metadata
license: mit
tags:
- formal-verification
- coq
- threshold-logic
- neuromorphic
tiny-5OutOf8-verified
Formally verified 5-out-of-8 threshold gate (majority). Single threshold neuron with 100% accuracy.
Architecture
| Component | Value |
|---|---|
| Inputs | 8 |
| Outputs | 1 |
| Neurons | 1 |
| Parameters | 9 |
| Weights | [1, 1, 1, 1, 1, 1, 1, 1] |
| Bias | -5 |
| Activation | Heaviside step |
Key Properties
- 100% accuracy (256/256 inputs correct)
- Coq-proven correctness
- Single threshold neuron
- Integer weights
- Fires when at least 5 of 8 inputs are true
- Note: Equivalent to Majority gate.
Usage
import torch
from safetensors.torch import load_file
weights = load_file('fiveoutof8.safetensors')
def fiveoutof8_gate(bits):
# bits: list of 8 binary values
inputs = torch.tensor([float(b) for b in bits])
weighted_sum = (inputs * weights['weight']).sum() + weights['bias']
return int(weighted_sum >= 0)
# Test
print({func}_gate([0,0,0,0,0,0,0,0])) # 0 (0/5, below threshold)
print({func}_gate([1,1,1,1,0,0,0,0])) # 0 (4/8, below threshold)
print({func}_gate([1,1,1,1,1,0,0,0])) # 1 (5/8, at threshold)
print(fiveoutof8_gate([1,1,1,1,1,1,1,1])) # 1 (8/8, above threshold)
Verification
Coq Theorem:
Theorem fiveout_eight_correct : forall x0 x1 x2 x3 x4 x5 x6 x7,
fiveout_eight_circuit [x0; x1; x2; x3; x4; x5; x6; x7] =
fiveout_eight_spec [x0; x1; x2; x3; x4; x5; x6; x7].
Proven axiom-free via:
- Exhaustive: All 256 inputs verified
- Universal: Quantified proof over boolean combinations
- Algebraic: Hamming weight ≥ 5
Full proof: coq-circuits/Threshold/FiveOutOfEight.v
Circuit Operation
Input with h true bits (Hamming weight h):
- Weighted sum: h - 5
- Output: 1 if h ≥ 5, else 0
Citation
@software{tiny_5outof8_prover_2025,
title={tiny-5OutOf8-verified: Formally Verified 5-out-of-8 threshold gate (majority)},
author={Norton, Charles},
url={https://huggingface.co/phanerozoic/tiny-5OutOf8-verified},
year={2025}
}