Prism-$Δ$: Differential Subspace Steering for Prompt Highlighting in Large Language Models

Abstract: Prompt highlighting steers a LLM to prioritize user-specified text spans during generation. A key challenge is extracting steering directions that capture the difference between relevant and irrelevant contexts, rather than shared structural patterns common to both. We propose PRISM-$Δ$ (Projection-based Relevance-Informed Steering Method), which decomposes the difference between positive and negative cross-covariance matrices to maximize discriminative energy while eliminating shared directions. Each attention head receives a continuous softplus importance weight, letting weak-but-useful heads contribute at reduced strength. The framework extends naturally to Value representations, capturing content-channel signal that Key-only methods leave unused. Across four benchmarks and five models, PRISM-$Δ$ matches or exceeds the best existing method on 19 of 20 configurations, with relative gains up to +10.6%, while halving the fluency cost of steering. PRISM-$Δ$ also scales to long-context retrieval, outperforming the best existing method by up to +4.8% relative gain. PRISM-$Δ$ is compatible with FlashAttention and adds negligible memory overhead.