Available kernels

When constructing a dcgp::kernel_set we can use the following names to add the corresponding kernels to the set.

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Kernel name	Function	Definition
Basic operations
“sum”	addition	\(\sum_i x_i\)
“diff”	subtraction	\(x_1 - \sum_{i=2} x_i\)
“mul”	multiplication	\(\prod_i x_i\)
“div”	division	\(x_1 / \prod_{i=2} x_i\)
“pdiv”	protected division	\(x_1 / \prod_{i=2} x_i\) or 1 if NaN
Unary non linearities (ignoring all inputs after the first one)
“sin”	sine	\(\sin x_1\)
“cos”	cosine	\(\cos x_1\)
“log”	natural logarithm	\(\log x_1\)
“exp”	exponential	\(e^{x_1}\)
“gaussian”	gaussian	\(e^{-x_1^2}\)
“sqrt”	square root	\(\sqrt{x_1}\)
“psqrt”	protected square root	\(\sqrt{|x_1|}\)
Non linearities suitable also for dCGPANN
“sig”	sigmoid	\(\frac{1}{1 + e^{-\sum_i x_i}}\)
“tanh”	hyperbolic tangent	\(\tanh \left(\sum_i x_i\right)\)
“ReLu”	rectified linear unit	\(\sum_i x_i\) if positive, 0 otherwise
“ELU”	exp linear unit	\(\sum_i x_i\) if positive, \(e^{\sum_i x_i} - 1\) otherwise
“ISRU”	Inverse square root unit	\(\frac{\sum_i x_i}{\sqrt{1 + \left(\sum_i x_i\right)^2}}\)
“sum”	addition	\(\sum_i x_i\)
“sin_nu”	sine (non unary)	\(\sin(\sum_i x_i)\)
“cos_nu”	cosine (non unary)	\(\cos(\sum_i x_i)\)
“gaussian_nu”	gaussian (non unary)	\(e^{\sum_i x_i}\)
“abs”	absolute value	\(\vert\sum_i x_i\vert\)
“inv_sum”	inverse sum	\(- \sum_i x_i\)
“step”	step function	1 if positive, 0 otherwise