Same idea as the layer above, more of it: instead of one hidden layer with four neurons, this network has two hidden layers with 128 and 64 — and that stacking is all the word "deep" has ever meant. It trains in your browser tab, right now, on 400 real handwritten digits, using ReLU activations, a softmax output and the Adam optimiser. Then you draw with your finger and it tells you what you drew. Nothing is precomputed and nothing is faked; if you refresh the page, it learns the whole thing again.
Draw big, and roughly centred.
64 numbers, 0–16. That is the whole input.
Your drawing is cropped to its ink, centred, and averaged down to an 8×8 grid of intensities — 64 numbers, which is genuinely all the network ever receives. Those 64 values flow through two hidden layers of 128 and 64 units, each applying a weight matrix, a bias, and the ReLU non-linearity that simply zeroes out negative values, before a final layer produces ten scores that softmax turns into probabilities summing to one. Training minimises cross-entropy loss — the surprise of the correct label — with Adam, which keeps a running estimate of each weight's gradient and its variance so that every parameter gets its own effective step size. The mathematics is identical to the XOR network one layer up; only the size, the optimiser and the output shape differ, which is the honest answer to what separates "neural networks" from "deep learning". Its blind spot is worth knowing: with no convolutions the model has no concept of a shape being the same shape when shifted, so a digit drawn in a corner may confuse it completely.