# How Do LLMs Perform Two-Hop Reasoning in Context?

arXiv: https://arxiv.org/abs/2502.13913 · HTML: https://mlsanity.com/paper/2502.13913/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 45 of its 48 references that are in the map.
- First posted on arXiv 19 Feb 2025.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 30 of 45)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Dissecting Recall of Factual Associations in Auto-Regressive Language Models](https://mlsanity.com/paper/2304.14767/) (2023)
- [Trained Transformers Learn Linear Models In-Context](https://mlsanity.com/paper/2306.09927/) (2023)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [MQuAKE: Assessing Knowledge Editing in Language Models via Multi-Hop Questions](https://mlsanity.com/paper/2305.14795/) (2023)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Transformers learn to implement preconditioned gradient descent for in-context learning](https://mlsanity.com/paper/2306.00297/) (2023)
- [Physics of Language Models: Part 3.1, Knowledge Storage and Extraction](https://mlsanity.com/paper/2309.14316/) (2023)
- [Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models](https://mlsanity.com/paper/2301.04213/) (2023)
- [Towards Understanding Grokking: An Effective Theory of Representation Learning](https://mlsanity.com/paper/2205.10343/) (2022)
- [Do Large Language Models Latently Perform Multi-Hop Reasoning?](https://mlsanity.com/paper/2402.16837/) (2024)
- [Birth of a Transformer: A Memory Viewpoint](https://mlsanity.com/paper/2306.00802/) (2023)
- [The mechanistic basis of data dependence and abrupt learning in an in-context classification task](https://mlsanity.com/paper/2312.03002/) (2023)
- [How Transformers Learn Causal Structure with Gradient Descent](https://mlsanity.com/paper/2402.14735/) (2024)

## Built on by (most cited first, 20 of 20)

- [A Survey on Latent Reasoning](https://mlsanity.com/paper/2507.06203/) (2025)
- [Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought](https://mlsanity.com/paper/2505.12514/) (2025)
- [Large Language Model Reasoning Failures](https://mlsanity.com/paper/2602.06176/) (2026)
- [Emergence of Superposition: Unveiling the Training Dynamics of Chain of Continuous Thought](https://mlsanity.com/paper/2509.23365/) (2025)
- [Do Latent-CoT Models Think Step-by-Step? A Mechanistic Study on Sequential Reasoning Tasks](https://mlsanity.com/paper/2602.00449/) (2026)
- [Generalization or Hallucination? Understanding Out-of-Context Reasoning in Transformers](https://mlsanity.com/paper/2506.10887/) (2025)
- [Loop the Loopies!](https://mlsanity.com/paper/2607.16051/) (2026)
- [Learning from Synthetic Data Improves Multi-hop Reasoning](https://mlsanity.com/paper/2603.02091/) (2026)
- [Latent Concept Disentanglement in Transformer-based Language Models](https://mlsanity.com/paper/2506.16975/) (2025)
- [Weak-to-Strong GraphRAG: Aligning Weak Retrievers with Large Language Models for Graph-based Retrieval Augmented Generation](https://mlsanity.com/paper/2506.22518/) (2025)
- [Breaking the Reversal Curse in Autoregressive Language Models via Identity Bridge](https://mlsanity.com/paper/2602.02470/) (2026)
- [Transformers Provably Learn to Internalize Chain-of-Thought](https://mlsanity.com/paper/2605.28600/) (2026)
- [Deductive Logic in Language Models: Horizontal vs Vertical Reasoning](https://mlsanity.com/paper/2510.09340/) (2025)
- [Do Language Models Reason Across Languages?](https://mlsanity.com/paper/2601.06644/) (2026)
- [Is Grokking Worthwhile? Functional Analysis and Transferability of Generalization Circuits in Transformers](https://mlsanity.com/paper/2601.09049/) (2026)
- [Opening the Black Box: A Survey on the Mechanisms of Multi-Step Reasoning in Large Language Models](https://mlsanity.com/paper/2601.14270/) (2026)
- [Positional versus Symbolic Attention Heads: Learning Dynamics, RoPE Geometry, and Length Generalization](https://mlsanity.com/paper/2605.31558/) (2026)
- [Can Language Models Compose Skills In-Context?](https://mlsanity.com/paper/2510.22993/) (2025)
- [Why Knowing Both Hops Is Not Enough: Understanding Two-Hop Generalization in Language Models](https://mlsanity.com/paper/2608.07261/) (2026)
- [Transformers Stop Thinking Too Early, and a Tiny LoRA Fixes It](https://mlsanity.com/paper/2609.36585/) (2026)

## Abstract (arXiv)

``Socrates is human. All humans are mortal. Therefore, Socrates is mortal.'' This form of argument illustrates a typical pattern of two-hop reasoning. Formally, two-hop reasoning refers to the process of inferring a conclusion by making two logical steps, each connecting adjacent concepts, such that the final conclusion depends on the integration of both steps. It is one of the most fundamental components of human reasoning and plays a crucial role in both formal logic and everyday decision-making. Despite recent progress in large language models (LLMs), we surprisingly find that they can fail at solving simple two-hop reasoning problems when distractors are present. We observe on a synthetic dataset that pre-trained LLMs often resort to random guessing among all plausible conclusions. However, after few steps of fine-tuning, models achieve near-perfect accuracy and exhibit strong length generalization. To understand the underlying mechanisms, we train a 3-layer Transformer from scratch on a synthetic two-hop reasoning task and reverse-engineer its internal information flow. We observe a clear progression in the attention logits throughout training. This pictures a sharp phase transition from an initial stage of random guessing to the emergence of a structured sequential query mechanism, where the model first retrieves the preceding and the bridge concepts in the early layers and then uses them to infer the final answer. Finally, we show that these dynamics can be captured by a minimal three-parameter attention-only network.