# Warm-up: numpy¶

A third order polynomial, trained to predict $$y=\sin(x)$$ from $$-\pi$$ to $$pi$$ by minimizing squared Euclidean distance.

This implementation uses numpy to manually compute the forward pass, loss, and backward pass.

A numpy array is a generic n-dimensional array; it does not know anything about deep learning or gradients or computational graphs, and is just a way to perform generic numeric computations.

import numpy as np
import math

# Create random input and output data
x = np.linspace(-math.pi, math.pi, 2000)
y = np.sin(x)

# Randomly initialize weights
a = np.random.randn()
b = np.random.randn()
c = np.random.randn()
d = np.random.randn()

learning_rate = 1e-6
for t in range(2000):
# Forward pass: compute predicted y
# y = a + b x + c x^2 + d x^3
y_pred = a + b * x + c * x ** 2 + d * x ** 3

# Compute and print loss
loss = np.square(y_pred - y).sum()
if t % 100 == 99:
print(t, loss)

# Backprop to compute gradients of a, b, c, d with respect to loss
grad_y_pred = 2.0 * (y_pred - y)