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:

Forward Pass

Compute hidden layer pre‑activations
z h
and activations
h
.

Compute output pre‑activation
z o
and prediction
y ^
.

Round each value to two decimals .

Error

Compute loss:

E = 1 2 ( y − y ^ ) 2

Round to two decimals .

Backward Pass (Chain Rule)

Compute output delta:

δ o = ( y − y ^ ) ⋅ y ^ ( 1 − y ^ )

Compute hidden deltas:

δ h = δ o ⋅ W o ⋅ h ( 1 − h )

Round all deltas to two decimals .

Weight Updates

Update output weights and bias:

W o ← W o + η ⋅ δ o ⋅ h

b o ← b o + η ⋅ δ o

Update hidden weights and biases:

W h ← W h + η ⋅ δ h ⋅ X

b h ← b h + η ⋅ δ h

Round all updated parameters to two decimals .

Question

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:

Forward Pass

Compute hidden layer pre‑activations 
 z h 
 and activations 
 h 
 .

Compute output pre‑activation 
 z o 
 and prediction 
 y ^ 
 .

Round each value to  two decimals .

Error

Compute loss:

E = 1 2 ( y − y ^ ) 2

Round to  two decimals .

Backward Pass (Chain Rule)

Compute output delta:

δ o = ( y − y ^ ) ⋅ y ^ ( 1 − y ^ )

Compute hidden deltas:

δ h = δ o ⋅ W o ⋅ h ( 1 − h )

Round all deltas to  two decimals .

Weight Updates

Update output weights and bias:

W o ← W o + η ⋅ δ o ⋅ h

b o ← b o + η ⋅ δ o

Update hidden weights and biases:

W h ← W h + η ⋅ δ h ⋅ X

b h ← b h + η ⋅ δ h

Round all updated parameters to  two decimals .

Answer

updated weights at Wo=[0.31,−0.24] and at 𝑊ℎ=[[0.25,−0.15],[0.40,0.20]]

Answer

updated weights at Wo=[0.45,−0.25] and at 𝑊ℎ=[[0.35,−0.63],[0.65,0.80]]

Answer

updated weights at Wo=[0.91,−0.84] and at 𝑊ℎ=[[0.85,−0.150],[0.76,0.280]]

Answer

updated weights at Wo=[0.01,−0.02] and at 𝑊ℎ=[[0.15,−0.13],[0.56,0.80]]

Crowdly

You are training a two‑layer neural network (2 inputs → 2 hidden neurons → 1 o...

Tasks:

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