# Introduction

The vectorized operations have been discussed in the last post Maths in a Neural Network: Vectorization. This post will focus on implementing the equations with numpy.

# Equations proved in the previous posts [1] [2]:

Note that this network takes one sample input at a time, I’ll discuss batch prediction/training later.

## Feed-forward:

## Weight update:

Output layer:

Hidden layer:

# Notebook:

The following code implemented a 2-3-3-2 network for XOR problem. Note that this network takes one sample input at a time, I’ll discuss batch prediction/training later.

In the end, the Mean Square Error of an epoch converges to a low value, which indicates the training was fine.

# Next

- Maths in a Neural Network: Element-wise
- Maths in a Neural Network: Vectorization
- Code a Neural Network with Numpy
- Maths in a Neural Network: Batch Training