Basic Neural Network

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• Input layer (receives data and passes it on)
• Hidden layer
• Output layer
• Weights between the layers
• Activation function (per hidden layer) (Sigmoid activation function)
• Feed-forward (perception) neural network (relays data directly from the front to the back)

input * weight + bias = output

Training Data

	Input	Output
Data 1	0 - 0 - 1	0
Data 2	1 - 1 - 1	1
Data 3	1 - 0 - 1	1
New Case	1 - 0 - 0	?

Every input will have a weight (positive or negative). This implies that an input having a big number of positive weight or a big number of negative weight will influence the resulting output more.

Procedure for the training process:

Taking inputs from the training dataset,

1. Perform some adjustments based on their weights, and siphon them via a method that computes the output of the neural net
2. Compute the back-propogated error rate. In this case it is the difference between the neuron's predicted output and the expected output of the training dataset
3. Based on the extent of the error, perform some minor weight adjustments using the Error Weighted Derivative formula
4. Iterate this process an arbitrary number of times (we chose 15000). Every iteration, the whole training set is processed simultaneously

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• exp - for generating the natural exponential
• array - for generating a matrix
• dot - for multiplying matrices
• random - for generating random numbers (we'll seed the random numbers to ensure their efficient distribution)