The purpose of an input gate in an LSTM (Long Short-Term Memory) cell is to control the flow of information into the cell. It decides which information from the current input and the previous hidden state should be stored and used for the current time step.

  An LSTM cell consists of several gates, including the input gate, forget gate, and output gate. Each gate has a specific function in controlling the flow of information.

  The input gate takes input from the current time step and the previous hidden state and applies a sigmoid activation function to the input. The sigmoid function outputs a value between 0 and 1 for each element in the input. This value represents how much of the input should be let through and stored in the cell state.

  The input gate also has a corresponding input modulation gate, which applies a tanh activation function to the input. This gate controls the magnitude of the input that gets added to the cell state. The combination of the input gate and the input modulation gate allows the LSTM to selectively update the information stored in the cell state.

  In summary, the input gate in an LSTM cell plays a crucial role in determining which information from the current input and the previous hidden state should be written to the cell state. It controls the flow of information into the cell, allowing the LSTM to capture and remember relevant information for making predictions.