Weight

In deep learning, weights are numbers that represent the importance of each input to a neuron.
They control how much influence an input has on the output of a neuron.

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Example:

Imagine you are judging a cake based on: - Taste - Look - Smell

You might feel that taste is the most important, followed by look, and smell is less important.

So you can assign: - Taste → Weight = 0.6

• Look → Weight = 0.3
• Smell → Weight = 0.1

Then, your overall score of the cake would be calculated as:

Score = (Taste Rating × 0.6) + (Look Rating × 0.3) + (Smell Rating × 0.1)

Thus, weights tell the model which input is more important in decision-making.

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In Deep Learning Neurons:

1. Each neuron receives multiple inputs (features).
2. Each input is multiplied by a weight.
3. The weighted inputs are added up.
4. The result is passed through an activation function to decide the output.

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Mathematical View:

Output = Activation(w₁ × x₁ + w₂ × x₂ + … + w_n × x_n + b)

Where:

• w₁, w₂, …, w_n = weights
• x₁, x₂, …, x_n = inputs
• b = bias
• Activation function = makes the output non-linear (like decision-making)

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Why are weights important?

Role	Explanation
Control Importance	Higher weight → More important input
Learn from data	Model adjusts weights during training
Prediction accuracy	Good weights help the model predict better

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Key points:

• Weights are not fixed.
• They are learned automatically during training using optimization algorithms (like gradient descent).
• Incorrect weights → Wrong predictions.
• Correct weights → Accurate predictions.

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How Does a Deep Learning Model Decide Weights?

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Simple Answer:

A deep learning model does not start with perfect weights.
It starts with random guesses for weights and learns better weights by looking at the errors it makes during predictions.

This learning process is done using algorithms like Gradient Descent.

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Step-by-Step Layman Explanation

Step 1: Start with random weights

• Model assigns random numbers (weights) to inputs.
• These are just guesses at the beginning.

Step 2: Make predictions using these weights

• The model predicts an output using these guessed weights.

Step 3: Check how wrong the model is (Calculate error)

• Model compares its prediction to the actual correct answer.
• Calculates the error (difference between predicted and actual).

Step 4: Adjust the weights to reduce the error

• Using Gradient Descent (a math method), the model adjusts the weights slightly:
  • If the prediction was too high, decrease the weights.
  • If the prediction was too low, increase the weights.
• This is done using the Perceptron Learning Rule or backpropagation in complex models.

Step 5: Repeat the process many times (Epochs)

• The model keeps repeating this process (over the entire dataset).
• Over time, the weights adjust to values that help the model make better and better predictions.

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Mathematical View (Simplified)

\[\large \text{New Weight} = \text{Old Weight} - \alpha \times \frac{\partial \text{Error}}{\partial \text{Weight}}\]

Where:

• α - Learning Rate (small positive number)

• $\frac{\partial \text{Error}}{\partial \text{Weight}}$ — Gradient of Error with respect to Weight

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Real-World Analogy

Learning to throw a basketball into a hoop:

1. First try (Random weight): You throw blindly.
2. Check the error: You see the ball missed the hoop.
3. Adjust your angle and force (Weight): Based on how far you missed.
4. Try again: Repeat until you start scoring baskets.

Deep learning models do the same. They adjust their ‘throw’ (weight) until the ‘ball’ (prediction) lands close to the ‘hoop’ (actual label).

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Summary Table

Step	What happens?
Initialize	Random weights assigned
Predict	Model makes predictions using current weights
Calculate Error	Compare predictions with actual output (Loss)
Update Weights	Use Gradient Descent to adjust weights to reduce error
Repeat	Do this over many passes (epochs)

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