IGNOU MMTE 7 2026 - Approximate the function for , by solving 1-

Question

Approximate the function $f(x) = 1 + \cos \pi x$ for $-1 \le x \le 1$ , by solving 1-2-1 network, using Back propagation algorithm. The weighted structure and initial input are as follows:
Weighted structures are:
$[W]^{\circ} = \begin{bmatrix} -0.25 \\ -0.40 \end{bmatrix}$ and bias $\phi_{(0)}^{(1)} = \begin{bmatrix} -0.50 \\ -0.1 \end{bmatrix}$
$[V]^{\circ} = \begin{bmatrix} 0.1 & -0.2 \end{bmatrix}$ and bias $\phi_{(0)}^{(2)} = [0.5]$
The initial input is 1.
Draw the architecture of the model. Perform one iteration.

10 Jan 2026

Answer :

Word Count : 300

Consider a 1–2–1 feed-forward neural network consisting of one input neuron, two hidden neurons, and one output neuron. The single input (x) is connected to the two hidden neurons through weights (w_1=-0.25) and (w_2=-0.40) with corresponding biases (\phi_1=-0.50) and (\phi_2=-0.10). The hidden layer outputs are connected to the output neuron through weights (v_1=0.1) and (v_2=-0.2) with output bias (\phi_o=0.5). A sigmoid activation function (\sigma(z)=\frac{1}{1+e^{-z}}) is used

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