Neutrino oscillations encode fundamental information about neutrino masses and mixing parameters, offering a unique window into physics beyond the Standard Model. Estimating these parameters from oscillation probability maps is, however, computationally challenging due to the maps' high dimensionality and nonlinear dependence on the underlying physics. Traditional inference methods, such as likelihood-based or Monte Carlo sampling approaches, require extensive simulations to explore the parameter space, creating major bottlenecks for large-scale analyses. In this work, we introduce a data-driven framework that reformulates atmospheric neutrino oscillation parameter inference as a supervised regression task over structured oscillation maps. We propose a hierarchical transformer architecture that explicitly models the two-dimensional structure of these maps, capturing angular dependencies at fixed energies and global correlations across the energy spectrum. To improve physical consistency, the model is trained using a surrogate simulation constraint that enforces agreement between the predicted parameters and the reconstructed oscillation patterns. Furthermore, we introduce a neural network-based uncertainty quantification mechanism that produces distribution-free prediction intervals with formal coverage guarantees. Experiments on simulated oscillation maps under Earth-matter conditions demonstrate that the proposed method is comparable to a Markov Chain Monte Carlo baseline in estimation accuracy, with substantial improvements in computational cost (around 240$\times$ fewer FLOPs and 33$\times$ faster in average processing time). Moreover, the conformally calibrated prediction intervals remain narrow while achieving the target nominal coverage of 90%, confirming both the reliability and efficiency of our approach.
University of Tübingen（蒂宾根大学）；Tübingen AI Center（蒂宾根人工智能中心）；Technical University of Darmstadt（达姆施塔特工业大学）；Hessian Center for AI (hessian.AI)（黑森人工智能中心（hessian.AI））
Hierarchical Shift Mixing -- Beyond Dense Attention in Transformers
Dept. of Electrical Engineering, Linköping University, Linköping, Sweden（电子工程系，林霍普大学）；RISE Research Institutes of Sweden, Linköping, Sweden（瑞典RISE研究机构）
Hierarchical Label-wise Attention Transformer Model for Explainable ICD Coding
University of New South Wales（新南威尔士大学）；The Australian e-Health Research Centre, CSIRO（澳大利亚联邦科学与工业研究组织澳大利亚电子健康研究中心）；Australian Institute of Health and Welfare（澳大利亚卫生与福利研究所）
