Multi-Step LLM Inference

Last Updated 31 May, 2026

by David Spuler, Ph.D.

What is Multi-Step LLM Inference?

Multi-step inference is an LLM using multiple queries to answer a question. This is commonly used as a reasoning method, often known as test-time compute, but the idea can be used generally in many ways. The model itself can perform multiple steps, or there can be steps with multiple different models, or even non-LLM components such as retrievers, plugins, tools, or an overall controller.

Multi-Step Inference: Book Excerpts and Blog Articles

Free online book excerpts with full text chapters online and free PDF downloads, and the Aussie AI blog, including related articles:

David Spuler, Ph.D., 16th August, 2025, List of AI Smartness Techniques, Aussie AI Blog, https://www.aussieai.com/blog/ai-smartness-techniques
David Spuler, December 2025, Reasoning Models, Chapter 9, "The Sweetest Lesson: Your Brain vs AI", https://www.aussieai.com/book/sweetest-lesson-9-reasoning-models
David Spuler, Michael Sharpe, June 2025, Reasoning and RAG, Chapter 13, "RAG Optimization: Accurate and Efficient LLM Applications", https://www.aussieai.com/book/rag-book-13-reasoning-rag
David Spuler, Ph.D., Dec 21st, 2024, Multi-Step Reasoning Inference Optimization, Aussie AI Blog, https://www.aussieai.com/blog/reasoning-inference-optimization
David Spuler, Michael Sharpe, 2025, Architectures of AI Projects, Chapter 12, in "Generative AI Applications", https://www.aussieai.com/book/ai-apps-book-12-architectures-project
David Spuler, Michael Sharpe, 2025, Prompt Engineering, Chapter 17, in "Generative AI Applications", https://www.aussieai.com/book/ai-apps-book-17-prompt-engineering
David Spuler, May 31st, 2026, Multi-Step Reasoning Harness, Chapter 5. Harness Engineering, in book LLM Inference Optimization: State-of-the-Art Research, Table of Contents: https://www.aussieai.com/book/llm-inference-optimization https://www.amazon.com/dp/B0H3FKR39T

Research on Multi-Step LLM Inference

Research papers include:

Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Thomas L. Griffiths, Yuan Cao, Karthik Narasimhan, 3 Dec 2023 (v2), Tree of Thoughts: Deliberate Problem Solving with Large Language Models, https://arxiv.org/abs/2305.10601 Code: https://github.com/princeton-nlp/tree-of-thought-llm
Lingjiao Chen, Jared Quincy Davis, Boris Hanin, Peter Bailis, Ion Stoica, Matei Zaharia, James Zou, 4 Jun 2024 (v2), Are More LLM Calls All You Need? Towards Scaling Laws of Compound Inference Systems, https://arxiv.org/abs/2403.02419
Justin Chih-Yao Chen, Archiki Prasad, Swarnadeep Saha, Elias Stengel-Eskin, Mohit Bansal, 18 Sep 2024, MAgICoRe: Multi-Agent, Iterative, Coarse-to-Fine Refinement for Reasoning, https://arxiv.org/abs/2409.12147 https://github.com/dinobby/MAgICoRe
Xiaohan Xu, Chongyang Tao, Tao Shen, Can Xu, Hongbo Xu, Guodong Long, Jian-guang Lou, 29 Feb 2024 (v2), Re-Reading Improves Reasoning in Large Language Models, https://arxiv.org/abs/2309.06275
Artem Shelamanov, Sep 2024, Why OpenAI’s o1 Model Is A Scam, https://pub.towardsai.net/why-openais-o1-model-is-a-scam-eb3356c3d70e
Rinon Gal, Adi Haviv, Yuval Alaluf, Amit H. Bermano, Daniel Cohen-Or, Gal Chechik, 2 Oct 2024, ComfyGen: Prompt-Adaptive Workflows for Text-to-Image Generation, https://arxiv.org/abs/2410.01731 https://comfygen-paper.github.io/
Yi Cheng, Xiao Liang, Yeyun Gong, Wen Xiao, Song Wang, Yuji Zhang, Wenjun Hou, Kaishuai Xu, Wenge Liu, Wenjie Li, Jian Jiao, Qi Chen, Peng Cheng, Wayne Xiong, Integrative Decoding: Improve Factuality via Implicit Self-consistency, 3 Oct 2024 (v2), https://arxiv.org/abs/2410.01556 (Prepends a previous response to improve decoding accuracy.)
