Forking Fast: Efficiently Estimating Uncertainty Dynamics in Text Generation

LLM reasoning is stochastic, and so understanding a model requires grappling with the distribution of reasoning chains that it might produce for a given question, i.e., its uncertainty. Resampling-based analyses characterize this distribution, revealing which steps of a rollout determine how the model arrives at its answer. However, a major limitation of these approaches is that resampling text sequences at every token or sentence in a reasoning chain is very costly. Our work strives to make resampling analysis more computationally efficient, while also shedding light on an important scientific question: what is the right statistical model for explaining uncertainty dynamics in text generation? We show that when resampling many reasoning chains, uncertainty dynamics converge to stable patterns, and noise is largely an artifact of sampling rather than an LLM's sensitivity to each individual token or reasoning step. We develop a statistical model for smoothing noisy low-sample rollout data to better approximate high-sample data, allowing us to significantly cut sampling costs.

Towards Understanding On-Policy Distillation through the Lens of Test-Time Scaling

On-policy distillation (OPD) has emerged as a promising post-training technique for enhancing LLM reasoning. It is commonly believed to enable the student model to distill knowledge from a stronger teacher model, thereby expanding capabilities beyond the pre-OPD base model. In this study, we examine this view through the lens of test-time scaling by varying the sampling budget K and evaluating performance with pass@K and avg@K. Specifically, across several OPD variants, we observe that OPD-trained models maintain superior avg@K performance across sampling budgets, while the advantage in pass@K gradually shifts to the pre-OPD base models as K increases. These results suggest that OPD primarily improves sampling efficiency rather than consistently expanding the student's reasoning capability boundary. The pass@K dynamics throughout OPD training further reveal a progressive shift toward stronger small-K performance at the expense of the large-K capability boundary. Furthermore, a problem-level solvability analysis using pass@1024 as the criterion reveals an asymmetry: OPD causes more previously solvable problems to become unsolvable than previously unsolvable problems to become solvable. Together, these findings suggest that, from the perspective of capability expansion, OPD behaves more like an "illusory distillation": its apparent gains arise primarily from improved sampling efficiency rather than from acquiring genuinely new reasoning capabilities from the teacher.