Nesting dolls

A console that runs a console, which runs a tiny network.

N is a tiny network: 9 numbers that turn two inputs (0 or 1) into one answer. The buttons give it different jobs: XOR, AND, OR…
Console 1 runs N, reading its 9 numbers.
Console 2 runs console 1, reading console 1's 103 numbers. So it runs N too, one level further down.
Try: click the buttons. Both columns of the table always give the same answers. Pick Custom to set N's numbers yourself.

N, the tiny network

XORANDORNANDx1 − x2Custom

w₁₁

-4-3-2-10123

w₂₁

-4-3-2-10123

w₁₂

-4-3-2-10123

w₂₂

-4-3-2-10123

b₁

-4-3-2-101234

b₂

-4-3-2-101234

v₁

-4-3-2-10123

v₂

-4-3-2-10123

-4-3-2-101234

Its 9 numbers. Pick Custom to change them.

The answers

x₁	x₂	console 1	console 2
0	0
0	1
1	0
1	1

Computed live by your browser, for all four inputs at once.

How it works (for the curious)

I1, as I2 sees it

The 103 numbers of I1 (weights offset to unsigned, then biases), fed to I2 as inputs. I2 knows I1's wiring, which unit feeds which, but none of these values.

The tower

Net		inputs	units	weights
N	the program	2	—	9
I1 = interpret(N)	runs any N	11	34	82	in CSS, ×4
I2 = interpret(I1)	runs I1 running N	114	1,866	3,324	in CSS, ×4
I3 = interpret(I2)	runs I2 running I1 running N	4,795	191,288	270,246	numpy only

Each level costs roughly the previous one's weights times their bit width. I3 is exact too (checked in numpy), but its activation bounds, which it needs for the products, reach 10¹⁸, far past what CSS computes exactly. So the tower stops at two in the browser.

Checked in numpy for the five presets and 400 random N (every weight −4…3, every bias −4…4) on all four inputs: I1 and I2 equal N exactly, and every sum stays under 2²⁴. The browser test checks every preset and some custom N's in Chromium, Firefox and WebKit. Built by handwired/scripts/tower.py.