Is diagram mein ek interesting concept dikhaya gaya hai: A neural network can use hidden neurons to detect different combinations of inputs.

Let's break it down.

1. Understand the diagram

We have:

• 2 input neurons: $x_1,x_2$$x_1,x_2$

• 4 hidden neurons: $h_1,h_2,h_3,h_4$$h_1,h_2,h_3,h_4$

• 1 output neuron: $y$$y$

• Bias = -2

The colour of the edges represents weights:

• Red edge = -1

• Blue edge = +1

2. Why are there 4 hidden neurons?

Notice the weights going into each hidden neuron.

These represent all possible combinations of two bipolar inputs.

If inputs are either -1 or +1, there are:

$2^2=4$$2^2=4$

possible combinations.

Each hidden neuron is designed to detect one particular combination.

3. How does a hidden neuron detect a combination?

Let's take $h_1$$h_1$.

Its weights are:

$w_1=-1,w_2=-1$$w_1=-1,\quad w_2=-1$

Bias = -2.

Its weighted sum is:

$z_1=-x_1-x_2-2$$z_1=-x_1-x_2-2$

For input $(-1,-1)$$(-1,-1)$:

$z_1=(-1)(-1)+(-1)(-1)-2$$z_1=(-1)(-1)+(-1)(-1)-2$

$=1+1-2=0$$=1+1-2=0$

For input $(+1,+1)$$(+1,+1)$:

$z_1=-1-1-2=-4$$z_1=-1-1-2=-4$

So $h_1$$h_1$ responds differently to these two combinations.

The same principle applies to the other three neurons.

4. What happens at the output layer?

All four hidden neurons connect to the output neuron through weights:

$w_1,w_2,w_3,w_4$$w_1,w_2,w_3,w_4$

The output neuron combines their outputs to produce the final prediction.

The exact output depends on these weights and the output activation function.

5. Important exam concept

Number of possible input combinations

$\boxed{{\displaystyle 2^d}}$$\boxed{2^d}$

Where $d$$d$ is the number of bipolar input variables.

One technical caution: With the given bias of -2, a matching input produces weighted sum exactly zero. Whether that counts as neuron activation depends on whether the perceptron uses a $z\ge 0$$z\geq0$ or $z>0$$z>0$ threshold. The diagram alone doesn't specify that convention.

The main idea to remember: Each hidden neuron can be designed to recognise one particular input combination.