Analysis of a Gated Activation Function

Consider a simplified SwiGLU activation function where the input vector h is [2, 1]. The learnable parameters are defined as follows:

• W1 = [[3], [1]], b1 = [0]
• W2 = [[2], [-1]], b2 = [1]
• The Swish activation function is defined as swish(x) = x * sigmoid(x).
• Assume sigmoid(7) ≈ 0.999.

Given the formula output = swish(hW1 + b1) ⊙ (hW2 + b2), where ⊙ is the element-wise product, calculate the output. Which of the following is the correct result?

The SwiGLU activation function is defined by the formula: σ_swish(hW₁ + b₁) ⊙ (hW₂ + b₂). Match each component of this formula to its primary role in the computation.