**Graph theory** describes hierarchy of related elements:

- vertices (nodes) are entities; edges represent the relationship between nodes
- can represent grouped paths in photoshop; a computer program;
- perceptron is a directed graph (info flows in one direction)
- recurrent neural networks allow cycles (loops) in their flow of info

Perceptron Implementation Notes:

- sign activation function: if number is greater than zero, output is 1; less than zero, output is -1
- bias input: always equal to one
- supervised training procedure:
- make predictions (ie, weights are random)
- have perceptron guess outputs; compare to actual known outputs
- compute the error; adjust all weights accordingly
- repeat

**HW**:- construct data sets, train it on all three (AND and OR should be 100% accurate)
- extra column of 1’s for bias input
- input is 2 columns (3 for bias input), output is 1 column
- AND set: true = 1, false = -1; two column pairs
- input [1,1], output = [1]; input [1, -1], output [-1], etc

- OR set
- XOR set will not be 100% accuracy (probably 50%)

- class Perceptron
- initializer function (number_of_input_dimensions, num_of_output_dimensions)
- weight = np.rand(num_input)

- predict(inputs)
- return array of output predictions

- training function(iterations, inputs, known outputs)
- for iter in range(num_iters):
- predict = (

- for iter in range(num_iters):
- myPerceptron = Perceptrion()
- myPerceptron.train()
- myPerceptron.predict()

- initializer function (number_of_input_dimensions, num_of_output_dimensions)

- construct data sets, train it on all three (AND and OR should be 100% accurate)

Linear separation:

- Exclusive Or: (a OR b) AND (NOT (a AND b))
- Both variables are dependent on each other, whereas in AND and OR models neither nodes need to know about each other
- not linearly separated like AND and OR

- Both variables are dependent on each other, whereas in AND and OR models neither nodes need to know about each other
- If machine-learning about whether pixels compose a picture of a person, the perceptron asks each pixel if it may be part of a picture of a person, and if more than 50% say yes, then the output is yes, the picture is of a person
- does not account for interdependency of pixels

Calculus Primer:

- Calculus is about approximating the analog world
- derivative: rate of change in some phenomenon
- power rule: multiply power by variable’s coefficient, reduce power by 1
- derivative of x^2 is 2x

- chain rule: f(g(x)) = f'(g(x))g'(x) >> nested function, able to compute derivative by splaying it out

- power rule: multiply power by variable’s coefficient, reduce power by 1