A rule that keeps learning

Start from a rule written by hand, then let it learn.

The rule: “red if it's inside the middle square”. It's written by hand as a tiny network, so it's right from the start.
Then it learns: every time you place a point, the browser trains that network on your points, 16 rounds, like any network.
Try: put red dots in the middle square and blue dots around: 100% right away. Then add red dots just to the right of the square: the red area grows to take them in. Click From random to start without the rule, and it learns much worse.

	x	y	1	out
h1	8	0	-32	-16
h2	-8	0	-32	-16
h3	0	8	-32	-16
h4	0	-8	-32	-16
out				64 (bias)

The rule's 17 numbers. Small grey: as written by hand. Blue: changed by learning.

How it works (for the curious)

How it trains

Step	CSS, per point p and hidden unit k
forward	`h = max(0, calc(x·a + y·b + c))`, `s = calc(Σ v·h + d)`
loss	`g = t · clamp(0, 57 − t·s, 1)`: the point's colour if it's wrong or within the margin
through the ReLU	`f = clamp(0, h, 1)`, the derivative [z > 0]
update	`v += Σ g·h / 31`, `a += v · Σ g·f·x / 151`, `b += v · Σ g·f·y / 151`, `c += v · Σ 2·g·f / 31`, `d += 4·Σ g`, each clamped

Integers throughout. Every divisor is odd, so CSS's rounding matches Python's exactly, and the clamps keep every sum under 2²⁴. The first layer's step is five times smaller than the rest: with a big step a box edge overshoots, flips, and its ReLU dies.

The browser test places the demo sets from handwired/scripts/unfrozen.py from both starts and checks all 17 numbers at every epoch, and every error count, against the numpy reference in Chromium, Firefox and WebKit.

mistakes after each round of learningclick a bar to see that round

How it trains