Neural Network Weight Change Impact in different stages

1. Story-Style Overview: The Neural Network Learning Journey

Imagine we’re training a neural network to guess if an email is spam or not.

  1. Initialization (Baby Brain): Like a newborn, the network starts with random weights — it knows nothing.
  2. Forward Pass (First Guess): It looks at features (e.g., “has link”, “capital letters”) and multiplies them with weights to make a guess — like: “Hmm, based on what I see, this email is probably 60% spam.”
  3. Loss Calculation (Teacher’s Feedback): A loss function compares the prediction (e.g., 0.60) with the true label (e.g., 1 for spam), and gives a score — the penalty for being wrong.
  4. Backpropagation (Learning from Mistakes): The network calculates how each weight contributed to the error and adjusts it slightly to reduce future mistakes.
  5. Repeat for All Emails (Practice Makes Perfect): Over thousands of examples, the weights get better — just like how we improve with feedback.

2. Weight Changes And impact :

We are training a neural network. Our weights decide how much importance we give to each input feature. These weights evolve at each processing step to improve prediction quality.

1.Weight Initialization (Start with a Blind Guess)

  • Weight Values: Small random numbers (e.g., from np.random.randn)
  • Why?: Prevent symmetry — each neuron needs a different path to learn uniquely
  • Impact:
    • Predictions are purely random initially.
    • Weights don’t “mean” anything yet.
  • Example:

    • weights = np.random.randn(n_features)

2.Forward Propagation (Use Current Weights to Make a Guess)

  • Weight Usage: We compute a weighted sum of inputs:
    z=w1x1+w2x2+…+b
    Activation: Sigmoid or softmax turns the raw score into probability.

Impact:

  • If weight w1 is high and x1=1 the prediction leans towards spam.
  • If weights are wrong, predictions will be far off.

Role of Weights Here: They define the slope of decision → higher weight = stronger influence from the corresponding feature.

3.Loss Computation (Measure How Bad the Guess Was)

  • Loss Example (Binary Cross Entropy):

Impact:

  • High loss → current weights led to a poor prediction.
  • Low loss → current weights are doing well.

Role of Weights Here: Indirect; they set up the prediction that determines the loss.

4.Backpropagation (Blame the Right Weights)

  • Gradient Calculation:

  • Impact:
    • If weight led to overprediction, it gets reduced.
    • If it underpredicted, it increases.
    • Features with higher values (x_i) affect weight change more.
  • Interpretation:
    • We learn which features were pushing the prediction in the wrong direction.
  • Effect:
    • Backprop gives precise responsibility scores to each weight.

5. Weight Update (Small Fixes for Big Gains)

  • Update Rule:

  • Impact:
    • Weights move a little closer to the “truth.”
    • The model now knows “this feature should matter more/less.”

6. Repeat for Many Samples (Training Epochs)

  • Weights are updated over:
    • Many samples → generalization
    • Many epochs → refinement
  • Early Training:
    • Weights change rapidly.
  • Impact:
    • We go from chaotic guesses → fine-tuned predictions.

7. Final Prediction (Learned Weights in Action)

  • Weights now:
    • Encapsulate which input features matter.
    • Reflect complex interactions (in deeper nets).
  • Impact:
    • High weights = strong signals for prediction.
    • Zero/low weights = ignored features.

3. Example of How Weight Affects Output

Let’s see an illustrative simulation with printed weights:

# After 0, 10, and final epoch

print(f”Initial Weights: {initial_weights}”)
print(f”After 10 Epochs: {weights_epoch_10}”)
print(f”Final Weights: {final_weights}”)