الملخص
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.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Yong, B., Su, Z., Guo, L., Li, H., Shen, J., & Zhou, Q. (2026). LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Prediction. https://omanscience.com/ar/articles/lln-learnable-lens-networks-for-parameter-efficient-long-horizon-dynamical-prediction
MLA 9
Yong, Binbin, et al. "LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Prediction." https://omanscience.com/ar/articles/lln-learnable-lens-networks-for-parameter-efficient-long-horizon-dynamical-prediction.
شيكاغو (المؤلف–التاريخ)
Yong, Binbin, Zhao Su, Lan Guo, Haoran Li, Jun Shen, and Qingguo Zhou. 2026. "LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Prediction." https://omanscience.com/ar/articles/lln-learnable-lens-networks-for-parameter-efficient-long-horizon-dynamical-prediction.
هارفارد
Yong, B., Su, Z., Guo, L., Li, H., Shen, J. and Zhou, Q. (2026) 'LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Prediction', Available at: https://omanscience.com/ar/articles/lln-learnable-lens-networks-for-parameter-efficient-long-horizon-dynamical-prediction.
فانكوفر
Yong B, Su Z, Guo L, Li H, Shen J, Zhou Q. LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Prediction. https://omanscience.com/ar/articles/lln-learnable-lens-networks-for-parameter-efficient-long-horizon-dynamical-prediction
IEEE
B. Yong, Z. Su, L. Guo, H. Li, J. Shen, and Q. Zhou, "LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Prediction," https://omanscience.com/ar/articles/lln-learnable-lens-networks-for-parameter-efficient-long-horizon-dynamical-prediction.