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Dual-Manifold Geometry Guided Representation Learning: Adaptive Coupling between Kernel and Data Spaces — arXiv:2608.12737

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.12737
License (as archived): CC0-1.0
Archived: 2026-10-19T04:55:34.438Z
SHA-256 of the archived text: a0daaa5c26fa4475335fcf625cbd9d412f9c2a2a6905df472665bf821cb7ea6e
Stable URL of this page: https://metraipolis.com/documento/dc_d13bf110f79a

How to cite

Dual-Manifold Geometry Guided Representation Learning: Adaptive Coupling between Kernel and Data Spaces — arXiv:2608.12737 — arXiv (en), https://arxiv.org/abs/2608.12737 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d13bf110f79a (Metraipolis archive dc_d13bf110f79a, sha256 a0daaa5c26fa4475335fcf625cbd9d412f9c2a2a6905df472665bf821cb7ea6e)

BibTeX

@misc{dcd13bf110f79a,
  title = {Dual-Manifold Geometry Guided Representation Learning: Adaptive Coupling between Kernel and Data Spaces — arXiv:2608.12737},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.12737},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d13bf110f79a; sha256 a0daaa5c26fa4475335fcf625cbd9d412f9c2a2a6905df472665bf821cb7ea6e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.12737. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Deep representation learning has primarily focused on how features evolve across network layers, while largely overlooking the structured geometry embedded in network parameters. We introduce a dual-manifold perspective in which each convolutional layer contains two coupled geometric spaces: a Kernel Manifold induced by convolutional filters and a Data Manifold characterized by intermediate feature representations. Because these manifolds share the same channel space, parameter geometry can provide complementary structural information to guide feature evolution. Based on this insight, we propose Kernel-Guided Feature Transform (KGFT), a lightweight module that derives a geometric guidance matrix from the kernel Gram matrix and uses it to transform the covariance structure of feature representations. Unlike conventional attention mechanisms that reweight feature responses, KGFT explicitly reshapes feature relationships by transferring geometric information from the kernel manifold to the data manifold. To accommodate network hierarchy, we further introduce Exploit and Explore modes with a depth-aware scheduling strategy and a learnable guidance strength that adaptively controls the contribution of geometric transformation. This design promotes geometric alignment in shallow layers while encouraging feature diversity in deeper layers, without imposing excessive constraints on representation learning. Theoretical analysis establishes the validity of the proposed transformation and characterizes its effect on feature covariance. Extensive experiments across CNN- and Transformer-based architectures, including ResNet, ViT, and LLaMA-7B, demonstrate consistent improvements on image classification and arithmetic reasoning tasks, validating the generality and effectiveness of kernel-guided dual-manifold representation learning. Code will be publicly available.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-08-14 in cs.CV).
Categorie arXiv: Computer Vision and Pattern Recognition (cs.CV).
Pagina del lavoro: https://arxiv.org/abs/2608.12737 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T04:46:30.059Z dalla pagina https://arxiv.org/catchup/cs.CV/2026-08-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).