Zhenwen Liang, Ye Liu, Tong Niu, Xiangliang Zhang, Yingbo Zhou, Semih Yavuz, 5 Oct 2024, Improving LLM Reasoning through Scaling Inference Computation with Collaborative Verification, https://arxiv.org/abs/2410.05318
Sonya Huang, Pat Grady, and o1, Sequoia, October 9, 2024 Generative AI’s Act o1, https://www.sequoiacap.com/article/generative-ais-act-o1/
Yingqian Cui, Pengfei He, Xianfeng Tang, Qi He, Chen Luo, Jiliang Tang, Yue Xing, 21 Oct 2024, A Theoretical Understanding of Chain-of-Thought: Coherent Reasoning and Error-Aware Demonstration, https://arxiv.org/abs/2410.16540
Jiangming Liu, Matt Gardner, Shay B. Cohen, Mirella Lapata, 7 Jun 2021 (v2), Multi-Step Inference for Reasoning Over Paragraphs, https://arxiv.org/abs/2004.02995
Aditya Kalyanpur, Kailash Karthik Saravanakumar, Victor Barres, CJ McFate, Lori Moon, Nati Seifu, Maksim Eremeev, Jose Barrera, Abraham Bautista-Castillo, Eric Brown, David Ferrucci 24 Jul 2024 (v4), Multi-step Inference over Unstructured Data https://arxiv.org/abs/2406.17987
Banghao Chen, Zhaofeng Zhang, Nicolas Langrené, Shengxin Zhu, 5 Sep 2024 (v5), Unleashing the potential of prompt engineering in Large Language Models: a comprehensive review, https://arxiv.org/abs/2310.14735
Xiaodong Liu, Kevin Duh, Jianfeng Gao, 30 Mar 2019 (v2), Stochastic Answer Networks for Natural Language Inference, https://arxiv.org/abs/1804.07888
TED, Oct 2024, Multi-Step Reasoning Agents, https://tedai-sanfrancisco.ted.com/glossary/multi-step-reasoning-agents/
Yao Fu, Hao Peng, Ashish Sabharwal, Peter Clark, Tushar Khot, 30 Jan 2023 (v2), Complexity-Based Prompting for Multi-Step Reasoning, https://arxiv.org/abs/2210.00720
Junting Lu, Oct 2024 (accessed), Awesome-LLM-Reasoning-Techniques, https://github.com/Junting-Lu/Awesome-LLM-Reasoning-Techniques
Cameron R. Wolfe, Dec 23, 2023, Tree of Thoughts Prompting. Solving multi-step problems with LLMs via deliberate planning and exploration, https://towardsdatascience.com/tree-of-thoughts-prompting-65a3e51f9ac4
Data Camp, Jul 10, 2024, Chain-of-Thought Prompting: Step-by-Step Reasoning with LLMs, https://www.datacamp.com/tutorial/chain-of-thought-prompting
Pankaj, Dec 21, 2023, Chain of Thought Prompting: Guiding LLMs Step-by-Step, https://medium.com/@pankaj_pandey/chain-of-thought-prompting-guiding-llms-step-by-step-e6eac32d02d8
Cobus Greyling, Aug 2, 2023, 12 Prompt Engineering Techniques, https://cobusgreyling.medium.com/12-prompt-engineering-techniques-644481c857aa
Cameron R. Wolfe, Aug 21, 2023, Tree of Thoughts Prompting. Solving multi-step problems with LLMs via deliberate planning and exploration, https://cameronrwolfe.substack.com/p/tree-of-thoughts-prompting
Cameron R. Wolfe, Jan 3, 2024, Graph-Based Prompting and Reasoning with Language Models. Understanding graph of thoughts prompting and several variants… https://towardsdatascience.com/graph-based-prompting-and-reasoning-with-language-models-d6acbcd6b3d8
Jason Wei and Denny Zhou, May 11, 2022, Language Models Perform Reasoning via Chain of Thought, https://research.google/blog/language-models-perform-reasoning-via-chain-of-thought/
Cameron R. Wolfe, Jul 24, 2023, Chain of Thought Prompting for LLMs: A practical and simple approach for “reasoning” with LLMs, https://towardsdatascience.com/chain-of-thought-prompting-for-llms-33c963eead38
Siwei Wu, Zhongyuan Peng, Xinrun Du, Tuney Zheng, Minghao Liu, Jialong Wu, Jiachen Ma, Yizhi Li, Jian Yang, Wangchunshu Zhou, Qunshu Lin, Junbo Zhao, Zhaoxiang Zhang, Wenhao Huang, Ge Zhang, Chenghua Lin, J.H. Liu, 22 Oct 2024 (v2), A Comparative Study on Reasoning Patterns of OpenAI's o1 Model, https://arxiv.org/abs/2410.13639
