Forget and input

The forget gate and the input gate together also update the cell state with the following equation,

$$\mathbf{c}^{(t)} = \mathbf{f}^{(t)} \otimes \mathbf{c}^{(t-1)} + \mathbf{i}^{(t)} \otimes \mathbf{\tilde{c}}^{(t)},$$

where $f^{(t)}$ and $i^{(t)}$ are the outputs of the forget gate and the input gate, respectively.

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