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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.18436255 |
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Table of Contents:
- <p>we present a geometric principle demonstrating that learnability across supervised and one-class learning paradigms is governed by a single fundamental constraint: the<br>comparison of local versus global structure in the input space. Starting from first principles specifically, the Locality Axiom and the Information Axiom—we derive three domain-specific metrics: ρclass for classification, ρreg for regression, and e for one-class anomaly detection. We show theoretically and empirically that these metrics instantiate a common geometric principle: </p> <p> <strong> Learning succeeds ⇔ Local structure differs from Global structure</strong></p> <p>Extensive empirical validation on 552 real classification datasets from OpenML (+0.903 Spearman correlation), 1,452 real regression datasets (identity theorem holds in 87% of cases), and 373 anomaly detection experiments confirms strong predictive accuracy. We further demonstrate algorithm-agnosticity through validation on SVM, Random Forest, Logistic Regression, and MLP across 100 datasets. These results establish Local Coherence as a fundamental principle describing intrinsic geometric constraints on learnability.</p>