# Deep Learning for Primordial B-mode Extraction

arXiv: https://arxiv.org/abs/2512.19577 · HTML: https://mlsanity.com/paper/2512.19577/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 86 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 10 of 10)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Horovod: fast and easy distributed deep learning in TensorFlow](https://mlsanity.com/paper/1802.05799/) (2018)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [DeepCMB: Lensing Reconstruction of the Cosmic Microwave Background with Deep Neural Networks](https://mlsanity.com/paper/1810.01483/) (2018)
- [Uncertainty Estimation and Propagation in Accelerated MRI Reconstruction](https://mlsanity.com/paper/2308.02631/) (2023)
- [Machine Learning and Cosmology](https://mlsanity.com/paper/2203.08056/) (2022)
- [Conformalized Generative Bayesian Imaging: An Uncertainty Quantification Framework for Computational Imaging](https://mlsanity.com/paper/2504.07696/) (2025)
- [Reconstructing Patchy Reionization with Deep Learning](https://mlsanity.com/paper/2101.01214/) (2021)
- [Reconstructing Cosmic Polarization Rotation with ResUNet-CMB](https://mlsanity.com/paper/2109.09715/) (2021)

## Abstract (arXiv)

The search for primordial gravitational waves is a central goal of cosmic microwave background (CMB) surveys. Isolating the characteristic B-mode polarization signal sourced by primordial gravitational waves is challenging for several reasons: the amplitude of the signal is inherently small; astrophysical foregrounds produce B-mode polarization contaminating the signal; and secondary B-mode polarization fluctuations are produced via the conversion of E modes. Current and future low-noise, multi-frequency observations enable sufficient precision to address the first two of these challenges such that secondary B modes will become the bottleneck for improved constraints on the amplitude of primordial gravitational waves. The dominant source of secondary B-mode polarization is gravitational lensing by large scale structure. Various strategies have been developed to estimate the lensing deflection and to reverse its effects the CMB, thus reducing confusion from lensing B modes in the search for primordial gravitational waves. However, a few complications remain. First, there may be additional sources of secondary B-mode polarization, for example from patchy reionization or from cosmic polarization rotation. Second, the statistics of delensed CMB maps can become complicated and non-Gaussian, especially when advanced lensing reconstruction techniques are applied. We previously demonstrated how a deep learning network, ResUNet-CMB, can provide nearly optimal simultaneous estimates of multiple sources of secondary B-mode polarization. In this paper, we show how deep learning can be applied to estimate and remove multiple sources of secondary B-mode polarization, and we further show how this technique can be used in a likelihood analysis to produce nearly optimal, unbiased estimates of the amplitude of primordial gravitational waves.