Notation of Fully Connected Neural Network
Elements of Deep Neural Network
Xi is a four-dimensional feature of a data point.
Xij represents each feature of the data point.
Y_Pred is a real number. This means here we are solving a regression problem in this example.
F is the Activation Function.
O is Output.
W is the weight.
We have weights associated with each of the edges. These weights get multiply with the Inputs of the next layer and summed. This Result passes through a function F. If the input is the same as the output we call the function an Identity function. Ex. Linear Regression.
The number of weight in each layer can be represented as the “number of Input” x “the number of the output” matrix
Let's consider weights between hidden layer 1 and hidden layer 2. Layer 1 has 4 units and Layer 3 has 3 units. So, the total number of weights will be 4 * 3 = 12. Similarly, between Layer 2 and Layer 3, the number of weights will be 3 * 2 = 6.
For simplicity I excluded Bias but we can have Bias term as well.