Fisher-IRG: Fisher-Induced Local Invariant Representation Geometry across Language and Vision Models
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Computer Science > Machine Learning
arXiv:2609.36458 (cs)
[Submitted on 29 Sep 2026]
Title:Fisher-IRG: Fisher-Induced Local Invariant Representation Geometry across Language and Vision Models
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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.
| Subjects: | Machine Learning (cs.LG); Computation and Language (cs.CL); Computer Vision and Pattern Recognition (cs.CV) |
| Cite as: | arXiv:2609.36458 [cs.LG] |
| (or arXiv:2609.36458v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.36458
arXiv-issued DOI via DataCite (pending registration)
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View a PDF of the paper titled Fisher-IRG: Fisher-Induced Local Invariant Representation Geometry across Language and Vision Models, by Abdullah All Tanvir and 1 other authors
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