In an LSTM (Long Short-Term Memory) cell, the purpose of a peephole connection is to allow the cell to have access to the internal memory state during the gating process.

  LSTM is a type of recurrent neural network specifically designed to address the vanishing gradient problem and effectively capture long-term dependencies in sequential data. It achieves this through the use of three different gates: the input gate, the forget gate, and the output gate. These gates control the flow of information through the cell, allowing it to selectively remember or forget information as needed.

  The peephole connection, which was introduced by Gers and Schmidhuber in 2000, extends the LSTM architecture by allowing the gates to have access to the internal memory state directly. This means that the input gate, the forget gate, and the output gate can consider the current memory content when deciding how much information to let through.

  The main purpose of the peephole connection is to improve the LSTM's ability to model long-term dependencies. By giving the gates access to the memory state, the LSTM cell can better determine the relevance and importance of the stored information in making decisions at each time step. This enhanced access to memory content helps the LSTM cell retain or discard information more effectively, allowing it to learn and capture long-term dependencies in the sequence data.

  Overall, the peephole connection in an LSTM cell enhances the model's ability to remember or forget information in a more context-dependent manner, improving its performance in tasks that require modeling long-term dependencies.