用雅可比矩阵解析提示词优化中的多目标冲突，让大模型更聪明地权衡事实性与置信度。
J6: Jacobian-Driven Role Attribution for Multi-Objective Prompt Optimization in LLMs
- 基于雅可比矩阵分解出六类梯度成分，揭示参数间交互机制
- 支持硬选择（argmax）和软加权（softmax）两种动态更新策略
- 可解释性强，适合需要精准控制优化方向的研究者
在大语言模型适配中，平衡事实性（heat）与置信度（低熵）等多项目标面临根本挑战，尤其当提示参数（如隐藏层插入 h 与嵌入修改 w）以非平凡方式相互作用时。现有方法依赖标量梯度聚合，忽略目标与参数间的深层几何结构。本文提出 J6，一种基于结构化雅可比的方法，将梯度交互矩阵分解为六种可解释成分。该分解支持硬决策（如通过 argmax 选择主导更新方向）和软策略（如通过 softmax 实现注意力式加权），形成适应局部冲突与协同的动态更新框架。此外，J6 的可解释结构可提供参数归因、任务干扰分析与几何对齐适配的洞察。本工作引入一种原则性强且可扩展的冲突感知提示优化机制，为多目标神经调优引入结构化雅可比推理开辟新路径。
原文摘要 · Abstract (English)
In large language model (LLM) adaptation, balancing multiple optimization objectives such as improving factuality (heat) and increasing confidence (via low entropy) poses a fundamental challenge, especially when prompt parameters (e.g., hidden-layer insertions h and embedding modifications w) interact in non-trivial ways. Existing multi-objective optimization strategies often rely on scalar gradient aggregation, ignoring the deeper geometric structure between objectives and parameters. We propose J6, a structured Jacobian-based method that decomposes the gradient interaction matrix into six interpretable components. This decomposition enables both hard decision-making (e.g., choosing the dominant update direction via argmax) and soft strategies (e.g., attention-style weighting via softmax over J6), forming a dynamic update framework that adapts to local conflict and synergy. Moreover, the interpretable structure of J6 provides insight into parameter attribution, task interference, and geometry-aligned adaptation. Our work introduces a principled and extensible mechanism for conflict-aware prompt optimization, and opens a new avenue for incorporating structured Jacobian reasoning into multi-objective neural tuning.
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