# Logit Arithmetic Elicits Long Reasoning Capabilities Without Training

arXiv: https://arxiv.org/abs/2510.09354 · HTML: https://mlsanity.com/paper/2510.09354/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 68 of its 83 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 30 of 68)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [A Survey on In-context Learning](https://mlsanity.com/paper/2301.00234/) (2022)

## Built on by (most cited first, 4 of 4)

- [Video Reasoning without Training](https://mlsanity.com/paper/2510.17045/) (2025)
- [Efficient Low-Resource Language Adaptation via Multi-Source Dynamic Logit Fusion](https://mlsanity.com/paper/2604.18106/) (2026)
- [SFT Leaves a Reproducible Signature in Activation Geometry: Calibrating Post-Training Interpretability Against Run-to-Run Noise](https://mlsanity.com/paper/2610.17093/) (2026)
- [DoubtLess: Training-Free Contrastive Decoding for Efficient Reasoning](https://mlsanity.com/paper/2610.18862/) (2026)

## Abstract (arXiv)

Large reasoning models exhibit long chain-of-thought reasoning with complex strategies such as backtracking and self-verification. Yet, these capabilities typically require resource-intensive 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, ThinkLogit, which utilizes logit arithmetic 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.