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

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arXiv:2606.11470v2 Announce Type: replace Abstract: 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 …

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