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A conventional unidirectional RNN combines the current input with its previous hidden state to produce a new hidden state. A separate output computation may produce a prediction, so the recurrent state should not automatically be called the previous prediction output. The state is an evolving representation rather than a complete lossless copy of everything encountered. Ordered data such as text, speech, and sensor time series can be modeled through this recurrent structure. Training commonly uses backpropagation through time, which views repeated recurrent computations as an unrolled dependency graph. Multiplying derivatives across many steps can lead to vanishing or exploding gradients, making long-distance dependency learning difficult. LSTM and GRU architectures use gates to regulate information flow. LSTM includes a cell state and input, forget, and output gating; gates can mitigate difficulties but do not guarantee perfect long-term memory. Attention-based transformer architectures offer more parallel computation across training positions and direct interactions among allowed positions. Autoregressive transformer generation can still proceed token by token, so parallel training should not be confused with completely parallel generation. A simple linear recurrence illustrates state updates: h-new equals one-half h-previous plus x. With h-previous two and x three, the new state is four. This is a stated illustration, not the complete nonlinear update of every RNN. A fixed-size recurrent inference state also differs from training memory, where storing or recomputing information across many steps creates additional costs.