Little Bits of Artificial Intelligence

Story Setup: Predicting Mood from Weather & Sleep

Imagine we’re building a small neural network that predicts “Our Mood” (Happy or Sad) based on:

• Weather (0 = Bad, 1 = Good)
• Hours of Sleep (0 = Low, 1 = Enough)

The Network Structure

We’ll use:

• 2 Inputs: Weather and Sleep
• 1 Hidden Layer: with 2 neurons
• 1 Output Layer: with 1 neuron (gives value between 0 and 1, representing probability of being happy)

Input Layer:    (Weather, Sleep)
                   |
                   ↓
Hidden Layer:   [Neuron H1]    [Neuron H2]
                   \           /
                    \         /
                     \       /
                      \     /
                    Output Neuron

Let’s Use Real Numbers

Step 1: Inputs

Let’s say:

• Weather = 1 (Good)
• Sleep = 0 (Low)

So, our input vector is: X = [1, 0]

Step 2: Hidden Layer Processing

Each hidden neuron gets inputs from both weather and sleep. Suppose:

Hidden Neuron H1:

• Weights: W1 = [0.5 (for weather), 0.4 (for sleep)]
• Bias: b1 = -0.3
• Activation: sigmoid

z_H1 = (1 * 0.5) + (0 * 0.4) + (-0.3) = 0.2
a_H1 = sigmoid(0.2) ≈ 0.55

Hidden Neuron H2:

• Weights: W2 = [0.3, 0.7]
• Bias: b2 = -0.1

z_H2 = (1 * 0.3) + (0 * 0.7) + (-0.1) = 0.2
a_H2 = sigmoid(0.2) ≈ 0.55

Step 3: Output Layer

Output neuron takes a_H1 and a_H2 as inputs.

• Weights: [0.6, 0.9]
• Bias: -0.2

z_output = (0.55 * 0.6) + (0.55 * 0.9) + (-0.2) ≈ 0.33 + 0.495 – 0.2 = 0.625
a_output = sigmoid(0.625) ≈ 0.65

So, the final output is 0.65, which we interpret as a 65% chance of being Happy.

How Hidden Layers Influence Prediction

Without a hidden layer, the network would have done:

Mood = sigmoid(W1*Weather + W2*Sleep + b)

That’s just a straight line — can’t capture complex relationships.

With hidden layers:

• Neurons learn intermediate “features”.
• H1 may learn “Is the day comfortable?”
• H2 may learn “Is the person well-rested?”
• These new concepts allow the network to combine inputs non-linearly.

Analogy:

Think of the hidden layer as detectives figuring out clues:

• “Is the weather good but sleep bad?” ➝ medium mood
• “Is both good?” ➝ high mood
• “Both bad?” ➝ low mood