XOR-Learning

Learning XOR problem with 1 hidden layer and two perceptron with sigmoid activation function.

Tech 🛠️ Languages and Tools :

             

• Python : Popular language for implementing Neural Network
• Jupyter Notebook : Best tool for running python cell by cell
• Google Colab : Best Space for running Jupyter Notebook with hosted server
• Numpy : Best Library for working with arrays in python
• MatPlotLib : Library for showing the charts in python
• SeaBorn : Best Library for beautifing MatPlotLib charts
• Sci-kit Learn : Best Library for implementing Neural Networks

Run the Notebook on Google Colab

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Mathematical Formulation

Hidden Layer (2 neurons)

$$z_1 = w_{11}x_1 + w_{12}x_2 + b_1$$ $$z_2 = w_{21}x_1 + w_{22}x_2 + b_2$$ $$h_1 = \sigma(z_1) = \frac{1}{1 + e^{-z_1}}$$ $$h_2 = \sigma(z_2) = \frac{1}{1 + e^{-z_2}}$$

Output Layer (1 neuron)

$$z_o = v_1h_1 + v_2h_2 + b_o$$ $$\hat{y} = \sigma(z_o) = \frac{1}{1 + e^{-z_o}}$$

License

This project is licensed under the MIT License.