# Why Knowing Both Hops Is Not Enough: Understanding Two-Hop Generalization in Language Models

arXiv: https://arxiv.org/abs/2608.07261 · HTML: https://mlsanity.com/paper/2608.07261/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 40 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 25 of 25)

- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Dissecting Recall of Factual Associations in Auto-Regressive Language Models](https://mlsanity.com/paper/2304.14767/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)
- [Do Large Language Models Latently Perform Multi-Hop Reasoning?](https://mlsanity.com/paper/2402.16837/) (2024)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Looped Transformers are Better at Learning Learning Algorithms](https://mlsanity.com/paper/2311.12424/) (2023)
- [Taken out of context: On measuring situational awareness in LLMs](https://mlsanity.com/paper/2309.00667/) (2023)
- [Hopping Too Late: Exploring the Limitations of Large Language Models on Multi-Hop Queries](https://mlsanity.com/paper/2406.12775/) (2024)
- [Steering Knowledge Selection Behaviours in LLMs via SAE-Based Representation Engineering](https://mlsanity.com/paper/2410.15999/) (2024)
- [Understanding and Patching Compositional Reasoning in LLMs](https://mlsanity.com/paper/2402.14328/) (2024)
- [The Impact of Depth on Compositional Generalization in Transformer Language Models](https://mlsanity.com/paper/2310.19956/) (2023)
- [VISIT: Visualizing and Interpreting the Semantic Information Flow of Transformers](https://mlsanity.com/paper/2305.13417/) (2023)
- [Interpreting Arithmetic Mechanism in Large Language Models through Comparative Neuron Analysis](https://mlsanity.com/paper/2409.14144/) (2024)
- [Back Attention: Understanding and Enhancing Multi-Hop Reasoning in Large Language Models](https://mlsanity.com/paper/2502.10835/) (2025)
- [How Do LLMs Perform Two-Hop Reasoning in Context?](https://mlsanity.com/paper/2502.13913/) (2025)
- [Lessons from Studying Two-Hop Latent Reasoning](https://mlsanity.com/paper/2411.16353/) (2024)
- [Does Your Model Classify Entities Reasonably? Diagnosing and Mitigating Spurious Correlations in Entity Typing](https://mlsanity.com/paper/2205.12640/) (2022)
- [Evolution of SAE Features Across Layers in LLMs](https://mlsanity.com/paper/2410.08869/) (2024)
- [Extractive Structures Learned in Pretraining Enable Generalization on Finetuned Facts](https://mlsanity.com/paper/2412.04614/) (2024)
- [Grokking in the Wild: Data Augmentation for Real-World Multi-Hop Reasoning with Transformers](https://mlsanity.com/paper/2504.20752/) (2025)
- [How Do Language Models Compose Functions?](https://mlsanity.com/paper/2510.01685/) (2025)

## Abstract (arXiv)

Large language models (LLMs) can solve complex multi-hop problems yet exhibit puzzling failures on simple two-hop queries: although a model may correctly store each individual hop, it often fails to combine them. To understand the internal mechanisms of this phenomenon, we train transformers from scratch in a controlled symbolic environment. Our experiments reveal a pattern in two-hop generalization: models generalize reliably when the second hop follows the training distribution, but always fail when it deviates. Through mechanistic analysis, we provide a complete explanation for these distinct generalization behaviors: in settings where models generalize successfully, performance is driven by the emergence of consistent intermediate representations for the same entities across contexts, whereas failures on settings where the second hop is out-of-distribution arise from a mismatch across layers: lower layers correctly construct these intermediate representations, but upper layers, while trained on corresponding atomic facts, primarily learn to map them to outputs rather than to reason over them. Driven by this insight, we propose a recurrent-style training strategy, which enables transformers to reuse their reasoning circuitry across input forms and substantially improves generalization on out-of-distribution two-hop queries. Our data and code are available at https://github.com/zzl-strong/two_hop .