metadata
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
threshold-atmost2outof8
At-most-2-out-of-8 detector. Fires when two or fewer inputs are active. The error-tolerance bound.
Circuit
x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
│ │ │ │ │ │ │ │
└──┴──┴──┴──┼──┴──┴──┴──┘
▼
┌─────────┐
│ w: -1×8 │
│ b: +2 │
└─────────┘
│
▼
HW ≤ 2?
The Double-Error Budget
This circuit allows:
- Zero active inputs (silence)
- One active input (single event)
- Two active inputs (pair/double event)
Three or more is considered "too many."
Mechanism
sum = -HW + 2
| HW | Sum | Output |
|---|---|---|
| 0 | +2 | 1 |
| 1 | +1 | 1 |
| 2 | 0 | 1 |
| 3 | -1 | 0 |
| 4+ | < -1 | 0 |
The bias of +2 grants a budget of two active inputs.
Error Detection Context
In coding theory:
- A code with minimum distance d can detect d-1 errors
- AtMost2 accepts patterns with ≤2 bit flips from all-zeros
- Useful for validating that corruption is within correctable limits
| Scenario | This circuit |
|---|---|
| No errors | Pass |
| Single-bit error | Pass |
| Double-bit error | Pass |
| Triple+ error | Fail |
Dual of AtLeast6
| Circuit | Condition | Sparse/Dense |
|---|---|---|
| AtLeast6 | HW ≥ 6 | Dense |
| AtMost2 | HW ≤ 2 | Sparse |
Bitwise NOT maps AtMost2 inputs to AtLeast6 inputs.
Coverage
| HW | C(8,k) | AtMost2? |
|---|---|---|
| 0 | 1 | Yes |
| 1 | 8 | Yes |
| 2 | 28 | Yes |
| 3-8 | 219 | No |
Fires on 1 + 8 + 28 = 37 of 256 inputs (14.5%).
Parameters
| Component | Value |
|---|---|
| Weights | all -1 |
| Bias | +2 |
| Total | 9 parameters |
Usage
from safetensors.torch import load_file
import torch
w = load_file('model.safetensors')
def atmost2(bits):
inp = torch.tensor([float(b) for b in bits])
return int((inp * w['weight']).sum() + w['bias'] >= 0)
# Double event: allowed
print(atmost2([1,0,0,0,1,0,0,0])) # 1
# Triple event: rejected
print(atmost2([1,0,0,1,1,0,0,0])) # 0
Files
threshold-atmost2outof8/
├── model.safetensors
├── model.py
├── config.json
└── README.md
License
MIT