Little Bits of Artificial Intelligence

1. Definition

Mean Squared Error (MSE) is a loss function used to measure how well a neural network predicts continuous output (regression). It calculates the average of the squares of the differences between predicted and actual values:

Where:

• yi​: actual value
• y^i: predicted value
• n: number of data points

2. Significance in Neural Networks

• Measures error: Tells how far the model’s predictions are from actual values.
• Drives learning: Guides the neural network on how to adjust weights to minimize error.
• Smooth and differentiable: Useful for gradient descent optimization.
• Penalizes larger errors: Squaring emphasizes large deviations more.

3. Plain Story-Based Explanation

Imagine a teacher grading students’ math papers. Each student predicts the height of a sunflower after 30 days. He already knows the actual heights.

For each student, he calculates:

• How far off they were (error)
• Square the error (to penalize bigger mistakes more)
• Average the scores of all students

That average squared error is the MSE. Now, if students were trained (like training a neural network), teacher can use this average error to help them improve their predictions next time.