Organizations: 1Purdue University, USA · 2Baruch College, City University of New York, USA · 3The Ohio State University, USA · 4AI Agent Lab, USA · 5Appcubic, USA · 6Wayne State University, USA · 7Central University of Finance and Economics, China · 8Cornell University, USA · 9Emory University, USA
Abstract
Long Chain-of-Thought (CoT) traces can improve reasoning accuracy, but repeatedly generating them is costly for smaller or latency-constrained language models. This paper studies a practical alternative: produce a rich rationale once with a capable \emph{thinking} model, compress it, and reuse the compressed trace as context for a cheaper \emph{answering} model. We introduce CoT-X, an adaptive framework for cross-model CoT transfer. CoT-X segments reasoning traces into semantic units, scores their diagnostic and logical importance, selects budget-feasible evidence paths, and reconstructs a coherent compressed rationale for the answering model. On 7,501 Japanese medical licensing questions spanning 10 specialties, CoT-X improves accuracy over direct truncation by up to 40.5% under the same token budget, with the largest gains at 64--256 tokens. Across 64 thinking--answering pairs from eight DeepSeek-R1 and Qwen3 models (1.5B--32B parameters), reasoning transfer is most reliable within a model family, yet remains effective across families once compression normalizes the trace. A Gaussian Process Bayesian optimization layer finds near-optimal model--budget configurations with 15 evaluations rather than an exhaustive search over all 64 pairs, reducing evaluation cost by 84%. These results show that reasoning quality, token budget, and model compatibility can be optimized jointly, making CoT-style reasoning more practical under realistic deployment constraints.
Large reasoning models (LRMs) often generate extensive chain-of-thought (CoT) traces before producing a final answer. As explicit textual artifacts, these traces can be passed to other models to solve the same task, enabling cross-model reasoning transfer. Yet successful transfer alone does not reveal how the provided CoT contributes to another model's answer. We study this question with a controlled provider--receiver framework, where a provider generates a reasoning trace and a receiver solves the same problem from increasingly longer trace prefixes. We compare force-answer, where the receiver answers directly from the prefix, with free-generation, where it may continue reasoning before answering. Across models and benchmarks, full traces often transfer successfully, but prefix trajectories reveal distinct mechanisms. In force-answer mode, AIME transfer is largely driven by explicit answer availability. MMLU-Pro instead reflects a larger role for receiver competence, while ZebraLogic depends on partial structured-answer information rather than complete-answer leakage alone. In free-generation mode, partial CoTs improve performance across benchmarks, indicating that prefixes can guide continued reasoning. Finally, answer agreement among receivers provides a gold-free signal for stopping provider reasoning early. Overall, cross-model CoT transfer is not a single phenomenon: it can reflect answer extraction, reasoning scaffolding, or receiver-dependent competence.
Extended chain-of-thought (CoT) traces improve LLM reasoning but incur substantial computational and memory costs. While existing CoT compression methods mitigate this by condensing thought steps into compact representations via memory tokens and retaining only these representations at inference time, the loss of fine-grained information makes subsequent steps more error-prone. To alleviate this, we propose \textbf{HybridThinker}, where in addition to preserved these representations, thought steps are also temporarily retained to provide fine-grained details. However, we observe that naively keeping thought steps accessible to subsequent steps \emph{during training} lets the model bypass memory tokens by retrieving information directly from these steps, leaving the model's ability to compress and retrieve information through memory tokens insufficiently trained. We therefore introduce a hybrid training scheme, in which only some thought steps are directly accessible through attention to subsequent steps, while the other thought steps are masked, forcing the model to use memory tokens for compression and retrieval. Across 4 reasoning benchmarks, HybridThinker matches the uncompressed baseline, advancing the state of the art in CoT compression by 5.8 points on average accuracy with similar inference time. Ablation studies confirm that both temporary thought-step retention and the hybrid training scheme contribute to these gains.
Chain-of-thought (CoT) reasoning improves multi-step problem solving, but long reasoning traces inflate inference cost. Token-level CoT compression reduces this cost by pruning full reasoning chains into shorter traces for model adaptation, making token selection the central challenge. Existing methods often rely on external scorers or heuristic signals only indirectly tied to the model's internal answer computation. We instead adopt a model-internal perspective: as the model forms an answer, each reasoning token leaves a ripple in the residual stream, the model's \emph{stream of thought}, and the magnitude of this ripple reflects the token's contribution to the answer computation. Building on this view, we propose \textsc{MIST} (Model-Internal Saliency for Token-level CoT compression), which defines token importance along two complementary axes: \emph{necessity}, the drop in answer likelihood when a token's internal contribution is removed, and \emph{sufficiency}, the gain in answer likelihood when that contribution alone is provided. Combining the two yields a unified importance score for pruning. Across four reasoning benchmarks and four models, \textsc{MIST} consistently outperforms baseline methods, suggesting that model-internal saliency provides an effective proxy for reasoning-token importance.