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LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Prediction — arXiv:2609.34493

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.34493
License (as archived): CC0-1.0
Archived: 2026-10-07T22:38:18.806Z
SHA-256 of the archived text: 32f7aa32fd1aac772b652a26177395cb147b234db08d4cd40c3e4807da7993f7
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How to cite

LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Prediction — arXiv:2609.34493 — arXiv (en), https://arxiv.org/abs/2609.34493 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3dfedc8a95fe (Metraipolis archive dc_3dfedc8a95fe, sha256 32f7aa32fd1aac772b652a26177395cb147b234db08d4cd40c3e4807da7993f7)

BibTeX

@misc{dc3dfedc8a95fe,
  title = {LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Prediction — arXiv:2609.34493},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.34493},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3dfedc8a95fe; sha256 32f7aa32fd1aac772b652a26177395cb147b234db08d4cd40c3e4807da7993f7},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.34493. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Explicit residual connections of the form (x+f(x)), often combined with normalization layers, have become a standard strategy for training very deep neural networks. However, residual addition primarily provides an algebraic shortcut for gradient propagation, while leaving the evolution of feature geometry across layers largely unconstrained. We introduce Learnable Lens Networks (LLN), a physics-inspired architecture that replaces direct feature-space residual accumulation with learnable optical transport in an augmented position-angle phase space. Each layer alternates between free propagation, which provides an implicit transport path, and a learnable lens field that performs nonlinear trajectory transformation and focusing. Theoretically, we establish that LLN transport is globally invertible and volume-preserving for any differentiable lens field, with the implemented coordinate-wise Gaussian transport further satisfying symplecticity. Importantly, these structural constraints do not limit expressivity: with unrestricted embeddings and readouts, LLN retain universal approximation of continuous end-to-end maps. Experiments across diverse dynamical systems demonstrate that LLN improves long-horizon prediction while using substantially fewer parameters than same-depth comparators. Further analysis reveals stable depth-wise gradient transport and interpretable learned dynamics under the coupled propagation and refraction design.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-29 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.34493 — 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 2026-10-07T22:14:28.209Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).