metadata
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- multiplexer
threshold-mux2
2:1 multiplexer. The fundamental building block for data selection, routing one of two inputs to the output based on a select signal.
Circuit
d0 d1
│ │
│ │ s (select)
│ │ │
├───────┼───────┤
│ │ │
▼ │ │
┌───────┐ │ │
│ sel0 │◄──┼───────┤
│d0∧¬s │ │ │
└───────┘ │ │
│ ▼ │
│ ┌───────┐ │
│ │ sel1 │◄──┘
│ │ d1∧s │
│ └───────┘
│ │
└───┬───┘
▼
┌───────┐
│ OR │
└───────┘
│
▼
output
Truth Table
| s | d0 | d1 | out | Description |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | Select d0 (0) |
| 0 | 0 | 1 | 0 | Select d0 (0) |
| 0 | 1 | 0 | 1 | Select d0 (1) |
| 0 | 1 | 1 | 1 | Select d0 (1) |
| 1 | 0 | 0 | 0 | Select d1 (0) |
| 1 | 0 | 1 | 1 | Select d1 (1) |
| 1 | 1 | 0 | 0 | Select d1 (0) |
| 1 | 1 | 1 | 1 | Select d1 (1) |
Formula: out = (d0 AND NOT s) OR (d1 AND s)
Mechanism
Layer 1 - Selection Gates:
The circuit uses two AND-with-complement gates that fire only when their respective data input is selected:
| Gate | Weights [d0, d1, s] | Bias | Function |
|---|---|---|---|
| sel0 | [1, 0, -1] | -1 | d0 AND NOT(s) |
| sel1 | [0, 1, 1] | -2 | d1 AND s |
sel0 fires when d0=1 AND s=0:
- The negative weight on s means s=1 inhibits firing
- Bias -1 requires d0=1 to reach threshold when s=0
sel1 fires when d1=1 AND s=1:
- Both d1 and s must be 1 to overcome bias -2
Layer 2 - Output:
Simple OR gate combines the two selection paths.
Architecture
| Component | Weights | Bias | Function |
|---|---|---|---|
| sel0 | [1, 0, -1] | -1 | d0 AND NOT(s) |
| sel1 | [0, 1, 1] | -2 | d1 AND s |
| or | [1, 1] | -1 | OR(sel0, sel1) |
Parameters
| Inputs | 3 (d0, d1, s) |
| Outputs | 1 |
| Neurons | 3 |
| Layers | 2 |
| Parameters | 11 |
| Magnitude | 10 |
Building Larger Multiplexers
The MUX2 is the primitive for constructing larger multiplexers:
MUX4 = MUX2(MUX2(d0,d1,s0), MUX2(d2,d3,s0), s1)
MUX8 = MUX2(MUX4(d0-d3), MUX4(d4-d7), s2)
MUX16 = MUX2(MUX8(d0-d7), MUX8(d8-d15), s3)
Each doubling adds one layer of MUX2 gates.
Usage
from safetensors.torch import load_file
import torch
w = load_file('model.safetensors')
def mux2(d0, d1, s):
inp = torch.tensor([float(d0), float(d1), float(s)])
# Layer 1: Selection
sel0 = int((inp @ w['sel0.weight'].T + w['sel0.bias'] >= 0).item())
sel1 = int((inp @ w['sel1.weight'].T + w['sel1.bias'] >= 0).item())
# Layer 2: Combine
l1 = torch.tensor([float(sel0), float(sel1)])
return int((l1 @ w['or.weight'].T + w['or.bias'] >= 0).item())
# Examples
print(mux2(1, 0, 0)) # 1 (selects d0)
print(mux2(1, 0, 1)) # 0 (selects d1)
print(mux2(0, 1, 1)) # 1 (selects d1)
Applications
- Data routing in ALUs
- Register file read ports
- Conditional assignment in hardware
- Building blocks for barrel shifters
- Crossbar switches
Files
threshold-mux2/
├── model.safetensors
├── model.py
├── create_safetensors.py
├── config.json
└── README.md
License
MIT