Arun Shankar, Oct 2024, Designing Cognitive Architectures: Agentic Workflow Patterns from Scratch, https://medium.com/google-cloud/designing-cognitive-architectures-agentic-workflow-patterns-from-scratch-63baa74c54bc
Tanay Jaipuria, Oct 29, 2024, OpenAI's o-1 and inference-time scaling laws, https://www.tanayj.com/p/openais-o-1-and-inference-time-scaling
Jinlin Wang, Suyuchen Wang, Ziwen Xia, Sirui Hong, Yun Zhu, Bang Liu, Chenglin Wu, 28 Oct 2024, FACT: Examining the Effectiveness of Iterative Context Rewriting for Multi-fact Retrieval, https://arxiv.org/abs/2410.21012
Latent Space, Nov 05, 2024, Inference, Fast and Slow. When System 1/System 2 analogies are not enough: The 6 types of LLM inference https://www.latent.space/p/inference-fast-and-slow
Shanghaoran Quan, Tianyi Tang, Bowen Yu, An Yang, Dayiheng Liu, Bofei Gao, Jianhong Tu, Yichang Zhang, Jingren Zhou, Junyang Lin, 31 Oct 2024, Language Models can Self-Lengthen to Generate Long Texts, https://arxiv.org/abs/2410.23933?
LangChain, Nov 7, 2024. SCIPE - Systematic Chain Improvement and Problem Evaluation, https://blog.langchain.dev/scipe-systematic-chain-improvement-and-problem-evaluation/ https://github.com/garg-ankush/scipe/tree/main
X Wang, L Mu, J Zhang, H Xu, 2024, Multi-pass Decoding for Grammatical Error Correction, Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 9904–9916, November 12-16, 2024, https://aclanthology.org/2024.emnlp-main.553.pdf
Siyun Zhao, Yuqing Yang, Zilong Wang, Zhiyuan He, Luna K. Qiu, Lili Qiu, 23 Sep 2024, Retrieval Augmented Generation (RAG) and Beyond: A Comprehensive Survey on How to Make your LLMs use External Data More Wisely, https://arxiv.org/abs/2409.14924
Guowei Xu, Peng Jin, Li Hao, Yibing Song, Lichao Sun, Li Yuan, 15 Nov 2024, LLaVA-o1: Let Vision Language Models Reason Step-by-Step, https://arxiv.org/abs/2411.10440
Carl Franzen, November 20, 2024, DeepSeek’s first reasoning model R1-Lite-Preview turns heads, beating OpenAI o1 performance, https://venturebeat.com/ai/deepseeks-first-reasoning-model-r1-lite-preview-turns-heads-beating-openai-o1-performance/
mshumer, Nov 2024, Open Reasoning Engine, https://github.com/mshumer/OpenReasoningEngine
Eric Horvitz , Harsha Nori , Naoto Usuyama , November 27, 2024 Advances in run-time strategies for next-generation foundation models, Microsoft Research Blog, https://www.microsoft.com/en-us/research/blog/advances-in-run-time-strategies-for-next-generation-foundation-models/
Harsha Nori, Naoto Usuyama, Nicholas King, Scott Mayer McKinney, Xavier Fernandes, Sheng Zhang, Eric Horvitz, 6 Nov 2024, From Medprompt to o1: Exploration of Run-Time Strategies for Medical Challenge Problems and Beyond, https://arxiv.org/abs/2411.03590
Hieu Tran, Zonghai Yao, Junda Wang, Yifan Zhang, Zhichao Yang, Hong Yu, 5 Dec 2024 (v2), RARE: Retrieval-Augmented Reasoning Enhancement for Large Language Models, https://arxiv.org/abs/2412.02830
Zhe Chen, Weiyun Wang, Yue Cao, Yangzhou Liu, Zhangwei Gao, Erfei Cui, Jinguo Zhu, Shenglong Ye, Hao Tian, Zhaoyang Liu, Lixin Gu, Xuehui Wang, Qingyun Li, Yimin Ren, Zixuan Chen, Jiapeng Luo, Jiahao Wang, Tan Jiang, Bo Wang, Conghui He, Botian Shi, Xingcheng Zhang, Han Lv, Yi Wang, Wenqi Shao, Pei Chu, Zhongying Tu, Tong He, Zhiyong Wu, Huipeng Deng, Jiaye Ge, Kai Chen, Min Dou, Lewei Lu, Xizhou Zhu, Tong Lu, Dahua Lin, Yu Qiao, Jifeng Dai, Wenhai Wang, 6 Dec 2024, Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling, https://arxiv.org/abs/2412.05271
