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2026
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| Online Access: | https://doi.org/10.5281/zenodo.18436255 |
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| author | Pérez Contreras, Benjamín Felipe |
| author_facet | Pérez Contreras, Benjamín Felipe |
| 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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18436255 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Principle of Local Coherence A Geometric Foundation for Learnability Analysis in Classification, Regression, and Anomaly Detection Pérez Contreras, Benjamín Felipe <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> |
| title | The Principle of Local Coherence A Geometric Foundation for Learnability Analysis in Classification, Regression, and Anomaly Detection |
| url | https://doi.org/10.5281/zenodo.18436255 |