Logit Arithmetic Elicits Long Reasoning Capabilities Without Training

Abstract

Large reasoning models exhibit long chain-of-thought reasoning with strategies such as backtracking and self-correction, though recent studies suggest that these abilities typically require additional training. We first investigate whether such behaviors can be elicited without any training. To this end, we propose a decoding-time approach, ThinkLogit, which utilizes logit arithmetic to tune a target large non-reasoning model for long reasoning using a substantially smaller reasoning model as the guider. We then show that we can further boost its performance by training the guider model with preference optimization over correct/incorrect reasoning pairs sampled from both the target and guider model, a setup we refer to as ThinkLogit-DPO. Our experiments demonstrate that ThinkLogit and ThinkLogit-DPO achieve a relative improvement in average accuracy by 24.5% and 29.1%, respectively, over five reasoning benchmarks using the Qwen2.5-32B guided by R1-Distill-Qwen-1.5B, a model 21x smaller. Moreover, we find that ThinkLogit remains effective when the guider and target come from different model families. It is also orthogonal to post-training methods for small models, as guiders improved through supervised distillation or reinforcement learning can be directly plugged in to yield stronger large models, offering a practical path to unlock long reasoning in large-scale models without costly post-training.