A396366 - OEIS

%I #16 May 31 2026 22:50:16

%S 1,0,5,0,7,0,0,9,8,7,3,5,5,4,8,0,4,9,3,4,1,9,3,3,4,9,8,5,2,9,4,6,0,6,

%T 3,5,1,9,5,8,9,8,1,2,0,4,3,7,6,4,0,4,5,4,6,9,7,7,8,7,8,3,8,7,8,0,1,9,

%U 9,4,6,2,0,3,9,7,7,0,0,2,6,3,7,2,0,8,3,0,0,3,2,9,1,6,1,4,9,9,3,6,6,5,4,1,8

%N Decimal expansion of the lambda (scale) constant in the SELU activation function.

%C SELU(x) = scale*(max(0,x)+min(0,alpha*(exp(x)-1))).

%C SELU is an activation function derived from ELU (Exponential Linear Unit), which uses the identity function for x >= 0 and exp(x)-1 for x <= 0.

%C It multiplies the negative-region output of ELU by the constant alpha and additionally scales the entire function by the constant lambda so that the outputs of a neural network converge toward zero mean and unit variance.

%H Günter Klambauer, Thomas Unterthiner, Andreas Mayr, and Sepp Hochreiter, <a href="https://arxiv.org/abs/1706.02515">Self-Normalizing Neural Networks</a>, arXiv:1706.02515 [cs.LG], 2017.

%F Equals sqrt(2/(1 + (sqrt(2/Pi)/(1 - exp(1/2)*erfc(1/sqrt(2))))^2*(1 - 2*exp(1/2)*erfc(1/sqrt(2)) + exp(2)*erfc(sqrt(2))))).

%e 1.0507009873554804934193349852946...

%t RealDigits[Sqrt[2/(1 + (Sqrt[2/Pi] / (1 - Exp[1/2]*Erfc[1/Sqrt[2]]))^2 * (1 - 2*Exp[1/2] * Erfc[1/Sqrt[2]] + Exp[2]*Erfc[Sqrt[2]]))], 10, 105][[1]] (* _Amiram Eldar_, May 24 2026 *)

%o (PARI) lambda = sqrt(2 / (1 + (sqrt(2/Pi) / (1 - exp(1/2)*erfc(1/sqrt(2.))))^2 * (1 - 2*exp(1/2)*erfc(1/sqrt(2.)) + exp(2)*erfc(sqrt(2.)))))

%Y Cf. A396365.

%K nonn,cons

%O 1,3

%A _Donghwi Park_, May 24 2026