Long short-term memory (LSTM) is a type of recurrent neural network (RNN) architecture specifically designed to address the vanishing gradient problem in RNNs. This problem occurs when the network is unable to remember information from long sequences due to the decreasing influence of previous input over time, leading to poor performance on tasks such as language modeling and machine translation.

LSTMs overcome this problem by introducing a cell state, which acts as a memory unit that can store information over long periods of time. The cell state is controlled by three gates – the input gate, forget gate, and output gate – which regulate the flow of information into and out of the cell state.

One example of LSTM in action is in language modeling, where the network is trained to predict the next word in a sentence based on the previous words. In this case, the cell state would store information about the context of the sentence, allowing the network to generate more coherent and accurate predictions.

Another example is in machine translation, where LSTMs can be used to translate a sentence from one language to another by storing information about the source sentence in the cell state and using it to generate a coherent translation in the target language.

Overall, LSTMs are an effective solution to the vanishing gradient problem and have been widely used in a variety of natural language processing tasks.