Evaluating the efficiency of latent spaces via the coupling-matrix

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dc.authorid0000-0003-1677-9496
dc.authorid0000-0001-7403-7592
dc.contributor.authorYavuz, Mehmet Canen_US
dc.contributor.authorYanıkoğlu, Berrinen_US
dc.date.accessioned2026-01-22T10:47:13Z
dc.date.available2026-01-22T10:47:13Z
dc.date.issued2025-09-08
dc.departmentIşık Üniversitesi, Mühendislik ve Doğa Bilimleri Fakültesi, Bilgisayar Mühendisliği Bölümüen_US
dc.departmentIşık University, Faculty of Engineering and Natural Sciences, Department of Computer Engineeringen_US
dc.description.abstractA central challenge in representation learning is constructing latent embeddings that are both expressive and efficient. In practice, deep networks often produce redundant latent spaces where multiple coordinates encode overlapping information, reducing effective capacity and hindering generalization. Standard metrics such as accuracy or reconstruction loss provide only indirect evidence of such redundancy and cannot isolate it as a failure mode. We introduce a redundancy index, denoted ρ(C), that directly quantifies inter-dimensional dependencies by analyzing coupling matrices derived from latent representations and comparing their off-diagonal statistics against a normal distribution via energy distance. The result is a compact, interpretable, and statistically grounded measure of representational quality. We validate ρ(C) across discriminative and generative settings on MNIST variants, Fashion-MNIST, CIFAR-10, and CIFAR-100, spanning multiple architectures and hyperparameter optimization strategies. Empirically, low ρ(C) reliably predicts high classification accuracy or low reconstruction error, while elevated redundancy is associated with performance collapse. Estimator reliability grows with latent dimension, yielding natural lower bounds for reliable analysis. We further show that Treestructured Parzen Estimators (TPE) preferentially explore lowρ regions, suggesting that ρ(C) can guide neural architecture search and serve as a redundancy-aware regularization target. By exposing redundancy as a universal bottleneck across models and tasks, ρ(C) offers both a theoretical lens and a practical tool for evaluating and improving the efficiency of learned representations.en_US
dc.description.versionPreprint's Versionen_US
dc.identifier.citationYavuz, M. C. & Yanıkoğlu, B. (2025). Evaluating the efficiency of latent spaces via the coupling-matrix. Arxiv, 1-11. https://www.arxiv.org/abs/2509.06314v1en_US
dc.identifier.endpage11
dc.identifier.startpage1
dc.identifier.urihttps://hdl.handle.net/11729/6947
dc.identifier.urihttps://www.arxiv.org/abs/2509.06314v1
dc.identifier.wosPPRN:159553073
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakPreprint Citation Indexen_US
dc.institutionauthorYavuz, Mehmet Canen_US
dc.institutionauthorid0000-0003-1677-9496
dc.language.isoenen_US
dc.publisherCornell Univen_US
dc.relation.ispartofArxiven_US
dc.relation.publicationcategoryÖn Baskı – Uluslararası – Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectRepresentation learningen_US
dc.subjectRedundancyen_US
dc.subjectDisentanglementen_US
dc.subjectEnergy distanceen_US
dc.subjectNeural architecture searchen_US
dc.titleEvaluating the efficiency of latent spaces via the coupling-matrixen_US
dc.typePreprinten_US
dspace.entity.typePublicationen_US

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