Projected Autoregression: Autoregressive Language Generation in Continuous State Space

arXiv:2601.04854v3 Announce Type: replace Abstract: 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. \textbf{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 \emph{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 \emph{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.