Cheatsheet: Neurons as numbers, layers as structure

The one idea that matters

neuron = a container holding one number between 0 and 1 (its "activation")
network = layers of neurons, with numbers flowing forward, layer to layer

No biology, no thinking. Just numbers in boxes, moving one direction.

The layers of the example network

Layer	Neurons	Each neuron holds
Input	784 (one per pixel of a 28x28 image)	that pixel’s brightness (0 = black, 1 = white)
Hidden 1	16	a value computed from the previous layer
Hidden 2	16	a value computed from the previous layer
Output	10 (one per digit 0-9)	a confidence score; tallest = the guess

Total: 784 + 16 + 16 + 10 = 826 neurons. (2 hidden layers of 16 is a design choice, not a rule.)

Key terms in one line each

• Activation: the number a neuron holds, 0 to 1. Near 1 = “lit up”; near 0 = quiet.
• Input layer: one neuron per pixel; loads the image as raw brightness values.
• Output layer: one neuron per possible answer; highest activation is the network’s guess.
• Hidden layer: any layer that is not input or output; does the work of turning pixels into a guess.
• Feedforward: numbers flow one direction only, input to output, no loops.

Worked numbers

Pixel into the input layer. Pixel at row 10, column 14, brightness 0.7. Numbering row by row: neuron number = 10 x 28 + 14 = 294. So input neuron 294 holds activation 0.7.

Reading the output layer. Output activations (digits 0 to 9):

0:0.02  1:0.01  2:0.05  3:0.92  4:0.03
5:0.04  6:0.01  7:0.02  8:0.01  9:0.02

Tallest is digit 3 at 0.92 → guess is 3, high confidence.

Pitfalls to dodge

• “A neuron is like a brain cell.” No. It is a container for one number, 0 to 1.
• “Activations are on or off.” No. Any value 0 to 1; the in-between is where the information lives.
• “2 layers of 16 is meaningful.” No. A clean teaching choice; real networks vary widely.
• “The first layer detects edges, the next detects loops.” That is the hope, not a proven fact. A trained network’s real patterns are messier and less human-readable.

The optimistic hope (hold it loosely)

Maybe hidden layer 1 notices small edges, hidden layer 2 combines them into loops and strokes, and the output assembles those into digits. Useful first picture, but a later lesson shows the reality is messier. Motivation, not description.

The one-line version

A neural network is just layers of numbers, and the only thing that ever moves through it is numbers.