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## PyTorch Recurrent Neural Network (RNN) Recurrent Neural Networks (RNN) are a class of neural network architectures specifically designed to handle sequential data, capable of capturing dynamic information in time series or ordered data, and can process sequential data such as text, time series, or audio. RNN has wide applications in natural language processing (NLP), speech recognition, time series prediction, and other tasks. The key feature of RNN is its ability to maintain a hidden state, allowing the network to remember information from previous time steps, which is crucial for processing sequential data. ### Basic Structure of RNN In traditional Feedforward Neural Networks, data flows from the input layer to the output layer, but in RNN, data not only flows through the network layers but also propagates to the current hidden state at each time step, thereby passing previous information to the next time step. **Hidden State:** RNN remembers information in the sequence through the hidden state. The hidden state is computed jointly from the previous time step's hidden state and the current input. The structure of the recurrent unit is as follows: * Input ($x_{t}$): The input vector at time step $t$. * Hidden State ($h_{t}$: The hidden state vector at time step $t$, used to store information from previous time steps. * Output ($y_{t}$): The output vector at time step $t$ (optional, depending on the specific task). Formula: $$ h_{t} = f left(right. W_{h h} h_{t - 1} + W_{x h} x_{t} + b_{h} left.right) $$ * h t: The hidden state at the current time step. * h t-1: The hidden state at the previous time step. * X t: The input at the current time step. * W hh, W xh: Weight matrices. * b: Bias term. * f: Activation function (such as Tanh or ReLU). **Output:** The output of RNN depends not only on the current input but also on the historical information of the hidden state. Formula: $$ y_{t} = W_{h y} h_{t} + b_{y} $$ * y t: The output vector at time step t (optional, depending on the specific task). * W hy: The weight matrix from hidden state to output.. ### How RNN Processes Sequential Data The unfolded view of Recurrent Neural Network when processing sequential data is as follows: !(#) RNN is a neural network for processing sequential data. It processes each element in the sequence through recurrent connections and passes information at each time step. The following is an explanation of each part in the figure: * Input Sequence (Xt, Xt-1, Xt+1, ...): The pink circles in the figure represent each element in the input sequence, such as