A neural network is built from layers of units called neurons. Numbers enter on the left, flow layer by layer to the right, and an answer comes out. Each neuron's value is calculated from all the neurons in the previous layer.
Our example network: 784 → 64 → 32 → 10. The middle layers are called hidden because you never see their values directly — they quietly transform the input into features the output can use.
Input layer: just holds your data (the 784 pixel values). Hidden layers: transform it step by step — early layers find edges, later ones combine edges into shapes. Output layer: 10 neurons, one per digit. The network's guess = whichever output neuron has the highest value.
a = wx + bHere's the whole secret of neural networks — and it's simpler than you'd think. Every connection between two neurons has a weight (how strongly they're linked). A neuron takes the value of each neuron before it, multiplies by that weight, and adds a bias. The result is the neuron's activation — its value.
a = the activation (value) of the new neuron. w = the weight — the strength of the connection (learned during training). x = the input — the previous neuron's value. b = the bias — a nudge up or down that helps the neuron learn.
Deciding whether to go outside. The input (x) is "how sunny is it, 0–1." The weight (w) is how much you personally care about sun. The bias (b) is your baseline mood — a cheerful person has a positive bias and goes out even on cloudy days. Multiply how sunny it is by how much you care, add your mood, and you get your "go outside" activation.
Drag the sliders for the weight, input, and bias. Watch a = wx + b compute live, then get squashed by the sigmoid into a 0–1 activation — exactly how a real neuron fires.
The raw wx+b can be any number (−5, 0, 100…). But we want each neuron's value in a tidy range like 0 to 1. The sigmoid function does this: big positive → near 1, big negative → near 0, zero → 0.5. It keeps the relative differences but bounds the output. (Other common squashers: ReLU, softmax.) Formula: sigmoid(z) = 1 / (1 + e^−z).
a = wx + b is the link between one neuron and the next. But a real neuron connects to every neuron in the previous layer — each with its own weight. So we sum them all, then squash:
A neuron in hidden layer 1 has 784 weights (one per input pixel) plus 1 bias. With 64 such neurons, that layer alone learns 784 × 64 + 64 = 50,240 numbers. These weights and biases are exactly what the network learns during training (Module 3).
Press Fire! and watch activation ripple left-to-right through the 784 → 64 → 32 → 10 network. The brighter a node, the higher its activation. The output layer picks a winner — the network's guess.
This left-to-right calculation is called the forward pass. The input's 784 numbers become 64, then 32, then finally 10 — and the biggest of those 10 is the network's answer.
a = wx + b, what is the weight (w)?784 → 64 → 32 → 10). Each neuron computes a = wx + b — sum of (weight × input) from every previous neuron, plus a bias — then squashes it to 0–1 with an activation like sigmoid. Values flow left-to-right (the forward pass), and the highest output neuron is the answer. The weights and biases are the numbers the network learns.Next up → Module 3: How it learns. We have the machine — but right now its weights are random, so it guesses garbage. How does it tune those millions of weights to get good? That's training, cost, and backpropagation.