Error Reduction in Prediction of Result – Conceptual Steps in Neural Network

1. Intuition: Why Error Reduces After Each Epoch

Think of training a neural network like teaching a child to throw a ball into a basket:

  • First attempt: The ball misses — too far.
  • Feedback: We tell the child, “That was too strong.”
  • Adjustment: Next time, the child throws with less force.
  • Over time, this trial-error-feedback-adjustment loop helps the child improve.

Similarly, in a neural network:

  • It makes a guess (prediction) using current weights.
  • It measures how wrong that guess is (error/loss).
  • It adjusts its weights to do better next time.

Mathematical Basis: How It Happens

Let’s formalize this in neural network language:

1. Loss Function: Measuring How Wrong We Are

We calculate Loss (Error) between prediction y^ and true label y. A common loss: Mean Squared Error (MSE) for regression tasks.

           n
Loss = 1 / n​∑​(yi​−y^​i​)^2
          i=1

2. Gradient Descent: Finding the Direction to Reduce Error

We want to minimize the loss, so we use gradient descent:

  • Calculate the gradient (slope) of the loss w.r.t. each weight www
  • This tells us how the loss changes when the weight changes

∂Loss / ∂w

3. Weight Update Rule: Learn from Mistakes

We update weights in the opposite direction of the gradient:

Screenshot

η is the learning rate — how big a step we take.

This moves the weight in the direction that reduces the error.

4. Epochs: Repeating the Process

An epoch means we’ve passed through the entire dataset once.

  • After each epoch, we’ve had many chances to adjust weights
  • If we keep doing this:
    • Predictions improve
    • Loss reduces
    • Weights move toward optimal values

What Causes Error to Decrease Over Epochs?

Reason Explanation
Gradient points toward error reduction Gradients indicate how to change weights to reduce loss
Small step-by-step learning Learning rate ensures weights are not changed drastically
Data coverage in each epoch Seeing full dataset helps generalize learning
Feedback loop Each prediction error leads to better weight tuning

Caveats: When Error Doesn’t Reduce

  1. Too high learning rate → overshoots optimal weights
  2. Too low learning rate → learning becomes very slow
  3. Model underfitting/overfitting → can’t learn or learns noise
  4. Poor initialization → can get stuck in local minima

Error Reduction in Prediction of Result Conceptual Steps in Neural Network – Error Reduction in prediction of Results with Simple Python