A Mathematical Conflict Framework for Contextual Data Modulation

Most prior works focused on conflicts between an LLM's internal parametric knowledge and externally provided context. In contrast, we investigate how LLMs handle conflicts that arise within contextual knowledge itself. We introduce a taxonomy of six types of contextual conflicts (factual, inferential, temporal, granularity, perspective, and ambiguity) and contribute a comprehensive dataset ContextConflict for this setting. The dataset contains 5,781 samples, covers both reasoning and summarization tasks, and includes both explicit contradictions and implicit conflicts that require multi-step reasoning. Experiments on nine LLMs show that current models still fall short in resolving contextual knowledge conflicts. We further provide mechanistic interpretability insights into how LLMs process such conflicts, revealing their latent awareness of conflicts and the representational geometry underlying conflict processing. In addition, our analysis uncovers a consistent model bias towards earlier evidence, and this positional preference serves as a key obstacle to effective conflict resolution. Motivated by these findings, we further propose a simple training-free, label-free steering method that steers activations to encourage a more comprehensive incorporation of evidences for better conflict resolution. On our dataset, the method consistently improves accuracy on reasoning tasks and generates higher-quality, more balanced summaries for summarization tasks.

When large language models generate from retrieved or augmented contexts, conflicts between external context and parametric priors remain a central reliability bottleneck. Existing contrastive decoding methods follow a \emph{context-aware} paradigm that unilaterally amplifies context over parametric priors, overwriting correct priors when the context is erroneous. We generalize this to the \textbf{conflict-aware} paradigm that dynamically allocates authority between prior and context based on conflict signals, rather than presupposing context trustworthiness. We show that the affine combination of prior and context logits yields a \textbf{power family} with an inherent \textbf{regime asymmetry}: extrapolation amplifies errors unboundedly when the prior is correct, interpolation under-corrects when the context is correct, and no static regime covers both. Existing contrastive decoding methods are instances of this family, mostly extrapolative. To evaluate both conflict directions, we propose TriState-Bench, a model-aware evaluation protocol that calibrates per-model prior knowledge to measure three conflict states: correction, resistance, and agreement. To resolve the asymmetry, we propose Adaptive Regime Routing (ARR), which routes between regimes at each step, lifting resistance EM from below 6 to 16--33 without sacrificing correction or agreement. Our code is available at https://github.com/keith-Jiang/conflict-aware-decoding.

Large language models accumulate extensive parametric knowledge through pre-training. However, knowledge conflicts occur when outdated or incorrect parametric knowledge conflicts with external knowledge in the context. Existing methods address knowledge conflicts through contrastive decoding, but in conflict-free scenarios, static approaches disrupt output distribution. Other dynamic decoding methods attempt to measure the degree of conflict but still struggle with complex real-world situations. In this paper, we propose a two-stage decoding method called Dynamic Cognitive Reconciliation Decoding (DCRD), to predict and mitigate context-memory conflicts. DCRD first analyzes the attention map to assess context fidelity and predict potential conflicts. Based on this prediction, the input is directed to one of two decoding paths: (1) greedy decoding, or (2) context fidelity-based dynamic decoding. This design enables DCRD to handle conflicts efficiently while maintaining high accuracy and decoding efficiency in conflict-free cases. Additionally, to simulate scenarios with frequent knowledge updates, we constructed ConflictKG, a knowledge conflict QA benchmark. Experiments on four LLMs across six QA datasets show that DCRD outperforms all baselines, achieving state-of-the-art performance.