发表机构
University of Nebraska Omaha（内布拉斯加大学奥马哈分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
Fisher-IRG通过预测敏感性度量局部表示方向，构建语义邻域并利用对比广义特征值问题恢复不变子空间，在语言和视觉模型中展现出更强的语义选择性和可复现性。
AI 中文摘要
语义保持变换可以在学习到的表示中引发显著的运动，而微小的变化可能强烈影响模型预测，这提出了一个基本问题：什么局部度量最能捕捉语义上重要的变化？我们提出了Fisher诱导的不变表示几何（Fisher-IRG），通过预测敏感性来度量局部表示方向。在每个表示周围，我们构建语义保持和语义变化的邻域，聚合它们的局部Fisher信息，并通过对比广义特征值问题恢复不变方向。受控位移分析首先表明，相当的欧几里得运动可能具有显著不同的预测后果，支持了对预测几何的需求。在语言和视觉模型中，Fisher-IRG相比基于协方差的几何，产生了更强的语义与干扰预测选择性，并且通常更可复现的子空间，同时恢复了系统性不同的局部方向。表示干预进一步将语义效果定位到Fisher导出的子空间，而保留数据的分离和检索表明，恢复的几何泛化超越了发现邻域。这些结果支持Fisher-IRG作为表征局部不变表示几何的原则性框架。
英文摘要
Semantic-preserving transformations can induce substantial motion in learned representations, while small changes may strongly affect model predictions, raising a basic question: what local metric best captures semantically consequential variation? We propose Fisher-induced invariant representation geometry (Fisher-IRG), which measures local representation directions through their predictive sensitivity. Around each representation, we construct semantic-preserving and semantic-changing neighborhoods, aggregate their local Fisher information, and recover invariant directions through a contrastive generalized eigenvalue problem. Controlled displacement analyses first show that comparable Euclidean motion can have substantially different predictive consequences, supporting the need for a predictive geometry. Across language and vision models, Fisher-IRG yields stronger semantic-versus-nuisance predictive selectivity and generally more reproducible subspaces than covariance-based geometry, while recovering systematically distinct local directions. Representation interventions further localize semantic effects to the Fisher-derived subspace, and held-out separation and retrieval show that the recovered geometry generalizes beyond the discovery neighborhoods. These results support Fisher-IRG as a principled framework for characterizing local invariant representation geometry.
