Deep learning · /neural-net

Neural network

A multilayer perceptron trained by backprop, playground-style: every neuron in the Internals graph shows its activation over the whole plane, and the output neuron IS the decision surface. Probe the canvas to light up a forward pass; the chain-rule formula is bound to a real edge with its live gradient.

class 0class 1filled = train, hollow = testhover to probe · click to pin

step 0BCE —train acc —test acc —

Data

datasetpoints150noise0.15seedsplitmouse

Layer transform

a^{(ℓ)} = φ (W^{(ℓ)} a^{(ℓ - 1)} + b^{(ℓ)}) ℓ = 1 \dots L

Activation at the first hidden neuron

z_{1}^{(1)} = z a_{1}^{(1)} = φ (z) = a

Hover to link this neuron in the network graph; its mini-heatmap is φ(z) over the whole plane.

Loss

p = σ (z^{(L)}) = p L_{BCE} + λ ∥ W ∥^{2} = L

Backprop chain rule for one weight

\frac{\partial L}{\partial w _{11}^{(1)}} = from layers above δ_{1}^{(1)} \cdot a_{1}^{(0)} = \partial w w_{11}^{(1)} = w

δ is accumulated backwards from the output — every edge gets this same treatment.

What's simplified here

Plain SGD, full-batch or mini-batch — no momentum, Adam, batchnorm or dropout in v1.
One sigmoid output unit with BCE; the hidden activation is your choice (tanh/ReLU/sigmoid).
Xavier-style init from the page seed, so runs are exactly reproducible.