L2 norm
The L2 norm is the nonnegative Euclidean magnitude of a vector, equal to the square root of the sum of its components’ squares, and to absolute value for a scalar.
Grokking Machine Learning
The L2 norm of a vector is the square root of the sum of the squared values of its components.
- How it is used
- Uses squared model coefficients as a complexity measure in regularization to help reduce overfitting.
- How deep it goes
- Defines the complexity measure, explains coefficient shrinkage, and excludes model bias from the calculation.
- Examples
- Uses movie recommendation coefficients and a polynomial regression exercise to illustrate complexity and ridge error.
- What you can do after
- Apply L2 regularization by adding a coefficient-complexity measure to regression error during training.
Natural Language Processing in Action, Second Edition
The L2 norm of a vector is the square root of the sum of the squares of its components.
- How it is used
- Supports measuring vector length, Euclidean distance, normalization, and cosine-based comparison in NLP vector spaces.
- How deep it goes
- Defines the formula, explains geometric consequences, and demonstrates NumPy normalization without deriving deeper linear-algebra theory.
- Examples
- Uses two-dimensional vector geometry, a four-element NumPy vector, TF vectors, and normalized sentence embeddings.
- What you can do after
- Apply it via NumPy to calculate vector lengths, normalize embeddings, and support cosine-similarity computations.
Read how Natural Language Processing in Action, Second Edition explains l2 norm →
Math and Architectures of Deep Learning
The Euclidean norm measuring a vector's length by squaring components, summing them, and taking the square root.
- How it is used
- Measures vector magnitude, model prediction error, and weight size used for regularization.
- How deep it goes
- Defines the formula, dot-product relationship, geometric meaning, normalization use, and regularization role without deriving matrix norms.
- Examples
- Uses error vectors across training data, right-triangle geometry, unit-vector normalization, and weight penalties.
- What you can do after
- Evaluate vector magnitude, interpret prediction error, normalize vectors, and understand L2 weight regularization.
Read how Math and Architectures of Deep Learning explains l2 norm →
Related concepts
- Euclidean distanceequivalent to · Euclidean distance is the straight-line distance between two points in Euclidean space, calculated as the square root of the sum of squared differences between corresponding coordinates.
- weight decayused by · Weight decay is a model-training regularization technique that discourages large parameter values by penalizing their magnitudes or shrinking them during optimization.
- L1 regularizationused by · L1 regularization is a technique that adds a penalty proportional to the sum of absolute model-parameter values, encouraging sparse parameter estimates.
- ridge regressionconfigures · Ridge regression is linear regression that applies an L2 penalty to coefficient magnitudes, shrinking estimates toward zero to reduce overfitting.
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