A latent autoregressive model addresses the challenge of variable-length histories by maintaining a hidden summary state, $h_t$, of past observations. Instead of conditioning directly on a growing sequence of past inputs, the model predicts the current observation $\hat{x}_t$ based on the current summary state ($\hat{x}_t = P(x_t \mid h_t)$). Simultaneously, it updates the summary state using the previous state and the previous observation ($h_t = g(h_{t-1}, x_{t-1})$). Because the state $h_t$ is never directly observed in the data, it is considered latent.