How deeply does Causal AI cover weight decay?

Defines the penalty and its effect on large estimates, but does not derive an update rule or implementation procedure.

Weight decay

As explained in Causal AI

L2 regularization is a regularization method that penalizes the sum of squared parameter values.

Weight decay, treated here as L2 regularization, modifies parameter estimation by adding a penalty proportional to the sum of squared parameter values to the loss. The penalty makes increasingly large parameters increasingly costly, steering optimization away from exceedingly large estimates. section 2.3.4

Operationally, weight decay connects three steps:

Begin with a loss function; negative log-likelihood is one example. section 2.3.4
Add the squared-parameter term to obtain a regularized objective. section 2.3.4
Use numerical optimization to seek parameter values that balance data fit against parameter magnitude. section 2.3.4

Neural-network estimation

When directly finding the likelihood-maximizing parameters is infeasible, optimize a loss augmented with the L2 penalty; the resulting candidate favors smaller parameter values rather than exceedingly large estimates. section 2.3.4

How Causal AI covers it

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Also explained in

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Grokking Machine LearningRidge regression is a linear regression technique that uses an L2 coefficient penalty, shrinking coefficients toward zero without usually making them zero.
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Machine Learning for Tabular Data: XGBoost, Deep Learning, and AIL2 regularization adds a penalty proportional to the squared values of model parameters to constrain model complexity.
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Deep Learning with PyTorch, Second EditionAn optimization method that shrinks parameters in proportion to their current values, generally distinct from L2 regularization for adaptive optimizers.
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Ensemble Methods for Machine LearningL2 regularization penalizes the squared magnitude of model parameters or other model complexity measures in an optimization objective.
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Deep Learning with R, Third EditionL2 regularization is a regularization method that adds a penalty proportional to the squared values of model parameters.
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Deep Learning with Python, Third Edition
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Machine Learning Algorithms in DepthA regularization method that adds a penalty proportional to the squared magnitude of model parameters to discourage large weights.
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Time Series Forecasting Using Foundation ModelsL2 regularization is a penalty method that discourages large model weights by adding their squared magnitudes to the optimization objective.

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Related concepts

regularizationkind of · Regularization is a modeling technique that constrains or penalizes solutions during fitting or optimization to discourage undesirable complexity or behavior and improve generalization or estimation.
overfittingaddresses · Overfitting is a modeling condition in which a model fits patterns or idiosyncrasies in its training data too closely and consequently generalizes poorly to new data.
ridge regressionused by · Ridge regression is linear regression that applies an L2 penalty to coefficient magnitudes, shrinking estimates toward zero to reduce overfitting.
l2 normuses · 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.
AlexNetused by · AlexNet is a convolutional neural network architecture designed for image classification and recognized for its landmark performance in large-scale image recognition.

This explainer was generated by Manning's knowledge graph from the text of Causal AI. The section links point to the parts of the book it draws on.