Neural Network
Examples
- \((x_{1}, x_{2}) \in \{0, 1\}\),
AND
$h_{\mathrm{AND}}(x) = \sum_{i=0}^{2} x_{i} \theta_{\mathrm{AND}} $,
| $x_{1}$ | $x_{2}$ | outputs |
|---|---|---|
| 0 | 0 | $-30 + 20 \times 0 + 20 \times 0$ |
| 0 | 1 | $-30 + 20 \times 0 + 20 \times 1$ |
| 1 | 0 | $-30 + 20 \times 1 + 20 \times 0$ |
| 1 | 1 | $-30 + 20 \times 1 + 20 \times 1$ |
OR
$h_{\mathrm{OR}}(x) = \sum_{i=0}^{2} x_{i} \theta_{\mathrm{OR}} $,
| $x_{1}$ | $x_{2}$ | outputs |
|---|---|---|
| 0 | 0 | $-10 + 20 \times 0 + 20 \times 0$ |
| 0 | 1 | $-10 + 20 \times 0 + 20 \times 1$ |
| 1 | 0 | $-10 + 20 \times 1 + 20 \times 0$ |
| 1 | 1 | $-10 + 20 \times 1 + 20 \times 1$ |
NOR
$h_{\mathrm{NOR}}(x) = \sum_{i=0}^{2} x_{i} \theta_{\mathrm{NOR}} $,
| $x_{1}$ | $x_{2}$ | outputs |
|---|---|---|
| 0 | 0 | $10 - 20 \times 0 - 20 \times 0$ |
| 0 | 1 | $10 - 20 \times 0 - 20 \times 1$ |
| 1 | 0 | $10 - 20 \times 1 - 20 \times 0$ |
| 1 | 1 | $10 - 20 \times 1 - 20 \times 1$ |
XOR = ($x_{1}$ AND $x_{2}$) OR ((NOT $x_{0}$) AND (NOT $x_{1}$))
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