Example for w₁₁ (E6): =SUM($A$2:$A$5 * R2:R5) (use Ctrl+Shift+Enter as array formula or SUMPRODUCT)
Use the Solver add-in in Excel to optimize the weights and biases. The Solver add-in can be found in the Data tab. Build Neural Network With Ms Excel
| | Cells | Purpose | |--------------------|------------------|--------------------------------------------| | Input data | A2:B5 | XOR truth table (0,0 → 0; 0,1 → 1; 1,0 → 1; 1,1 → 0) | | Target output | C2:C5 | [0, 1, 1, 0] | | Weights & biases | E1:H5 | Initial small random values (e.g., ±0.5) | | Forward pass | J2:O5 | Hidden layer activations, output predictions | | Error & gradients | Q2:U5 | Loss, delta output, delta hidden | | Weight updates | E1:H5 (circular) | New weight = old weight – learning rate × gradient | Example for w₁₁ (E6): =SUM($A$2:$A$5 * R2:R5) (use
The next step is to replicate this logic in Python using NumPy. You will find that your Excel spreadsheet is merely a visual, cell-by-cell version of a NumPy array. You will find that your Excel spreadsheet is
Derivative of Sigmoid: Sigmoid(Z) * (1 - Sigmoid(Z))