Mingchen Zhuge, Changsheng Zhao, Dylan Ashley, Wenyi Wang, Dmitrii Khizbullin, Yunyang Xiong, Zechun Liu, Ernie Chang, Raghuraman Krishnamoorthi, Yuandong Tian, Yangyang Shi, Vikas Chandra, Jürgen Schmidhuber, 16 Oct 2024 (v2), Agent-as-a-Judge: Evaluate Agents with Agents, https://arxiv.org/abs/2410.10934
Kyle Wiggers, December 14, 2024, ‘Reasoning’ AI models have become a trend, for better or worse, https://techcrunch.com/2024/12/14/reasoning-ai-models-have-become-a-trend-for-better-or-worse/
Ekin Akyürek, Mehul Damani, Linlu Qiu, Han Guo, Yoon Kim, Jacob Andreas, 11 Nov 2024, The Surprising Effectiveness of Test-Time Training for Abstract Reasoning, https://arxiv.org/abs/2411.07279
Noam Brown, Tuomas Sandholm, 16 Nov 2017 (v3), Safe and Nested Subgame Solving for Imperfect-Information Games, https://arxiv.org/abs/1705.02955 (An early pre-AI paper on reasoning in multiple steps.)
Maxwell Zeff, November 20, 2024, Current AI scaling laws are showing diminishing returns, forcing AI labs to change course, https://techcrunch.com/2024/11/20/ai-scaling-laws-are-showing-diminishing-returns-forcing-ai-labs-to-change-course/ ("at least 10 to 20x gains in model performance ...intelligent prompting, UX decisions, and passing context at the right time into the models...")
Agnostiq, Dec 2024, multi-agent-llm: LLM based Multi-Agent methods: Lean implementation of various multi-agent LLM methods, including Iteration of Thought (IoT), https://github.com/AgnostiqHQ/multi-agent-llm
Maxwell Nye, Anders Johan Andreassen, Guy Gur-Ari, Henryk Michalewski, Jacob Austin, David Bieber, David Dohan, Aitor Lewkowycz, Maarten Bosma, David Luan, Charles Sutton, Augustus Odena, 30 Nov 2021, Show Your Work: Scratchpads for Intermediate Computation with Language Models, https://arxiv.org/abs/2112.00114
Xiangjue Dong, Maria Teleki, James Caverlee, 18 Dec 2024, A Survey on LLM Inference-Time Self-Improvement, https://arxiv.org/abs/2412.14352 https://github.com/dongxiangjue/Awesome-LLM-Self-Improvement (Broad survey of reasoning improvement methods from multi-step inference to RALM to decoding algorithms.)
Xingyu Chen, Jiahao Xu, Tian Liang, Zhiwei He, Jianhui Pang, Dian Yu, Linfeng Song, Qiuzhi Liu, Mengfei Zhou, Zhuosheng Zhang, Rui Wang, Zhaopeng Tu, Haitao Mi, Dong Yu, 30 Dec 2024, Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs, https://arxiv.org/abs/2412.21187
Rohin Manvi, Anikait Singh, Stefano Ermon, 3 Oct 2024, Adaptive Inference-Time Compute: LLMs Can Predict if They Can Do Better, Even Mid-Generation, https://arxiv.org/abs/2410.02725
Yiwei Li, Peiwen Yuan, Shaoxiong Feng, Boyuan Pan, Xinglin Wang, Bin Sun, Heda Wang, and Kan Li, 19 Jan 2024, Escape sky-high cost: Early-stopping self-consistency for multi-step reasoning. The Twelfth International Conference on Learning Representations, 2024, https://arxiv.org/abs/2401.10480 https://github.com/Yiwei98/ESC (Uses "early stopping" idea to improve CoT efficiency during inference.)
Akash Bajwa, Jan 06, 2025, Test-Time Search: A Path To AGI: Stacking Scaling Laws And Reward Engineering, https://akashbajwa.substack.com/p/test-time-search-a-path-to-agi
NovaSky, Jan 2025, Sky-T1: Train your own O1 preview model within $450, https://novasky-ai.github.io/posts/sky-t1/
Tong Xiao, Jingbo Zhu, 16 Jan 2025, Foundations of Large Language Models, https://arxiv.org/abs/2501.09223 (Huge 230 page paper on many topics such as training, prompting, alignment, and long context.)
