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This research introduces Fisher-IRG, a novel framework for analyzing local representation geometry in both language and vision models by prioritizing predictive sensitivity over standard Euclidean distance. The study demonstrates that this approach effectively isolates semantically meaningful variations from nuisance noise, offering a more robust metric for understanding model behavior than traditional covariance-based methods. By recovering invariant directions through contrastive generalized eigenvalue problems, the work provides a principled tool for characterizing how small input perturbations impact model predictions across different modalities.
Fisher-IRG: Fisher-Induced Local Invariant Representation Geometry across Language and Vision Models
arXiv:2609.36458v1 Announce Type: cross Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Computation and Language (cs.CL); Computer Vision and Pattern Recognition (cs.CV)
arXiv:2609.36458 [cs.LG]
(or arXiv:2609.36458v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.36458 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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