DIÁKRISIS · discernment · how a machine learns to tell things apart · kept by MINOS (who draws the boundary and sorts each to its class)

THE PERCEPTRON ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP

1958: the first thing that LEARNED. A single artificial neuron adjusts its weights every time it guesses wrong, nudging its decision line toward the mistake — and on data that CAN be split by a line, it’s guaranteed to find one, in finite time. It’s the seed of every neural network. (Its famous limit — it can’t learn XOR — is why we stack layers.) Slide the epochs and watch the line snap into place.

◆ LIT▲ AMBER
◧ THE MEASURE · 2D
◍ ONE NEURON LEARNS · 3D · the ancestor of every net
◆ THE FOURTH · 4D · a tesseract turns
◐ THE SHADOW · one dimension down
👶 THE TODDLER CORNER — one fat tap
epochs
misclassified
weights
separated?

◆ LIT — exact / checkable

The perceptron is a linear binary classifier: y = sign(w·x + b). It learns by the PERCEPTRON RULE — on each misclassified example, w ← w + y·x (and b ← b + y) — nudging the boundary toward the error. The Perceptron Convergence Theorem guarantees it finds a separating hyperplane in finitely many updates IF the data is linearly separable. It cannot solve non-linearly-separable problems (famously XOR, Minsky–Papert 1969), which motivated multi-layer networks and backprop. A fail-loud self-check throws unless it reaches 0 errors on linearly-separable data. ◆ real machine learning, node-verified.

▲ AMBER — the figure

Convergence is guaranteed ONLY for linearly-separable data (else it never settles); the single neuron is the ancestor of, not a substitute for, deep networks. The update rule and convergence are exact.

DIÁKRISIS: every classifier is a line drawn through the world; the art is where to draw it.  — MINOS
David Lee Wise / ROOT0, with AVAN · DIÁKRISIS — kept by MINOS, the sorter