Consider the following eqautions used in LSTM ( taken from Andrew ng’s course on Sequential model)

In an LSTM model, LSTM Cell has three inputs at any time step t

- Input($ X_t , a^{(t-1)}, C^{(t-1)})$ ,
Here $ X_t$ is the input vector, $ a^{(t-1)}$ is the previous hidden state and $ C^{(t-1)}$ is the previous cell state

Now the new cell state $ c^t$ is given by the following formula :

$ C^t = $ forget_gate * $ C^{(t-1)} + $ update_gate* $ \overline{C^t}$

**Question**:

If I swap the places of forget_gate and update_gate, I still get a valid $ C^t$ , So why are we multilyting the previous cell state with forget gate only and the current cell state with update gate only, what if Imultiply previous cell state with update gate ?

Edit : After swapping, the formula would look like this,

$ C^t = $ update_gate * $ C^{(t-1)} + $ forget_gate* $ \overline{C^t}$