Zekun Xi, Wenbiao Yin, Jizhan Fang, Jialong Wu, Runnan Fang, Ningyu Zhang, Jiang Yong, Pengjun Xie, Fei Huang, Huajun Chen, 16 Jan 2025, OmniThink: Expanding Knowledge Boundaries in Machine Writing through Thinking, https://arxiv.org/abs/2501.09751 (Iteratively going deeper into a topic while generating.)
Siddharth Narayanan, James D. Braza, Ryan-Rhys Griffiths, Manu Ponnapati, Albert Bou, Jon Laurent, Ori Kabeli, Geemi Wellawatte, Sam Cox, Samuel G. Rodriques, Andrew D. White, 30 Dec 2024, Aviary: training language agents on challenging scientific tasks, https://arxiv.org/abs/2412.21154 (Using smaller models combined with multi-step reasoning to compete with big models with 100x less inference cost.)
Kuang-Huei Lee, Ian Fischer, Yueh-Hua Wu, Dave Marwood, Shumeet Baluja, Dale Schuurmans, Xinyun Chen, 17 Jan 2025, Evolving Deeper LLM Thinking, https://arxiv.org/abs/2501.09891 (An alternative search strategy broad/deep, compared to CoT and reflection.)
Edward Beeching, Lewis Tunstall, Sasha Rush Dec 16, 2024, Scaling Test Time Compute with Open Source Models, https://huggingface.co/spaces/HuggingFaceH4/blogpost-scaling-test-time-compute
Maciej Besta, Julia Barth, Eric Schreiber, Ales Kubicek, Afonso Catarino, Robert Gerstenberger, Piotr Nyczyk, Patrick Iff, Yueling Li, Sam Houliston, Tomasz Sternal, Marcin Copik, Grzegorz Kwaśniewski, Jürgen Müller, Łukasz Flis, Hannes Eberhard, Hubert Niewiadomski, Torsten Hoefler, 23 Jan 2025 (v3), Reasoning Language Models: A Blueprint, https://arxiv.org/abs/2501.11223 (Survey and blueprint for how to build a Large Reasoning Model.)
Enze Xie, Junsong Chen, Yuyang Zhao, Jincheng Yu, Ligeng Zhu, Yujun Lin, Zhekai Zhang, Muyang Li, Junyu Chen, Han Cai, Bingchen Liu, Daquan Zhou, Song Han, 30 Jan 2025, SANA 1.5: Efficient Scaling of Training-Time and Inference-Time Compute in Linear Diffusion Transformer, https://arxiv.org/abs/2501.18427 (Diffusion model optimization using block-level depth pruning and inference-time scaling.)
S Wang, X Zhang, J Ma, A Hwang, Z Yu, Jan 2025, JumpStarter: Getting Started on Personal Goals with Adaptive Personal Context Curation, https://sitong-wang.github.io/data/JumpStarter.pdf (Long-term planning of goal-oriented long multi-step projects.)
Niklas Muennighoff, Zitong Yang, Weijia Shi, Xiang Lisa Li, Li Fei-Fei, Hannaneh Hajishirzi, Luke Zettlemoyer, Percy Liang, Emmanuel Candès, Tatsunori Hashimoto, 3 Feb 2025 (v2), s1: Simple test-time scaling, https://arxiv.org/abs/2501.19393 https://github.com/simplescaling/s1 (Method of "budget forcing" that allows either shortening or lengthening multi-step reasoning sequences.)
Manish Sanwal, 3 Feb 2025 (v2), Layered Chain-of-Thought Prompting for Multi-Agent LLM Systems: A Comprehensive Approach to Explainable Large Language Models, https://arxiv.org/abs/2501.18645
Sebastian Raschka, PhD, Feb 05, 2025, Understanding Reasoning LLMs: Methods and Strategies for Building and Refining Reasoning Models https://magazine.sebastianraschka.com/p/understanding-reasoning-llms
Ling Yang, Zhaochen Yu, Bin Cui, Mengdi Wang, 10 Feb 2025, ReasonFlux: Hierarchical LLM Reasoning via Scaling Thought Templates, https://arxiv.org/abs/2502.06772 https://github.com/Gen-Verse/ReasonFlux (RALM-like retrieval of reasoning prompt templates at inference time.)
