Consider a two-input neuron with weight vector W = [3, 2], input... | Agrigyan

• Artificial Neural Network Neuron Activation:
• Given neuron parameters:
• Weight vector: $W = [w_1, w_2] = [3, 2]$
• Input vector: $X = [x_1, x_2]^T = [-5, 7]^T$
• Bias: $b = 1$
• Calculating net input ($n$):

$$n = W X + b = (w_1 x_1 + w_2 x_2) + b$$ $$n = (3 \times (-5) + 2 \times 7) + 1 = (-15 + 14) + 1 = -1 + 1 = 0$$

• Evaluating transfer functions at net input $n = 0$:
• Log-Sigmoid (Logistic Function):

$$f(n) = \frac{1}{1 + e^{-n}} = \frac{1}{1 + e^0} = \frac{1}{1 + 1} = \frac{1}{2} = 0.5$$

• Hard limit: Returns 1 for $n \ge 0$, and 0 for $n \lt 0$.
• Linear: Returns $f(0) = 0$.
• Conclusion: Log-sigmoid transfer function produces an output of 0.5 (Option 4).

Correct option: (4) Log-sigmoid