Build Deep Learning Framework:Step7 Auto Backpropagation

Post at — Feb 23, 2025
#Deep_Learning_Framework

How to Build Deep Learning Framework Step By Step Using 60 steps:Step7

In step6,we must calc each fun’s backward like this:

1
2
3
4
y.grad = np.array(1.0)
b.grad = C.backward(y.grad)
a.grad = B.backward(b.grad)
x.grad = A.backward(a.grad)

if the function call graph is complex,the code will be tedious,so how to solve it?

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
import numpy as np


class Variable:
    def __init__(self, data):
        self.data = data
        self.grad = None
        self.creator = None

    def set_creator(self, func):
        self.creator = func

    def backward(self):
        f = self.creator  # 1. Get a function
        if f is not None:
            x = f.input  # 2. Get the function's input
            x.grad = f.backward(self.grad)  # 3. Call the function's backward
            x.backward()


class Function:
    def __call__(self, input):
        x = input.data
        y = self.forward(x)
        output = Variable(y)
        output.set_creator(self)  # Set parent(function)
        self.input = input
        self.output = output  # Set output
        return output

    def forward(self, x):
        raise NotImplementedError()

    def backward(self, gy):
        raise NotImplementedError()


class Square(Function):
    def forward(self, x):
        y = x ** 2
        return y

    def backward(self, gy):
        x = self.input.data
        gx = 2 * x * gy
        return gx


class Exp(Function):
    def forward(self, x):
        y = np.exp(x)
        return y

    def backward(self, gy):
        x = self.input.data
        gx = np.exp(x) * gy
        return gx

A = Square()
B = Exp()
C = Square()

x = Variable(np.array(0.5))
a = A(x)
b = B(a)
y = C(b)

# backward
y.grad = np.array(1.0)
y.backward()
print(x.grad)

you can use the following image to understand the code: