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Predictive Latents for Autoregressive Language Models: Possibility, Gauge, and Obstruction

Yuzhou Hong · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28540 · cited by 0 works (OpenAlex) · open-access PDF

Japanese

このノートは、次のトークンのクロスエントロピーによってトレーニングされているが、いくつかの最近のシステムは、トークンを発行することなく隠れた状態を繰り返す:継続的な思考、休止ステップ、および繰り返しの深さ。このノートは、隠れたプロセスで3つのリスクを分離します。トークンのリスク $R_{\mathrm{tok}}$は、読み取りを記録します。教師によって強制された隠れたリスク $R_1$は、真の隠れた状態を表示する1ステップのマップを記録します。オープンロップリスク $R_H$は、独自の出力で繰り返された後、同じマップを記録します。Bayesの次のトークンの後ろのリスクが、フルランク

Machine translation (Meta M2M100); the English original follows.

Abstract

Autoregressive language models are trained by next-token cross-entropy, yet several recent systems also iterate a hidden state without emitting a token: continuous thoughts, pause steps, and recurrent depth. This note separates three risks on one latent process. The token risk $R_{\mathrm{tok}}$ scores a readout. The teacher-forced latent risk $R_1$ scores a one-step map that sees the true hidden state. The open-loop risk $R_H$ scores the same map after it has been iterated on its own outputs. If the Bayes next-token posterior is a function of a $k$-dimensional statistic with full-rank covariance, a width-$k$ latent, a linear least-squares transition, and a refit unembedding match the Bayes token predictor. The statistic is identified only up to an invertible gauge: whitening the residual stream does not change the token law once the unembedding is refit. The matching obstructions are sharp. A constant latent drives $R_1$ to zero while token cross-entropy falls back to the marginal entropy. A perfect token predictor can still hide a null-space walk whose open-loop error grows linearly in the horizon. A small next-latent loss does not certificate next-token prediction, and a small next-token loss does not certificate free latent rollout, unless a rank or injectivity condition is stated with the number.

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Topics: Security token, Mathematics, Autoregressive model, Statistic, Statistics, Bayes' theorem

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