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. 2023 Apr 28;25(5):733. doi: 10.3390/e25050733

Algorithm 1 Residual Driven Target Propagation (RDTP)

Input: training set

D = {{(x_{j}, {\hat{y}}_{j})}_{j = 1}^{N}}

, the network

N

, the output layer

i + 1

Output: the propagated targets at layer i. For

N

, layer i corresponds to the single hidden layer.

1:
for $j = 1$ to N do
2:
$y_{j} \leftarrow F_{i + 1} (x_{j})$
3:
$y_{z, j} \leftarrow {\hat{y}}_{j} - y_{j}$
4:
${\tilde{a}}_{z, j} \leftarrow σ_{i + 1}^{- 1} (y_{z, j})$
5:
for $u = 1$ to $d_{i}$ do
6:
$r_{u}^{(i)} (x_{j}) = \frac{σ_{i} (a_{u})}{\sum_{s = 1}^{d} σ_{i} (a_{s})}$
7:
$z_{u}^{(i)} = \frac{r_{u}^{(i)} {\tilde{a}}_{z}}{w_{u}^{(i + 1)}}$
8:
$h_{u}^{(i)} = σ_{i} (a_{u})$
9:
${\hat{h}}_{u}^{(i)} = h_{u}^{(i)} + z_{u}^{(i)}$
10:
end for
11:
${\hat{h}}_{i, j} = ({\hat{h}}_{1}^{(i)}, . . ., {\hat{h}}_{d_{i}}^{(i)})$
12:
end for