This equation represents the output gate of an LSTM. It transforms an external signal, \(x^{\htmlClass{sdt-0000000047}{g^\text{output}}}\), consisting of outputs of other LSTM blocks and other neurons in the neural network similarly to a typical multi-layer perceptron.
| \( g^\text{output} \) | This symbol represents the state of the output gate of the LSTM. |
| \( \mathbf{W} \) | This symbol represents the matrix containing the weights and biases of a layer in a neural network. |
| \( \sigma \) | This symbol represents the sigmoid function. |
| \( n \) | This symbol represents any given whole number, \( n \in \htmlClass{sdt-0000000014}{\mathbb{W}}\). |
Notice that the equation is analogous to the activation of a single layer \[\htmlClass{sdt-0000000050}{x^\kappa} = \htmlClass{sdt-0000000051}{\sigma}(\htmlClass{sdt-0000000059}{\mathbf{W}}[1;x^{\htmlClass{sdt-0000000015}{k} - 1}])\].
Derivation of this equation follows the same steps as the Activation of a layer, but the activation function is strictly sigmoid. No other activations can be used.