metadata
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
threshold-majority
Strict majority detector for 8 inputs. Fires when more than half are active.
Circuit
x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
│ │ │ │ │ │ │ │
└──┴──┴──┴──┼──┴──┴──┴──┘
▼
┌─────────┐
│ w: all 1│
│ b: -5 │
└─────────┘
│
▼
HW ≥ 5?
Mechanism
- Sum = (number of 1s) - 5
- Fires when Hamming weight ≥ 5 (more 1s than 0s)
A tie (4-4) doesn't count as majority. You need strictly more than half.
Functionally identical to threshold-5outof8.
Duality with Minority
| Circuit | Weights | Bias | Fires when |
|---|---|---|---|
| Majority | all +1 | -5 | HW ≥ 5 |
| Minority | all -1 | +3 | HW ≤ 3 |
Majority: "enough votes to pass" Minority: "not enough votes to block"
These are not complements (they don't sum to 1). The gap at HW=4 belongs to neither.
Parameters
| Weights | [1, 1, 1, 1, 1, 1, 1, 1] |
| Bias | -5 |
| Total | 9 parameters |
Optimality
Exhaustive enumeration of all 27,298,155 weight configurations at magnitudes 0-13 confirms this circuit is already at minimum magnitude (13). There is exactly one valid configuration at magnitude 13, and no valid configurations exist below it.
Usage
from safetensors.torch import load_file
import torch
w = load_file('model.safetensors')
def majority(bits):
inputs = torch.tensor([float(b) for b in bits])
return int((inputs * w['weight']).sum() + w['bias'] >= 0)
Files
threshold-majority/
├── model.safetensors
├── model.py
├── config.json
└── README.md
License
MIT