Hanmeng Liu, Zhizhang Fu, Mengru Ding, Ruoxi Ning, Chaoli Zhang, Xiaozhang Liu, Yue Zhang, 13 Feb 2025, Logical Reasoning in Large Language Models: A Survey, https://arxiv.org/abs/2502.09100
Zeping Yu, Yonatan Belinkov, Sophia Ananiadou, 15 Feb 2025, Back Attention: Understanding and Enhancing Multi-Hop Reasoning in Large Language Models, https://arxiv.org/abs/2502.10835
Dacheng Li, Shiyi Cao, Chengkun Cao, Xiuyu Li, Shangyin Tan, Kurt Keutzer, Jiarong Xing, Joseph E. Gonzalez, Ion Stoica, 20 Feb 2025, S*: Test Time Scaling for Code Generation, https://arxiv.org/abs/2502.14382 https://github.com/NovaSky-AI/SkyThought
Ben Dickson, February 20, 2025, How test-time scaling unlocks hidden reasoning abilities in small language models (and allows them to outperform LLMs), https://venturebeat.com/ai/how-test-time-scaling-unlocks-hidden-reasoning-abilities-in-small-language-models-and-allows-them-to-outperform-llms/
Zhiyuan Zeng, Qinyuan Cheng, Zhangyue Yin, Yunhua Zhou, Xipeng Qiu, 17 Feb 2025, Revisiting the Test-Time Scaling of o1-like Models: Do they Truly Possess Test-Time Scaling Capabilities? https://arxiv.org/abs/2502.12215
Shubham Parashar, Blake Olson, Sambhav Khurana, Eric Li, Hongyi Ling, James Caverlee, Shuiwang Ji, 18 Feb 2025, Inference-Time Computations for LLM Reasoning and Planning: A Benchmark and Insights, https://arxiv.org/abs/2502.12521
Zihao Zeng, Xuyao Huang, Boxiu Li, Zhijie Deng, 19 Feb 2025, SIFT: Grounding LLM Reasoning in Contexts via Stickers, https://arxiv.org/abs/2502.14922 https://github.com/zhijie-group/SIFT (Multi-step reasoning where the LLM first generates a modified prompt that summarizes the key points, and then does inference for both the original and modified prompts, then comparing results and adjusting forwards and backwards.)
Marthe Ballon, Andres Algaba, Vincent Ginis, 21 Feb 2025, The Relationship Between Reasoning and Performance in Large Language Models -- o3 (mini) Thinks Harder, Not Longer, https://arxiv.org/abs/2502.15631
Maxwell Zeff, February 24, 2025, Anthropic launches a new AI model that ‘thinks’ as long as you want, https://techcrunch.com/2025/02/24/anthropic-launches-a-new-ai-model-that-thinks-as-long-as-you-want/
Kif Leswing, Feb 26 2025, Nvidia CEO Huang says AI has to do ’100 times more’ computation now than when ChatGPT was released, https://www.cnbc.com/2025/02/26/nvidia-ceo-huang-says-next-generation-ai-will-need-more-compute.html (The thesis that AI reasoning will need 100 times more compute, regardless of whether it is a single-step "long answers" model thinking out loud, or a multi-step test time compute model.)
Zhong-Zhi Li, Duzhen Zhang, Ming-Liang Zhang, Jiaxin Zhang, Zengyan Liu, Yuxuan Yao, Haotian Xu, Junhao Zheng, Pei-Jie Wang, Xiuyi Chen, Yingying Zhang, Fei Yin, Jiahua Dong, Zhijiang Guo, Le Song, Cheng-Lin Liu, 25 Feb 2025 (v2), From System 1 to System 2: A Survey of Reasoning Large Language Models, https://arxiv.org/abs/2502.17419
Wenkai Yang, Shuming Ma, Yankai Lin, Furu Wei, 25 Feb 2025, Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning, https://arxiv.org/abs/2502.18080 (Trying to generate the "shortest correct response" by examining the lengths needed for CoT.)
Yuchen Yan, Yongliang Shen, Yang Liu, Jin Jiang, Mengdi Zhang, Jian Shao, Yueting Zhuang, 13 Mar 2025 (v2), InftyThink: Breaking the Length Limits of Long-Context Reasoning in Large Language Models, https://arxiv.org/abs/2503.06692
Qiguang Chen, Libo Qin, Jinhao Liu, Dengyun Peng, Jiannan Guan, Peng Wang, Mengkang Hu, Yuhang Zhou, Te Gao, Wanxiang Che, 13 Mar 2025 (v2), Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models, https://arxiv.org/abs/2503.09567 (Massive and broad survey of all types of reasoning.)
