You are training a two‑layer neural network (2 inputs → 2 hidden neurons → 1 output neuron) to learn the XOR gate using sigmoid activation and Gradient Descent.

Tasks:

1. Forward Pass

   • Compute hidden layer pre‑activations

     zh

     and activations

     h

     .

   • Compute output pre‑activation

     zo

     and prediction

     y^

     .

   • Round each value to two decimals.

2. Error

   • Compute loss:

• Round to two decimals.

1. Backward Pass (Chain Rule)

   • Compute output delta:

• Compute hidden deltas:

• Round all deltas to two decimals.

1. Weight Updates

   • Update output weights and bias:

• Update hidden weights and biases:

• Round all updated parameters to two decimals.

A model predicts house price as 𝑤⋅𝑥.True price = 300, input 𝑥=10, current weight w= 20.

and its Gradient :

Perform Manally one RMSProp update with learning rate 0.01.

RMSProp parameters: