0.2939, 0.5185],
        [0.6977, 0.8000, 0.1610, 0.2823],
        [0.6816, 0.9152, 0.3971, 0.8742],
        [0.4194, 0.5529, 0.9527, 0.0362],
        [0.1852, 0.3734, 0.3051, 0.9320],
        [0.1759, 0.2698, 0.1507, 0.0317],
        [0.2081, 0.9298, 0.7231, 0.7423]], requires_grad=True)

# t, is the targets
t = Variable(torch.rand(10), requires_grad=True)
t

tensor([0.5263, 0.2437, 0.5846, 0.0332, 0.1387, 0.2422, 0.8155, 0.7932, 0.2783,
        0.4820], requires_grad=True)

# w, is the weights
w = Variable(torch.zeros(4), requires_grad=True)

# b, is the bias
b = Variable(torch.zeros(1), requires_grad=True)

# y, is the predictions, based on w and X
y = torch.matmul(w,torch.transpose(X,0,1)) + b
y

tensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], grad_fn=<AddBackward0>)

def Loss(vector_y, vector_t):
    return 1 - torch.cos(vector_y - vector_t)
    

def AvgLoss(vector_y, vector_t):
    return torch.sum(Loss(vector_y, vector_t)) / len(vector_y)

Loss = AvgLoss(y, t)

Loss.backward()

# Autograd calculation
print(w.grad)

tensor([-0.1418, -0.2397, -0.1770, -0.1813])

# Manual Calculation of ∂Loss/∂y
torch.matmul(-torch.sin(t-y), X) / len(y)

tensor([-0.1418, -0.2397, -0.1770, -0.1813], grad_fn=<DivBackward0>)

print(b.grad)

tensor([-0.3886])

# Manual Calculation of ∂Loss/∂b
torch.sum(-torch.sin(t-y)) / len(y)

tensor(-0.3886, grad_fn=<DivBackward0>)