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Protected division

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

Protected division is a division operation that returns a defined fallback result when its denominator would make ordinary division invalid.

Protected division replaces ordinary division when the denominator produces an invalid result, allowing numerical expressions to continue with a defined fallback value. section 4.1.1

A NumPy implementation handles both scalar and array evaluation:

  • Suppresses divide-by-zero and invalid-operation warnings while computing the quotient. section 4.1.1
  • Replaces infinities and NaNs with 1 for array results and scalar results. section 4.1.1
  • Registers the protected operator in a genetic-programming primitive set so evolved expressions remain evaluable. section 4.1.1

Symbolic regression

A genetic-programming regression uses protected division while evolving expressions over four NumPy inputs. The compiled expression is evaluated across 10,000 rows, and squared error measures fitness against the generated target. section 4.1.1

Listing 4.1 EDL_4_1_GP_Regression.ipynb: Setting up the expression
pset = gp.PrimitiveSet("MAIN", 4)                     #1
 
pset.addPrimitive(np.add, 2, name="vadd")             #2
pset.addPrimitive(np.subtract, 2, name="vsub")
pset.addPrimitive(np.multiply, 2, name="vmul")
pset.addPrimitive(protectedDiv, 2)
pset.addPrimitive(np.negative, 1, name="vneg")
pset.addPrimitive(np.cos, 1, name="vcos")
pset.addPrimitive(np.sin, 1, name="vsin")
 
pset.addEphemeralConstant("rand101", lambda: 
 random.randint(-1,1))                              #3
 
pset.renameArguments(ARG0='x1')                       #4
pset.renameArguments(ARG1='x2')
pset.renameArguments(ARG2='x3')
pset.renameArguments(ARG3='x4')

Inspect the primitive-set setup that adds protected division alongside arithmetic, trigonometric, and negation operators. section 4.1.1

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

How deep it goes
Implements scalar and array fallback handling, but does not develop a broader theory of numerical safeguards.
Examples
Uses a four-input regression equation, compiled expression trees, and a 10,000-row NumPy dataset.
What it assumes
Assumes familiarity with NumPy arrays, arithmetic expressions, and genetic-programming primitive sets.
What you can do after
Apply it via NumPy when constructing evaluable arithmetic primitives for symbolic regression.
How it connects
Connects protected division with NumPy, genetic programming, symbolic regression, expression trees, and fitness evaluation.
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.