Xavier Initialization applicability in Neural Network

1. Simple Explanation – Where Xavier Helps (Real-World Use Case)

Use Case: Handwritten Digit Recognition (like MNIST)

Imagine we’re building a neural network to identify handwritten digits (0–9) from images.

Problem Without Proper Initialization:

If we randomly assign too small or too large weights:

  • Activations shrink to near zero → Vanishing Gradient
  • Or they explode → Exploding Gradient

Our network may:

  • Learn very slowly
  • Or never converge

How Xavier Helps:

Xavier initialization chooses weights in a way that:

  • Maintains same variance across layers (inputs ≈ outputs)
  • Ensures smooth gradient flow during backpropagation

Simple Step-by-Step:

  • Decide number of inputs (n_in) and outputs (n_out) to a neuron.
  • Use this formula to set the range of initial weights:

    • Screenshot

  • This avoids overly large or small initial signals and keeps training stable.

Xavier Initialization applicability in Neural Network – Xavier Initialization example with Simple Python