L1 Regularization vs L2 Regularization Selection for different use cases in Neural Network

1. L1 vs L2 Regularization – Simple Difference

Aspect L1 Regularization L2 Regularization
Also called Lasso Ridge
Penalty term Sum of absolute values of weights: `λ * Σ` w
Effect on weights Can make some weights exactly 0 Makes weights small, but rarely zero
Output Sparse model (feature selection) Smooth model (all features considered)
Geometric Shape Diamond-shaped constraint (L1 ball) Circular/elliptical constraint (L2 ball)
Optimization May lead to non-differentiable points Always differentiable, easier to solve
Use cases When we want feature selection When we want stability & generalization

Visual Intuition (Very Simple)

Imagine fitting a line, but we want to control how big the coefficients (weights) get.

  • L1 Regularization: Punishes weights so strongly that some are pushed to zero — removing unimportant features
  • L2 Regularization: Punishes the size of weights but not to zero — keeps all features but makes them smaller

2. When to Choose L1 vs L2? (Step-by-Step Guide)

Step 1: Check Feature Relevance

  • Do we think only a few features are truly useful? → Go for L1 to automatically remove the rest

Step 2: Check Model Stability

  • Do we want all features to contribute but gently? → Use L2 to shrink weights but not eliminate

Step 3: Need Interpretability?

  • Want to know which features matter (i.e., get rid of noise)? → L1 gives you a sparse model: easy to interpret

Step 4: Expecting Collinearity?

  • If our features are highly correlated: → L2 handles this better by distributing weight more smoothly

Step 5: Experiment Both

  • Try Elastic Net: a combination of L1 and L2

    • Useful when you’re not sure which one works better
    • Loss = MSE + α × L1 + β × L2

3. Real-World Use Cases

Use Case Best Regularization Reason
Text Classification (e.g. spam detection) L1 Sparse text data — L1 removes irrelevant words
Stock Price Prediction L2 Many features, all have some impact — no need to zero out
Image Recognition L2 Weights need to be smooth and stable
Medical Diagnosis (with many irrelevant features) L1 Helps pick the most relevant signals from noise
Logistic Regression in Finance (e.g. credit risk) L1 or Elastic Net Interpretability is key, and L1 selects key drivers

L1 Regularization vs L2 Regularization Selection for different use cases in Neural Network – Basic Math Concepts