Neural Network from Scratch Using Tensorflow

#Tensorflow #machinelearning #neuralnetworks #python

In this article I show how to build a neural network from scratch. The example is simple and short to make it easier to understand but I haven’t took any shortcuts to hide details.

Looking for PyTorch version of this same tutorial? Go here.

import tensorflow as tf
import matplotlib.pyplot as plt

First we create some random data. x is just 1-D tensor and the model will predict one value y.

x = tf.Variable([[1.,2.]])
x.shape

CONSOLE: TensorShape([1, 2])

y = 5.

The parameters are initialized using normal distribution where mean is 0 and variance 1.

def initalize_parameters(size, variance=1.0):
    return tf.Variable((tf.random.normal(size) * variance))

first_layer_output_size = 3

weights_1 = initalize_parameters((x.shape[1], first_layer_output_size))
weights_1

CONSOLE: <tf.Variable 'Variable:0' shape=(2, 3) dtype=float32, 
          numpy=array([
                [ 0.0535108 ,  1.1256728 ,  0.19349864],
                [-0.8206305 ,  1.8411716 , -0.18347588]],   
                dtype=float32)>

bias_1 = initalize_parameters([1])
bias_1

CONSOLE: <tf.Variable 'Variable:0' shape=(1,) dtype=float32,
          numpy=array([-1.7967013], dtype=float32)>

weights_2 = initalize_parameters((first_layer_output_size,1))
weights_2

CONSOLE: <tf.Variable 'Variable:0' shape=(3, 1) dtype=float32,
          numpy=array([[-0.68191385],
               [-1.3771404 ],
               [-0.59087867]], dtype=float32)>

bias_2 = initalize_parameters([1])
bias_2

CONSOLE: <tf.Variable 'Variable:0' shape=(1,) dtype=float32, 
          numpy=array([-0.93876433], dtype=float32)>

The neural network contains two linear functions and one non-linear function between them.

def simple_neural_network(xb):
    # linear (1,2 @ 2,3 = 1,3)
    l1 = xb @ weights_1 + bias_1
    # non-linear
    l2 = tf.math.maximum(l1, tf.Variable([0.]))
    # linear (1,3 @ 3,1 = 1,1)
    l3 = l2 @ weights_2 + bias_2
    return l3

Loss function measures how close the predictions are to the real values.

def loss_func(preds, yb):
    # Mean Squared Error (MSE)
    return tf.math.reduce_mean((preds-yb)**2)

Learning rate reduces gradient making sure parameters are not changed too much in each step.

lr = tf.constant([10E-4])

Training contains three simple steps:

Make prediction
Calculate how good the prediction was compared to the real value (When calculating loss it automatically calculates gradient so we don’t need to think about it)
Update parameters by subtracting gradient times learning rate

The code continues taking steps until the loss is less than or equal to 0.1. Finally it plots the loss change.

losses = []

while(len(losses) == 0 or losses[-1] > 0.1):
    with tf.GradientTape() as tape:
    # 1. predict
        preds = simple_neural_network(x)
        # 2. loss
        loss = loss_func(preds, y)
    dW1, db1, dW2, db2 = tape.gradient(loss, 
                                       [weights_1, bias_1, 
                                        weights_2, bias_2])

    # 3. update parameters
    weights_1.assign_sub(dW1 * lr)
    bias_1.assign_sub(db1 * lr)

    weights_2.assign_sub(dW2 * lr)
    bias_2.assign_sub(db2 * lr)

    losses.append(loss)

plt.plot(list(range(len(losses))), losses)
plt.ylabel('loss (MSE)')
plt.xlabel('steps')
plt.show()