Eric Zhao, Pranjal Awasthi, Sreenivas Gollapudi, 20 Feb 2025 (v2), Sample, Scrutinize and Scale: Effective Inference-Time Search by Scaling Verification https://arxiv.org/abs/2502.01839 (Wrapping a single model with a Best-of-N approach that self-selects the best answer can significantly improve reasoning rates.)
Qianjun Pan, Wenkai Ji, Yuyang Ding, Junsong Li, Shilian Chen, Junyi Wang, Jie Zhou, Qin Chen, Min Zhang, Yulan Wu, Liang He, 8 May 2025 (v2), A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Law, https://arxiv.org/abs/2505.02665
Michael Nuñez, July 15, 2025, OpenAI, Google DeepMind and Anthropic sound alarm: ‘We may be losing the ability to understand AI’, https://venturebeat.com/ai/openai-google-deepmind-and-anthropic-sound-alarm-we-may-be-losing-the-ability-to-understand-ai/ (Monitoring the text-based interim "thinking-out-loud" reasoning of models in CoT.)
Tomek Korbak, Mikita Balesni, (and many more authors) July 2025, Chain of Thought Monitorability: A New and Fragile Opportunity for AI Safety, https://tomekkorbak.com/cot-monitorability-is-a-fragile-opportunity/cot_monitoring.pdf
Sebastian Raschka, Mar 8, 2025, Inference-Time Compute Scaling Methods to Improve Reasoning Models: Part 1: Inference-Time Compute Scaling Methods, https://sebastianraschka.com/blog/2025/state-of-llm-reasoning-and-inference-scaling.html
Runze Liu, Junqi Gao, Jian Zhao, Kaiyan Zhang, Xiu Li, Biqing Qi, Wanli Ouyang, Bowen Zhou, 10 Feb 2025, Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling, https://arxiv.org/abs/2502.06703
Shubham Parashar, Blake Olson, Sambhav Khurana, Eric Li, Hongyi Ling, James Caverlee, Shuiwang Ji, 18 Feb 2025, Inference-Time Computations for LLM Reasoning and Planning: A Benchmark and Insights, https://www.arxiv.org/abs/2502.12521
Yilong Chen, Junyuan Shang, Zhenyu Zhang, Yanxi Xie, Jiawei Sheng, Tingwen Liu, Shuohuan Wang, Yu Sun, Hua Wu, Haifeng Wang, 23 Feb 2025 (v2), Inner Thinking Transformer: Leveraging Dynamic Depth Scaling to Foster Adaptive Internal Thinking, https://arxiv.org/abs/2502.13842
Brown Ebouky, Andrea Bartezzaghi, Mattia Rigotti, 13 Jun 2025, Eliciting Reasoning in Language Models with Cognitive Tools, https://arxiv.org/abs/2506.12115
Tao Xu, Dung-Yang Lee and Momiao Xiong, 21 Jul 2025, Reinforcement Learning in hyperbolic space for multi-step reasoning, https://arxiv.org/abs/2507.16864
Tong Yang, Yu Huang, Yingbin Liang, Yuejie Chi, 11 Aug 2025, Multi-head Transformers Provably Learn Symbolic Multi-step Reasoning via Gradient Descent, https://arxiv.org/abs/2508.08222
Jiaye Lin, Yifu Guo, Yuzhen Han, Sen Hu, Ziyi Ni, Licheng Wang, Mingguang Chen, Daxin Jiang, Binxing Jiao, Chen Hu, Huacan Wang, 4 Aug 2025, SE-Agent: Self-Evolution Trajectory Optimization in Multi-Step Reasoning with LLM-Based Agents, https://arxiv.org/abs/2508.02085
Jiashuo Yu, Yue Wu, Meng Chu, Zhifei Ren, Zizheng Huang, Pei Chu, Ruijie Zhang, Yinan He, Qirui Li, Songze Li, Zhenxiang Li, Zhongying Tu, Conghui He, Yu Qiao, Yali Wang, Yi Wang, Limin Wang, 4 Aug 2025, VRBench: A Benchmark for Multi-Step Reasoning in Long Narrative Videos, https://arxiv.org/abs/2506.10857
Shaofeng Yin, Ting Lei, Yang Liu, 5 Aug 2025, ToolVQA: A Dataset for Multi-step Reasoning VQA with External Tools, https://arxiv.org/abs/2508.03284
Aske Plaat, Annie Wong, Suzan Verberne, Joost Broekens, Niki van Stein, Thomas Back, 13 Aug 2025, Multi-Step Reasoning with Large Language Models, a Survey, https://arxiv.org/abs/2407.11511
