Logit Arithmetic Elicits Long Reasoning Capabilities Without Training

Large reasoning models exhibit long chainof-thought reasoning with complex strategies such as backtracking and self-verification. Yet, these capabilities typically require resourceintensive post-training. We investigate whether such behaviors can be elicited in large models without any gradient updates. To this end, we propose a decoding-time approach, THIN-KLOGIT, which utilizes logit arithmetic (Liu et al., 2024) to transfer these capabilities from a substantially smaller reasoning guider to a large non-reasoning target. We further show that we can boost performance by training the guider to correct the target's errors using preference optimization over mixed model outputs, a setup we refer to as THINKLOGIT-DPO. We evaluate these methods across six reasoning benchmarks spanning math, science, and coding domains using the Qwen2.5-32B guided by R1-Distill-Qwen-1.5B, a model 21x smaller. Our experiments demonstrate that THINKLOGIT and THINKLOGIT-DPO achieve a relative improvement of 21.5% and 24.2%, respectively, over the target model. Moreover, THINKLOGIT remains effective even when the guider and target come from different model families. Crucially, our method requires zero training for the large model and would incur minimal inference overhead when logits are computed in parallel, presenting a practical solution for enabling long reasoning at scale. 1