Threshold Logic Circuits
Collection
Boolean gates, voting functions, modular arithmetic, and adders as threshold networks.
β’
248 items
β’
Updated
β’
1
Computes Hamming weight mod 5 for 8-bit inputs. Multi-layer network with thermometer encoding.
xβ xβ xβ xβ xβ xβ
xβ xβ
β β β β β β β β
ββββ΄βββ΄βββ΄βββΌβββ΄βββ΄βββ΄βββ
βΌ
βββββββββββββββ
β Thermometer β Layer 1: 9 neurons
β Encoding β
βββββββββββββββ
β
βΌ
βββββββββββββββ
β MOD-5 β Layer 2: 4 neurons
β Detection β Pattern (1,1,1,1,-4)
βββββββββββββββ
β
βΌ
βββββββββββββββ
β Classify β Output: 5 classes
βββββββββββββββ
β
βΌ
{0, 1, 2, 3, 4}
Pattern (1, 1, 1, 1, -4) causes cumulative sums to cycle mod 5:
HW=0: sum=0 β 0 mod 5
HW=1: sum=1 β 1 mod 5
HW=2: sum=2 β 2 mod 5
HW=3: sum=3 β 3 mod 5
HW=4: sum=4 β 4 mod 5
HW=5: sum=0 β 0 mod 5 (reset: 1+1+1+1-4=0)
HW=6: sum=1 β 1 mod 5
HW=7: sum=2 β 2 mod 5
HW=8: sum=3 β 3 mod 5
| Layer | Neurons | Function |
|---|---|---|
| Input | 8 | Binary bits |
| Hidden 1 | 9 | Thermometer encoding |
| Hidden 2 | 4 | MOD-5 detection |
| Output | 5 | One-hot classification |
Total: 18 neurons, 146 parameters
| Class | HW values | Count/256 |
|---|---|---|
| 0 | 0, 5 | 57 |
| 1 | 1, 6 | 36 |
| 2 | 2, 7 | 36 |
| 3 | 3, 8 | 57 |
| 4 | 4 | 70 |
from safetensors.torch import load_file
import torch
w = load_file('model.safetensors')
def forward(x):
x = x.float()
x = (x @ w['layer1.weight'].T + w['layer1.bias'] >= 0).float()
x = (x @ w['layer2.weight'].T + w['layer2.bias'] >= 0).float()
out = x @ w['output.weight'].T + w['output.bias']
return out.argmax(dim=-1)
threshold-mod5/
βββ model.safetensors
βββ model.py
βββ config.json
βββ README.md
MIT