Ayoub Ben Chaliah and Hela Dellagi, 18 Aug 2025, Datarus-R1: An Adaptive Multi-Step Reasoning LLM for Automated Data Analysis, https://arxiv.org/abs/2508.13382
Wen Ye, Jinbo Liu, Defu Cao, Wei Yang, Yan Liu, 1 Sep 2025, When LLM Meets Time Series: Can LLMs Perform Multi-Step Time Series Reasoning and Inference, https://arxiv.org/abs/2509.01822
Zhiwei Wang, Yunji Wang, Zhongwang Zhang, Zhangchen Zhou, Hui Jin, Tianyang Hu, Jiacheng Sun, Zhenguo Li, Yaoyu Zhang, Zhi-Qin John Xu, 9 Sep 2025, Understanding the Language Model to Solve the Symbolic Multi-Step Reasoning Problem from the Perspective of Buffer Mechanism, https://arxiv.org/abs/2405.15302
Zidong Chen, Zihao Guo, Peng Wang, ThankGod Itua Egbe, Yan Lyu, Chenghao Qian, 16 Sep 2025, Dense-Jump Flow Matching with Non-Uniform Time Scheduling for Robotic Policies: Mitigating Multi-Step Inference Degradation, https://arxiv.org/abs/2509.13574
Mingliang Zhai, Hansheng Liang, Xiaomeng Fan, Zhi Gao, Chuanhao Li, Che Sun, Xu Bin, Yuwei Wu, Yunde Jia, 23 Oct 2025, Multi-Step Reasoning for Embodied Question Answering via Tool Augmentation, https://arxiv.org/abs/2510.20310
Teng Wang, Zhangyi Jiang, Zhenqi He, Shenyang Tong, Wenhan Yang, Yanan Zheng, Zeyu Li, Zifan He, Hailei Gong, Zewen Ye, Shengjie Ma, Jianping Zhang, 26 Oct 2025, Towards Hierarchical Multi-Step Reward Models for Enhanced Reasoning in Large Language Models, https://arxiv.org/abs/2503.13551
Tian Qin, Yuhan Chen, Zhiwei Wang, Zhi-Qin John Xu, 27 Sep 2025, Limit Analysis for Symbolic Multi-step Reasoning Tasks with Information Propagation Rules Based on Transformers, https://arxiv.org/abs/2509.23178
Kyumin Lee, Minjin Jeon, Sanghwan Jang, Hwanjo Yu, 9 Oct 2025, STEPER: Step-wise Knowledge Distillation for Enhancing Reasoning Ability in Multi-Step Retrieval-Augmented Language Models, https://arxiv.org/abs/2510.07923
David Spuler, Ph.D., 16th August, 2025, List of AI Smartness Techniques, Aussie AI Blog, https://www.aussieai.com/blog/ai-smartness-techniques
David Spuler, December 2025, Reasoning Models, Chapter 9, "The Sweetest Lesson", https://www.aussieai.com/book/sweetest-lesson-9-reasoning-models
David Spuler, Michael Sharpe, June 2025, Reasoning and RAG, Chapter 13, "RAG Optimization: Accurate and Efficient LLM Applications", https://www.aussieai.com/book/rag-book-13-reasoning-rag
David Spuler, Ph.D., Dec 21st, 2024, Multi-Step Reasoning Inference Optimization, Aussie AI Blog, https://www.aussieai.com/blog/reasoning-inference-optimization
Ben Dickson, April 17, 2026, Train-to-Test scaling explained: How to optimize your end-to-end AI compute budget for inference, https://venturebeat.com/orchestration/train-to-test-scaling-explained-how-to-optimize-your-end-to-end-ai-compute-budget-for-inference
David Spuler, Michael Sharpe, 2025, Architectures of AI Projects, Chapter 12, in "Generative AI Applications", https://www.aussieai.com/book/ai-apps-book-12-architectures-project
David Spuler, Michael Sharpe, 2025, Prompt Engineering, Chapter 17, in "Generative AI Applications", https://www.aussieai.com/book/ai-apps-book-17-prompt-engineering
David Spuler, May 31st, 2026, Multi-Step Reasoning Harness, Chapter 5. Harness Engineering, in book LLM Inference Optimization: State-of-the-Art Research, Table of Contents: https://www.aussieai.com/book/llm-inference-optimization https://www.amazon.com/dp/B0H3FKR39T