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Component-wise differentiation

As explained in Evolutionary Deep Learning: Genetic algorithms and neural networks

Component-wise differentiation computes candidate changes independently for each vector component using differences between other candidate vectors.

Component-wise differentiation modifies each candidate-vector component independently by adding a scaled difference between other candidate vectors. Differential evolution uses this mechanism to avoid relying on global gradients when approximating discontinuous or difficult functions. section 4.5.1

A simplified differential-evolution update proceeds as follows:

  • Select three random agents, a, b, and c, from the population. section 4.5.1
  • Evaluate the trial agent and replace the target only when its fitness improves. section 4.5.1

Approximating discontinuous functions

The EDL_4_5_DE.ipynb experiment applies differential evolution to polynomial, absolute, and step functions. Changing the function type and MAX_TIME lets you compare performance, including DE and ES results on a step function. section 4.5.1

How Evolutionary Deep Learning: Genetic algorithms and neural networks covers it

How deep it goes
Explains candidate selection, scaled differences, crossover, fitness replacement, and executable hyperparameters, without deriving convergence theory.
Examples
Demonstrates polynomial, absolute, and step-function approximation through an executable DEAP notebook.
What it assumes
Assumes candidate populations and fitness evaluation while contrasting the method with gradient-based deep learning optimization.
What you can do after
Apply it via DEAP by implementing vector mutation, evaluating trial agents, and tuning population and runtime parameters.
How it connects
Contrasts differential evolution with backpropagation, gradient optimization, and genetic evolution.
Cover of Evolutionary Deep Learning: Genetic algorithms and neural networks
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Evolutionary Deep Learning: Genetic algorithms and neural networks. The section links point to the parts of the book it draws on.