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.

In Large Language Models (LLMs) generation, there exist knowledge conflicts, and scenarios where parametric knowledge contradicts knowledge provided in the context. Previous works studied tuning, decoding algorithms, or locating and editing context-aware neurons to adapt LLMs to be faithful to new contextual knowledge. However, they are usually inefficient or ineffective for large models, not workable for black-box models, or unable to continuously adjust LLMs’ sensitivity to the knowledge provided in the context. To mitigate these problems, we propose CSKS (Continuously Steering Knowledge Sensitivity), a simple framework that can steer LLMs’ sensitivity to contextual knowledge continuously at a lightweight cost. Specifically, we tune two small LMs (i.e. proxy models) and use the difference in their output distributions to shift the original distribution of an LLM without modifying the LLM weights. In the evaluation process, we not only design synthetic data and fine-grained metrics to measure models’ sensitivity to contextual knowledge but also use a real conflict dataset to validate CSKS’ practical efficacy. Extensive experiments demonstrate that our framework achieves continuous and precise control over LLMs’ sensitivity to contextual knowledge, enabling both increased sensitivity and reduced sensitivity, thereby allowing LLMs to prioritize either contextual or parametric knowledge as needed flexibly. Our data and code are available at https://github.com/OliveJuiceLin/CSKS.