How a neural network actually learns

A six-step walk-through for anyone new to neural nets. Click the chapters below — the live model on this page will reconfigure itself to match each idea.

Meet the puzzle. Each dot below has two coordinates — call them x₁ and x₂ — and a label that's either +1 or −1.

The network has never seen the rule. Our job is to teach it the boundary between the two groups using only the examples.

Each circle is a neuron. Lines are weights — green positive, pink negative.click any node →

● Forward — green pulses are activations flowing left → right. The network is computing its guess.line thickness = |weight| · line colour = sign (green +, pink −)

initializing network…

Dataset

Two interleaved spirals — needs curves to separate

Architecture

2 inputs → 6 hidden → 6 hidden → 1 output

Activation

Learning Rate

0.050too high = unstable · too low = slow

How Wrong Over Time

0.00000

The loss after each training step. Down = the network is getting smarter.

awaiting training data

Step 0Step 0

What the Network Thinks

Background colour = the network's prediction at every point on the plane (green = class +1, pink = class −1). Dots = the actual training examples. As training progresses, the coloured regions should grow to match the dots on the Spiral dataset.

Inference — Try the Trained Network

This is the same network running inference — only the forward pass on a new input you control. Move the sliders (or the point on the plot) and watch the prediction change. The point you choose is the same coordinate the boundary plot above colours.

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The Examples We're Teaching With

Spiral · synthetic 2D

2 inputs · 2 classes

The network never sees the underlying rule — only these labelled dots. It has to figure out the pattern from the examples alone.