The Two-Hop Curse: LLMs trained on A$\rightarrow$B, B$\rightarrow$C fail to learn A$\rightarrow$C

[Notice: This version is outdated. Recent research contradicts some key claims; we are working on a major revision with more nuanced analysis. Please wait for the updated version.] While LLMs excel at multi-hop questions (e.g. "Who is the spouse of the performer of Imagine?") when using chain-of-thought reasoning (CoT), they struggle when forced to reason internally (without CoT). Previous work on the size and nature of this gap produced mixed evidence with inconclusive results. In this paper, we introduce a controlled setting for investigating two-hop reasoning in LLMs, where the above-chance performance constitutes undeniable evidence for latent reasoning. We fine-tune LLMs (including Llama 3 8B Instruct and GPT-4o) on fictional facts and confirm that they generalize to answering two-hop questions about them using CoT. We find that models can perform latent reasoning when facts appear together during training or in the prompt. However, to our surprise, models completely fail at two-hop reasoning without CoT when learned facts only appear in different documents, achieving chance-level accuracy and chance-level test loss. We call this complete failure to compose separately learned facts the Two-Hop Curse. Moreover, we evaluate 9 frontier LLMs on real-world facts, finding that models completely fail at two-hop no-CoT reasoning for over half of question categories while maintaining partial success with CoT across most categories. These results suggest that LLMs lack a general capability for latent multi-hop reasoning independent of the question type.