# The Periodic Table of LLM Reasoning: A Structured Survey of Reasoning Paradigms, Methods, and Failure Modes

arXiv: https://arxiv.org/abs/2606.11470 · HTML: https://mlsanity.com/paper/2606.11470/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 262 of its 342 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)
- Retrieval-augmented generation / [Agentic RAG, agents and memory](https://mlsanity.com/rag/agentic-rag-agents-and-memory/)

## Builds on (most cited first, 30 of 262)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [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)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [A Multitask, Multilingual, Multimodal Evaluation of ChatGPT on Reasoning, Hallucination, and Interactivity](https://mlsanity.com/paper/2302.04023/) (2023)
- [Multimodal Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2302.00923/) (2023)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructions](https://mlsanity.com/paper/2406.15877/) (2024)
- [Language Models are Multilingual Chain-of-Thought Reasoners](https://mlsanity.com/paper/2210.03057/) (2022)
- [Visual-RFT: Visual Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.01785/) (2025)
- [From Crowdsourced Data to High-Quality Benchmarks: Arena-Hard and BenchBuilder Pipeline](https://mlsanity.com/paper/2406.11939/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Video-R1: Reinforcing Video Reasoning in MLLMs](https://mlsanity.com/paper/2503.21776/) (2025)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://mlsanity.com/paper/2508.06471/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [TabFact: A Large-scale Dataset for Table-based Fact Verification](https://mlsanity.com/paper/1909.02164/) (2019)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Accelerating scientific discovery with Co-Scientist](https://mlsanity.com/paper/2502.18864/) (2025)
- [LongBench v2: Towards Deeper Understanding and Reasoning on Realistic Long-context Multitasks](https://mlsanity.com/paper/2412.15204/) (2024)

## Abstract (arXiv)

Reasoning has become central to how Large Language Models (LLMs) are evaluated and interpreted, spanning Chain-of-Thought (CoT), mathematical problem-solving, multi-hop question answering, code generation, retrieval-augmented reasoning, tool use, and multimodal decision-making. In this survey, we introduce the Periodic Table of LLM Reasoning, a framework organizing 300+ recent papers by reasoning paradigm, methodological mechanism, evaluation setting, and failure mode. We classify LLM reasoning into nine paradigms: Chain-of-Thought, Multi-Hop, Mathematical, Commonsense, Visual and Temporal, Code and Algorithmic, Retrieval-Augmented, Tool-Augmented or Agentic, and Reinforcement Learning-based reasoning. For each, we review approaches, including prompting, architectural interventions, supervised fine-tuning, verifier-guided inference, reward modeling, retrieval, tool interfaces, agentic workflows, and benchmark design. We argue that LLM reasoning is not a single emergent capability but a family of scaffolded behaviors shaped by model scale, task structure, external memory, supervision, and evaluation protocols. We synthesize recurring failure modes, including hallucinated reasoning, brittle multi-step inference, spurious rationales, weak causal grounding, poor out-of-distribution generalization, benchmark contamination, and unreliable self-verification. Progress is difficult to compare across paradigms because gains may arise from prompting, retrieval, verifier design, or benchmark structure rather than general reasoning ability. The survey connects methods to their assumptions, strengths, and failure modes, providing a reference map of the field and a diagnostic framework for future work. We conclude that robust LLM reasoning will require meta-reasoning, multimodal and temporal grounding, adaptive tool use, and principled evaluation under distribution shift.