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Expressive power

As explained in Inside Deep Learning: Math, Algorithms, Models

The set of functions or behaviors that a model architecture can express.

Expressive power is the set of functions or behaviors a model architecture can represent. Increasing capacity lets a network fit more complex functions, including memorizing a dataset. section 6.2.7

Use these distinctions when diagnosing model behavior:

  • A model that cannot fit randomly assigned labels may be too small; one that fits them has enough capacity to memorize the dataset. section 6.2.7
  • Normalization layers do not increase representational capacity, but they improve what the model can learn and can help avoid a harder-to-reason-about training situation. section 6.2.7

Normalization without added power

A normalization layer follows a linear layer, yet algebra can rewrite the combined operations so the normalized form does not add representational power. Its value is improved learning rather than a larger function class. section 6.2.7

How Inside Deep Learning: Math, Algorithms, Models covers it

How deep it goes
Defines capacity, tests memorization with random labels, and proves normalization does not add representational power algebraically.
Examples
Uses random-label memorization, function-complexity diagrams, and normalization-layer algebra.
What you can do after
Evaluate whether a model lacks capacity and understand why normalization can improve learning without expanding its function class.
How it connects
Connects expressive power to model capacity, overfitting, regularization, optimization, and normalization layers.

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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Inside Deep Learning: Math, Algorithms, Models. The section links point to the parts of the book it draws on.