Funnel of Thoughts: Efficient Test-Time Scaling via Early Voting and Rollout Pruning

Large Reasoning Models produce diverse, sometimes inconsistent answers across repeated queries on the same problem, so multi-sample inference is a prerequisite for reliable deployment. Majority voting at k rollouts is the standard solution and the de facto accuracy target for this regime, but it is prohibitively expensive at the scale LRMs require. We introduce Funnel of Thoughts (FoT), an inference-time method that preserves the full 32-trajectory voted accuracy while halving its attention FLOPs, a 28.8% reduction in full-model inference cost. Across 115K reasoning trajectories from six LRMs, we find that unproductive trajectories often reveal themselves through repeated hesitation markers such as "Wait", "Actually", and "perhaps." These trajectories are less likely to reach the correct answer and consume disproportionate attention FLOPs, degenerating into no-answer loops in the worst case. Built on this training-free lexical signal, FoT identifies the vocabulary that captures these pathological patterns and prunes affected trajectories before completion, reducing online generation attention FLOPs by 56.1% and wall time by 37.6% without any additional model inference; the same signal transfers without retuning across held-out architectures and out-of-domain tasks.

Answer-Conditioned Chains of Thought Degrade Verifiable-Reasoning Distillation in Large Language Models

A standard recipe for distilling the reasoning ability of large language models (LLMs) is to sample chains of thought from the model, keep those that reach the correct final answer, and fine-tune on the survivors. When sampling fails, a common fix shows the generator the gold answer and asks it to write a chain that reaches that answer. We show that this second step degrades the training data in a way that correctness filtering cannot catch. We run a controlled experiment that fixes the generator, the problem set, and the correctness filter, and varies only whether the chain is generated under answer-conditioning, the gold answer shown with a request to reach it. Training a strong instruction-tuned reasoning model on its own answer-conditioned chains sharply lowers its verifiable-reasoning accuracy. The loss grows with difficulty, reaching as much as about 27 points on the hardest competition problems. The mechanism is legible in the chains themselves, which rationalize backward from the shown answer instead of deriving it, with the early final-answer statement as the measurable symptom. The harm is a property of the data rather than the generator, read off unlabeled generations before any fine-tuning, ordering the penalty across eight thinking models from four families, and transferring across teacher families. A prompt ablation localizes it to the rationalize-toward instruction rather than the answer's bare visibility. The practical takeaway is to generate answer-blind, because no correctness filter can see this damage in the data.