The ``Residual-to-Residual DNN series for high-Dynamic range imaging'' (R2D2)
approach was recently introduced for Radio-Interferometric (RI) imaging in
astronomy. R2D2's reconstruction is formed as a series of residual images,
iteratively estimated as outputs of Deep Neural Networks (DNNs) taking the
previous iteration's image estimate and associated data residual as inputs. In
this work, we investigate the robustness of the R2D2 image estimation process,
by studying the uncertainty associated with its series of learned models.
Adopting an ensemble averaging approach, multiple series can be trained,
arising from different random DNN initializations of the training process at
each iteration. The resulting multiple R2D2 instances can also be leveraged to
generate ``R2D2 samples'', from which empirical mean and standard deviation
endow the algorithm with a joint estimation and uncertainty quantification
functionality. Focusing on RI imaging, and adopting a telescope-specific
approach, multiple R2D2 instances were trained to encompass the most general
observation setting of the Very Large Array (VLA). Simulations and real-data
experiments confirm that: (i) R2D2's image estimation capability is superior to
that of the state-of-the-art algorithms; (ii) its ultra-fast reconstruction
capability (arising from series with only few DNNs) makes the computation of
multiple reconstruction samples and of uncertainty maps practical even at large
image dimension; (iii) it is characterized by a very low model uncertainty.

这篇研究论文使用 Residual-to-Residual DNN（R2D2）方法进行高动态范围成像，通过集成学习的方式生成多个 R2D2 实例，从而提供了一种同时估计和量化不确定性的功能。结果表明，R2D2 的图像估计能力优于现有算法，计算多个重建样本和不确定性图在大图像尺寸下也非常实用，并且模型的不确定性非常低。

无线电天文学中带有模型不确定性量化的 R2D2 图像重建

R2D2 image reconstruction with model uncertainty quantification in radio  astronomy

Deep neural networks can achieve remarkable generalization performances while
interpolating the training data perfectly. Rather than the U-curve emblematic
of the bias-variance trade-off, their test error often follows a "double
descent" - a mark of the beneficial role of overparametrization. In this work,
we develop a quantitative theory for this phenomenon in the so-called lazy
learning regime of neural networks, by considering the problem of learning a
high-dimensional function with random features regression. We obtain a precise
asymptotic expression for the bias-variance decomposition of the test error,
and show that the bias displays a phase transition at the interpolation
threshold, beyond which it remains constant. We disentangle the variances
stemming from the sampling of the dataset, from the additive noise corrupting
the labels, and from the initialization of the weights. Following up on Geiger
et al. 2019, we first show that the latter two contributions are the crux of
the double descent: they lead to the overfitting peak at the interpolation
threshold and to the decay of the test error upon overparametrization. We then
quantify how they are suppressed by ensemble averaging the outputs of K
independently initialized estimators. When K is sent to infinity, the test
error remains constant beyond the interpolation threshold. We further compare
the effects of overparametrizing, ensembling and regularizing. Finally, we
present numerical experiments on classic deep learning setups to show that our
results hold qualitatively in realistic lazy learning scenarios.

研究发现，通过过度参数化，深度神经网络能够在插值训练数据的同时实现卓越的泛化性能，并且在测试误差上具有双下降现象，该现象可以通过集成平均估计器进行抑制。