M08 / FOUNDATIONS

The MLP. Watch one training step
flow through the network.

The multi-layer perceptron is the atom of deep learning. Here a tiny 2→2→1 network trains in front of you: the signal flows forward (yellow), the error flows backward (magenta), weights update, the loss drops. Every number is shown in sync with the animation — nothing hidden.

EXPERIMENT 08.01 · MLP.TRACE NET · 2 → 2 → 1 · sigmoid LOSS · ½(ŷ−y)² STATUS · LIVE

FORWARD · hidden layer cycle 1

PREDICTION ŷ vs TARGET y

ŷ = 0.50 error = 0.40 target = 0.90

LOSS over cycles

loss — · step 0

THIS PHASE · the math

CONTROLS

SPEED1.0×

lr η3.0

hidden layers2

neurons / layer3

activation tanh

loss mse

optimizer adam

x₁0.10

x₂0.30

target y0.90

WEIGHTS live

On weight initialization → notice the weights start as small random numbers (Xavier-style: scaled by 1/√fan-in), never zero. If every weight were identical, all hidden neurons would compute the same thing and receive the same gradient forever — they'd never differentiate. Random init breaks that symmetry. Hit RE-INITIALIZE to draw a fresh set and watch training restart.

This is the entire algorithm. Forward → loss → backprop → update, on repeat. A real network does exactly this with millions of weights over millions of examples. To see it train on a real dataset as a living diagram, open Training MLP in the Laboratory.