aiqbench analysis
This paper introduces Complementary Feature Domains (CFD) theory, demonstrating that preserving Shannon information through invertible transformations does not guarantee the preservation of predictive value in specific decision contexts. By formalizing a "contribution defect," the authors provide a quantitative framework showing how recoding alters model accuracy under fixed learners, with an ECG experiment validating that exact behavioral inversion can restore lost predictive contributions. This work advances theoretical understanding of representation learning by separating raw information content from context-dependent utility.
Complementary Feature Domains: Information Preservation Does Not Imply Predictive-Contribution Preservation
arXiv:2610.07565v1 Announce Type: new Abstract: Complementary Feature Domains (CFD) theory characterizes predictive value as a context-indexed contribution system induced jointly by representations and their realization family. We show that Shannon-information preservation does not imply preservation of this contribution system: an invertible representation transformation can leave target information unchanged while altering predictive contribution under a restricted decision family. We formalize the resulting transition through a CFD contribution defect that measures how contextual contributions change under controlled recoding. For bounded Lipschitz utility, we show that each coalition utility shift is bounded by the behavioral distance between the attainable action sets before and after recoding; consequently, every contextual contribution defect is bounded by the sum of the corresponding coalition incompatibilities. Exact behavioral closure yields invariance, while increasingly accurate compensation yields restoration. A controlled ECG experiment illustrates the mechanism: a nonlinear bijective recoding preserves the information in a frozen time-frequency representation but changes accuracy under a fixed affine learner; applying the exact inverse restores all tested coalition accuracies. The result separates information preservation from realization-dependent contribution and provides a quantitative transition law for multi-representation prediction.
Abstract:Complementary Feature Domains (CFD) theory characterizes predictive value as a context-indexed contribution system induced jointly by representations and their realization family. We show that Shannon-information preservation does not imply preservation of this contribution system: an invertible representation transformation can leave target information unchanged while altering predictive contribution under a restricted decision family. We formalize the resulting transition through a CFD contribution defect that measures how contextual contributions change under controlled recoding. For bounded Lipschitz utility, we show that each coalition utility shift is bounded by the behavioral distance between the attainable action sets before and after recoding; consequently, every contextual contribution defect is bounded by the sum of the corresponding coalition incompatibilities. Exact behavioral closure yields invariance, while increasingly accurate compensation yields restoration. A controlled ECG experiment illustrates the mechanism: a nonlinear bijective recoding preserves the information in a frozen time-frequency representation but changes accuracy under a fixed affine learner; applying the exact inverse restores all tested coalition accuracies. The result separates information preservation from realization-dependent contribution and provides a quantitative transition law for multi-representation prediction.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.07565 [cs.LG]
(or arXiv:2610.07565v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.07565 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 273 words
