Neural Network Tutorial

C++ Neural Network Backpropagation tutorial from scratch.

In this playlist, I teach the neural network architecture and the learning processes to make the ANN able to learn from a dataset.

The Tutorials are divided in each part of the neural network and we start coding it in C++ in Visual Studio 2017. Once you have completed the tutorial you will be able to design your own neural network and optimize it.

  1. Introduction
  2. Neuron & Layer
  3. Input & Output Layer
  4. Hidden Layer
  5. Neural network
  6. Training
  7. FeedForward & Backpropagation

Download theory paper: Backpropagation

C++ Source code uploaded in GitHub: Neural Network Tutorial



w_{i j}^{k}: weight for node j in layer l_k for incoming node i.
b_{i}^{k}: bias for node i in layer l_k.
a_{i}^{k}: product sum plus bias (activation) for node i in layer l_k.
o_i^k: output for node i in layer l_k.
n_k: number of nodes i layer l_k.

g: activation function for the hidden layer nodes.
g_o: activation function for the output layer nodes.


    \[ a_i^k=b_i^k+\sum_{j=1}^{n_{k-1}}{w^k_{ji}o_j^{k-1}} \]

    \[ o_i^k=g(a_{i}^{k}) \]


    \[ E=\frac{1}{2}(y-o_i^k)^2 \]


    \[ \frac{\partial E}{\partial w_{i j}^{k}} = \frac{\partial E}{\partial o_{i}^{k}} \frac{\partial o_{i}^{k}}{\partial a_{i}^{k}} \frac{\partial a_{i}^{k}}{\partial w_{i j}^{k}} \]

    \[ \delta_j^k \equiv \frac{\partial E}{\partial a_{j}^{k}} = \frac{\partial E}{\partial o_{i}^{k}} \frac{\partial o_{i}^{k}}{\partial a_{i}^{k}} \]

    \[ \frac{\partial a_{i}^{k}}{\partial w_{i j}^{k}} = \frac{\partial}{w_{i j}^{k}}(b_i^k+\sum_{j=1}^{n_{k-1}}{w^k_{ji}o_j^{k-1}}) = o_i^{k-1} \]

    \[ \frac{\partial E}{\partial w_{i j}^{k}} = \delta^k_j o_i^{k-1} \]


    \[ \delta_j^k = \frac{\partial E}{\partial a_{j}^{k}} = (g_o(a_j^l)-y)g'_o(a_j^l) \]

    \[ \frac{\partial E}{\partial w_{i j}^{k}} = \delta_j^k o_i^{k-1} = (g_o(a_j^l)-y) g'_o(a_j^l) o_i^{l-1} \]


where l ranges from 1 to r_{k+1}, number of nodes in the next layer.

    \[ \delta_j^k = \frac{\partial E}{\partial a_{j}^{k}} = \sum_{l=1}^{n_{k+1}}{\delta_l^{k+1}\frac{\partial a_l^{k+1}}{\partial a_j^k}} \]

    \[ a_l^{k+1} = \sum_{j=1}^{n_k}{ w^{k+1}_{j l} g(a_j^k)} \]

    \[ \frac{\partial a_l^{k+1}}{\partial a_j^k} = w_{j l}^{k+1}g'(a_j^k) \]

    \[ \delta_j^k = \sum_{l=1}^{n_{k+1}}{\delta_l^{k+1}w_{j l}^{k+1}g'(a_j^k)} = g'(a_j^k) \sum_{l=1}^{n_{k+1}}{\delta_l^{k+1}w_{j l}^{k+1}} \]

    \[ \frac{\partial E}{\partial w_{i j}^{k}} = \delta_j^k o_i^{k-1} = g'(a_j^k)o_i^{k-1}\sum_{l=1}^{n_{k+1}}w_{j l}^{k+1}\delta_k^{k+1} \]


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