Broken Chains: The Cost of Incomplete Reasoning in LLMs

Long chain-of-thought~(CoT) reasoning improves the problem-solving capability of large reasoning models~(LRMs), but often incurs substantial inference cost and overthinking. Existing efficiency methods primarily rely on prompting, post-hoc compression, or length-regularized optimization; these approaches can be sensitive to model scale, depend on external estimators, or under-allocate reasoning to difficult instances. We propose Draft-Thinking, a lightweight adaptation framework that learns a model-adapted draft CoT: a compact, self-contained working derivation that directly supports the final answer. We identify a Cross-Scale Draft Mismatch: concise traces generated by a strong teacher can be too sparse for a smaller target model. To address this mismatch, Progressive Draft Adaptation first transfers a concise reasoning-form prior through supervised fine-tuning (SFT) and then applies two-stage reinforcement learning (RL) with progressively harder data and relaxed response budgets to calibrate the reasoning granularity to the target model. The method requires neither post-hoc trajectory compression nor an explicit length-penalty reward. At inference time, draft, adaptive, and step-by-step prompts provide efficiency-oriented, balanced, and detailed reasoning modes, respectively. The step-by-step mode largely preserves the original model's accuracy while using fewer tokens. With only 847 training problems and 120 RL optimization steps, Draft-Thinking substantially reduces reasoning cost across six mathematical and scientific reasoning benchmarks. On MATH500, its draft mode reduces the average response length from 5,668 to 986 tokens, an 82.6% reduction, while achieving 90.6% accuracy compared with 93.0% for the original long CoT model.

Chain-of-thought reasoning is often treated as a monotone way to improve language-model accuracy by letting a model think longer. We identify a countervailing effect, the coupling tax: when reasoning traces and final answers share one output-token budget, long traces can crowd out the answer they are meant to support. Across GSM8K, MATH-500, and five BIG-Bench Hard tasks with Qwen3 models at three scales, non-thinking mode matches or outperforms thinking mode on GSM8K and MATH-500 at every budget up to 2048 tokens, while harder tasks shift the crossover to larger budgets. We derive a truncation-waste decomposition, $\mathrm{Acc}_{\mathrm{think}}(b)=α_c F_L(b)+α_t(1-F_L(b))$, that predicts this crossover from chain-length and accuracy statistics and explains inverse scaling within the Qwen family. A DeepSeek-R1-Distill-Llama-8B replication shows the same pattern under a different thinking interface. As a mitigation, split-budget generation decouples reasoning and answer budgets; on full MATH-500, IRIS reaches 74.0% accuracy, a strengthened extraction variant reaches 78.8%, and a fixed non-oracle SC+IRIS gate reaches 83.6%. The results show that test-time reasoning should be evaluated as a budget-allocation problem, not only as a question of whether longer traces are available.

Large Language Models (LLMs) have achieved remarkable success in complex reasoning tasks through Chain-of-Thought (CoT) prompting. However, these models often exhibit "computational overthinking," generating redundant reasoning steps that increase latency and cost without improving accuracy. Recent studies suggest that CoT trajectories can be significantly pruned, yet existing methods often rely on forcing a static thinking budget, heuristic filtering, sub-optimal early exit via classification, or expensive re-training. In this paper, we introduce OS-Pruner, a lightweight plug-in framework that formulates chain-of-thought pruning as an optimal stopping problem. Given a reasoning prefix, OS-Pruner learns whether further reasoning is worth its token cost by optimizing an explicit utility that trades off final-answer accuracy against generated length. Our novel formulation enables the model to dynamically assess the sufficient point of termination for a reasoning chain. OS-Pruner is designed to be lightweight during both training and inference, and to provide users with fine-grained control over the reasoning-effort vs. accuracy trade-off. On diverse reasoning benchmarks and base models, OS-Pruner achieves 20-60% reduction in generation length with minimal accuracy sacrifice.