threshold-nor3
3-input NOR gate. Fires only when all inputs are silent. The silence detector.
Circuit
a b c
│ │ │
└───┼───┘
│
▼
┌──────────┐
│w: -1,-1,-1│
│ b: 0 │
└──────────┘
│
▼
NOR(a,b,c)The Perfect Silence Test
3-input NOR fires only on complete absence:
Inputs Sum Output 000 0 1 001 -1 0 010 -1 0 011 -2 0 100 -1 0 101 -2 0 110 -2 0 111 -3 0
Any activity silences the gate.
Zero-Budget Design
With bias 0, we start exactly at threshold:
sum = -a - b - c + 0 = -HW
fires when -HW >= 0
fires when HW = 0No tolerance. The slightest input pushes us below threshold.
Functional Completeness
Like NAND, NOR is universal:
NOT(x) = NOR(x, x, x)
OR(x,y,z) = NOR(NOR(x,y,z), NOR(x,y,z), NOR(x,y,z))
AND(x,y,z) = NOR(NOR(x,x,x), NOR(y,y,y), NOR(z,z,z))
NOR logic powered the Apollo Guidance Computer.
Extension of 2-input NOR
Gate Weights Bias NOR(a,b) [-1, -1] 0 NOR(a,b,c) [-1, -1, -1] 0 NOR(a,b,c,d) [-1, -1, -1, -1] 0
All have bias 0. Only the number of inputs changes.
Parameters
Component Value Weights [-1, -1, -1] Bias 0 Total 4 parameters
Optimality
Exhaustive enumeration of all 129 weight configurations at magnitudes 0-3 confirms this circuit is already at minimum magnitude (3) . There is exactly one valid configuration at magnitude 3, and no valid configurations exist below it.
Usage
1 from safetensors . torch import load_file
2 import torch
3
4 w = load_file ( 'model.safetensors' )
5
6 def nor3 ( a , b , c ) :
7 inp = torch . tensor ( [ float ( a ) , float ( b ) , float ( c ) ] )
8 return int ( ( inp * w [ 'weight' ] ) . sum ( ) + w [ 'bias' ] >= 0 )
9
10 print ( nor3 ( 0 , 0 , 0 ) ) # 1
11 print ( nor3 ( 0 , 0 , 1 ) ) # 0
Files
threshold-nor3/
├── model.safetensors
├── model.py
├── config.json
└── README.mdLicense
MIT
