aiqbench analysis
This study provides empirical evidence that decision regions in image classifiers are simply connected, confirming that loops within same-label boundaries can always be filled without encountering topological holes at tested resolutions. The findings reveal significant differences in construction effort between trained models and randomly initialized ones, offering deeper insight into the geometric structure underlying neural network predictions.
Empirical Evidence for Simply Connected Decision Regions in Image Classifiers
arXiv:2605.06380v2 Announce Type: replace-cross Abstract: The topology of a classifier's decision regions determines how inputs with the same predicted label can be connected and deformed without changing that prediction. Prior empirical work constructed paths between same-label images within a single region, but did not examine whether loops bound surfaces within that region. We investigate this question using adaptive quadrilateral meshes with targeted repair of off-label interior vertices, while holding the same-label boundary loop fixed. A finite-resolution acceptance criterion distinguishes completed constructions from those left unresolved at the refinement ceiling. Across the pretrained classifiers studied, every tested loop admits an accepted filling. Construction effort varies by orders of magnitude within classes and is greater for mean-score-adjusted randomly initialised classifiers than for trained classifiers. An analytic control with a known hole leaves winding loops unresolved at the tested hole radii at or above the resolution threshold. These results provide empirical evidence consistent with simply connected decision regions at the tested resolution.
Abstract:The topology of a classifier's decision regions determines how inputs with the same predicted label can be connected and deformed without changing that prediction. Prior empirical work constructed paths between same-label images within a single region, but did not examine whether loops bound surfaces within that region. We investigate this question using adaptive quadrilateral meshes with targeted repair of off-label interior vertices, while holding the same-label boundary loop fixed. A finite-resolution acceptance criterion distinguishes completed constructions from those left unresolved at the refinement ceiling. Across the pretrained classifiers studied, every tested loop admits an accepted filling. Construction effort varies by orders of magnitude within classes and is greater for mean-score-adjusted randomly initialised classifiers than for trained classifiers. An analytic control with a known hole leaves winding loops unresolved at the tested hole radii at or above the resolution threshold. These results provide empirical evidence consistent with simply connected decision regions at the tested resolution.
Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)
arXiv:2605.06380 [cs.CV]
(or arXiv:2605.06380v2 [cs.CV] for this version)
https://doi.org/10.48550/arXiv.2605.06380 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 252 words
