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 = 0

No 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

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def nor3(a, b, c):
    inp = torch.tensor([float(a), float(b), float(c)])
    return int((inp * w['weight']).sum() + w['bias'] >= 0)

print(nor3(0, 0, 0))  # 1
print(nor3(0, 0, 1))  # 0

Files

threshold-nor3/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT