Context-Informed Grounding Supervision

Large language models (LLMs) are often supplemented with external knowledge to provide information not encoded in their parameters or to reduce hallucination. In such cases, we expect the model to generate responses by grounding its response in the provided external context. However, prior work has shown that simply appending context at inference time does not ensure grounded generation. To address this, we propose Context-INformed Grounding Supervision (CINGS), a post-training supervision in which the model is trained with relevant context prepended to the response, while computing the loss only over the response tokens and masking out the context. Our experiments demonstrate that models trained with CINGS exhibit stronger grounding in both textual and visual domains compared to standard instruction-tuned models. In the text domain, CINGS outperforms other training methods across 11 information-seeking datasets and is complementary to inference-time grounding techniques. In the vision-language domain, replacing a vision-language model's LLM backbone with a CINGS-trained model reduces hallucinations across four benchmarks and maintains factual consistency throughout the generated response. This improved grounding comes without degradation in general downstream performance. Finally, we analyze the mechanism underlying the enhanced grounding in CINGS and find that it induces a shift in the model's prior knowledge and behavior, implicitly encouraging greater reliance on the external context.

Differential Information: An Information-Theoretic Perspective on Preference Optimization

Direct Preference Optimization (DPO) has become a standard technique for aligning language models with human preferences in a supervised manner. Despite its empirical success, the theoretical justification behind its log-ratio reward parameterization remains incomplete. In this work, we address this gap by utilizing the Differential Information Distribution (DID): a distribution over token sequences that captures the information gained during policy updates. First, we show that when preference labels encode the differential information required to transform a reference policy into a target policy, the log-ratio reward in DPO emerges as the uniquely optimal form for learning the target policy via preference optimization. This result naturally yields a closed-form expression for the optimal sampling distribution over rejected responses. Second, we find that the condition for preferences to encode differential information is fundamentally linked to an implicit assumption regarding log-margin ordered policies-an inductive bias widely used in preference optimization yet previously unrecognized. Finally, by analyzing the entropy of the DID, we characterize how learning low-entropy differential information reinforces the policy distribution, while high-entropy differential information induces a smoothing effect, which explains the log-likelihood displacement phenomenon. We validate our theoretical findings in synthetic experiments and extend them to real-world instruction-following datasets. Our results suggest that learning high-entropy differential information is crucial for general instruction-following, while learning low-entropy differential information benefits knowledge-intensive question answering. Overall, our work presents a unifying perspective on the DPO objective, the structure of preference data, and resulting policy behaviors through the lens of differential information.