Forward propagation is the process of turning inputs into predictions. Set up a data table in row format below your parameters. 1. Compute the Hidden Layer Activation
To keep the model visual and manageable, we will build a network designed to solve the . The XOR gate is a classic benchmark because it is non-linearly separable, meaning a straight line cannot divide the outputs. A single-layer neuron cannot solve it; it requires a hidden layer. Our network architecture will feature: Input Layer: 2 neurons ( X1cap X sub 1 X2cap X sub 2 Hidden Layer: 2 neurons ( H1cap H sub 1 H2cap H sub 2 Output Layer: 1 neuron ( Phase 1: Setting Up the Network Topology
): Delta_H1 = (Delta_O1 * Wo1) * A_H1 * (1 - A_H1) Delta_H2 = (Delta_O1 * Wo2) * A_H2 * (1 - A_H2) 3. Weight Gradients
If you would like to expand your spreadsheet network, let me know:
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Next, apply the Sigmoid function in an adjacent cell to get the actual activation ( AH1cap A sub cap H 1 end-sub ): =1 / (1 + EXP(-Z_H1)) Repeat this process for H2cap H sub 2 3. Calculating the Output Layer Now, use the hidden layer activations ( ) as inputs for the final output node ( O1cap O sub 1 ): Z_O1 = (A_H1 * Wo1) + (A_H2 * Wo2) + B2
=(Prediction - Target) * Prediction * (1 - Prediction) 2. Hidden Layer Error Gradients ( δH1delta sub cap H 1 end-sub δH2delta sub cap H 2 end-sub