Projected Autoregression: Autoregressive Language Generation in Continuous State Space

Standard autoregressive language models generate text by repeatedly selecting a discrete next token, coupling prediction with irreversible commitment at every step. We show that token selection is not the only viable autoregressive interface. Projected Autoregression replaces token selection with continuous prediction in embedding space followed by discrete projection at commitment time. The model predicts next-token vectors via regression and contrastive objectives, while discrete tokens arise only by nearest-neighbor projection. An optional mutable suffix (``liquid tail'') enables iterative refinement before commitment, but the central change is more basic: next-step prediction is continuous, and discrete tokens are produced only as a downstream interface. Projected Autoregression establishes a concrete alternative to token-selection autoregression: language generation can be organized around continuous-state prediction with delayed discrete commitment. Refinement remains local to a short causal suffix within a left-to-right causal process, rather than a sequence-wide denoising process. This separation has two consequences. First, it induces a distinct generation regime: even with immediate projection (K=1), continuous prediction yields text structure and dynamics that differ from tested token-space AR baselines, including a compute-matched best-of-16 reranking baseline. Second, it exposes a continuous control surface inside autoregressive generation: direction rate, history noise, delayed commitment, state-space guidance, and embedding geometry act directly on the evolving generative state before token commitment. Taken together, these results place repeated token selection within a larger family of autoregressive interfaces and expose continuous state space as a broader algorithmic design space for language generation.