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fix formulars
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lukas-heiligenbrunner 2024-10-28 13:22:38 +01:00
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typstalt/materialandmethods.typ
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@ -99,7 +99,7 @@ The Softmax function @softmax #cite(<liang2017soft>) converts $n$ numbers of a v
Its a generalization of the Sigmoid function and often used as an Activation Layer in neural networks. Its a generalization of the Sigmoid function and often used as an Activation Layer in neural networks.
$ $
sigma(bold(z))_j = (e^(z_j)) / (sum_(k=1)^k e^(z_k)) "for" j=(1,...,k) sigma(bold(z))_j = (e^(z_j)) / (sum_(k=1)^k e^(z_k)) "for" j:={1,...,k}
$ <softmax> $ <softmax>
The softmax function has high similarities with the Boltzmann distribution and was first introduced in the 19th century #cite(<Boltzmann>). The softmax function has high similarities with the Boltzmann distribution and was first introduced in the 19th century #cite(<Boltzmann>).
@ -112,7 +112,7 @@ And equation~\eqref{eq:crelbinary} is the special case of the general Cross Entr
$ $
H(p,q) &= -sum_(x in cal(X)) p(x) log q(x)\ H(p,q) &= -sum_(x in cal(X)) p(x) log q(x)\
H(p,q) &= -p log(q) + (1-p) log(1-q)\ H(p,q) &= -(p log(q) + (1-p) log(1-q))\
cal(L)(p,q) &= -1/N sum_(i=1)^(cal(B)) (p_i log(q_i) + (1-p_i) log(1-q_i)) cal(L)(p,q) &= -1/N sum_(i=1)^(cal(B)) (p_i log(q_i) + (1-p_i) log(1-q_i))
$ $