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arXiv · 2604.04855

The Role of Generator Access in Autoregressive Post-Training

Amit Kiran Rege
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Abstract

We study how generator access constrains autoregressive post-training. The central question is whether the learner is confined to fresh root-start rollouts or can return to previously built prefixes and query the next-token rule there. In the root-start regime, output sampling, generated-token log probabilities, top-$k$ reports, and full next-token distributions along sampled trajectories all reduce to one canonical experiment, limited by the on-policy probability of reaching informative prefixes. Weak prefix control breaks this barrier, and once control is available, richer observations such as conditional sampling or logits can outperform top-$1$ access. Changing only the generator interface creates an exponential gap for KL-regularized outcome-reward post-training.

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Amit Kiran Rege. 2026-04-06. The Role of Generator Access in Autoregressive Post-Training. https://arxiv.org/abs/2604.04855

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