Mathematical eq for neural network model

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Mathematical eq for neural network model

Model specifications:
Let assume we have a Neural network (NN) model with 4 independent variables(input) and one dependent variable(output)
And we implemented a sequential model with 4 hidden layers using activation function ReLu for all hidden layers .
The first hidden layer with 50 nodes,second hidden layer with 20 nodes, third hidden layer with 10 nodes and forth hidden layer with 5 layer, and the output layer with one node
Learning rate = 0.0001, optimizer is Adagrad is an algorithm for gradient-based optimization, batch size is 8

Mathematical requirements for this model

1-some mathematical introduction with equations for Neural network, and for our specific model

2-cost function as mean square error , mathematical explanation , formula, and how it is important, why it is preferable over other function

3-mathematical explanation for the learning rate(formula with mathematical explanation) , and how it is work

4-mathematical explanation for Adagrad(optimizer) is an algorithm for gradient-based optimization, and how it is work in this model

Use requirements 1-4 as a heading and highlight them following by the relevant material

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