We investigate the prospect of reconstructing the ``cosmic distance ladder''
of the Universe using a novel deep learning framework called LADDER - Learning
Algorithm for Deep Distance Estimation and Reconstruction. LADDER is trained on
the apparent magnitude data from the Pantheon Type Ia supernovae compilation,
incorporating the full covariance information among data points, to produce
predictions along with corresponding errors. After employing several validation
tests with a number of deep learning models, we pick LADDER as the best
performing one. We then demonstrate applications of our method in the
cosmological context, that include serving as a model-independent tool for
consistency checks for other datasets like baryon acoustic oscillations,
calibration of high-redshift datasets such as gamma ray bursts, use as a
model-independent mock catalog generator for future probes, etc. Our analysis
advocates for interesting yet cautious consideration of machine learning
applications in these contexts.

使用一种称为 LADDER（深度距离估计与重建学习算法）的新型深度学习框架，我们研究了利用宇宙的 “宇宙距离阶梯” 进行重建的前景。LADDER 通过使用巴拿松型 Ia 型超新星样本中的表观星等数据，并将数据点之间的完全协方差信息纳入训练，以产生带有相应误差的预测。我们在多个深度学习模型上进行了数个验证测试后，选定 LADDER 作为表现最佳的模型。接着，我们展示了我们的方法在宇宙学背景下的应用，包括作为模型独立的工具用于一致性检查其他数据集，如重子声学振荡、校准高红移数据集，例如伽玛射线暴，以及将其作为未来探测任务的模型独立模拟目录生成器等。我们的分析主张在这些情境中对机器学习应用的有趣但谨慎的考虑。