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Robustness of Neural Networks for CMB Polarization Foreground Removal

Luca Gomez Bachar, Cora Dvorkin, Alberto Daniel Supanitsky

Abstract

The detection of Cosmic Microwave Background primordial $B$-mode polarization would constitute a ``smoking gun" signal of primordial gravitational waves. However, this measurement requires accurate removal of polarized Galactic foregrounds to avoid systematic biases when estimating the tensor-to-scalar ratio. Methods based on Machine Learning techniques (ML), such as Convolutional Neural Networks (CNNs), have recently been proposed as alternative foreground cleaning techniques, but their applicability to real data relies on their ability to generalize beyond the models assumed during training. In this work, we focus on a variety of foreground models (FMs) used for training and conduct a systematic study of the generalization properties of a CNN-based method. We train various CNN architectures on simulations generated from different Galactic FMs, and test their performance on models not used during the training. By characterizing the statistical properties of the FMs using variance, skewness, and Shannon entropy, we define a statistical complexity hierarchy among them. We show that training on the more complex FMs reduces bias and improves precision when testing on unseen FMs, whereas training on the simplest model could introduce systematic errors. These results evidence that a lack of generalization is a relevant source of systematic uncertainty, and emphasize the importance of understanding the impact of the models assumed during training in ML-based methods before applying them to real data.

Robustness of Neural Networks for CMB Polarization Foreground Removal

Abstract

The detection of Cosmic Microwave Background primordial -mode polarization would constitute a ``smoking gun" signal of primordial gravitational waves. However, this measurement requires accurate removal of polarized Galactic foregrounds to avoid systematic biases when estimating the tensor-to-scalar ratio. Methods based on Machine Learning techniques (ML), such as Convolutional Neural Networks (CNNs), have recently been proposed as alternative foreground cleaning techniques, but their applicability to real data relies on their ability to generalize beyond the models assumed during training. In this work, we focus on a variety of foreground models (FMs) used for training and conduct a systematic study of the generalization properties of a CNN-based method. We train various CNN architectures on simulations generated from different Galactic FMs, and test their performance on models not used during the training. By characterizing the statistical properties of the FMs using variance, skewness, and Shannon entropy, we define a statistical complexity hierarchy among them. We show that training on the more complex FMs reduces bias and improves precision when testing on unseen FMs, whereas training on the simplest model could introduce systematic errors. These results evidence that a lack of generalization is a relevant source of systematic uncertainty, and emphasize the importance of understanding the impact of the models assumed during training in ML-based methods before applying them to real data.
Paper Structure (28 sections, 17 equations, 7 figures, 3 tables)

This paper contains 28 sections, 17 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Simulations
  3. Lensed CMB polarization maps
  4. Instrumental noise
  5. Foreground models
  6. Gaussian fluctuations in the SED parameters (GP)
  7. Rotating the sky before extracting the patch (RP)
  8. PySM3 d11s6
  9. PySM3 d4s2
  10. PySM3 d12s7
  11. Foreground cleaning methods
  12. Maximum likelihood parametric method
  13. Internal Linear Combination (ILC) method
  14. CNN-based method
  15. Data pre-processing
  16. ...and 13 more sections

Figures (7)

  • Figure 1: Apodized version of the mask applied to the full-sky simulations. The observed patch is centered at (RA, DEC) = $(316^\circ, -56^\circ)$, corresponding to the center of the sky patch observed by the QUBIC instrument. The apodization scale applied in this mask is $0.5^\circ$.
  • Figure 2: Pixel-level distributions of the statistical metrics computed for the polarization amplitude $P=\sqrt{Q^2+U^2}$ of the foreground models used for the training. The vertical dotted lines indicate the mean value over all pixels in the analyzed block, which are reported in Table \ref{['metrics_num']}.
  • Figure 3: Median and 68% Probability Interval (PI) of the ratio defined in Eq. \ref{['ratio']}. Left panels correspond to E-modes, while right panels correspond to B-modes. A logarithmic scale is used for the B-modes. We compare the CNN-based method with the traditional methods described in Sections \ref{['parametricmet']} and \ref{['ILCmet']}.
  • Figure 4: Median and 68% Probability Interval (PI) of the ratio defined in Eq. \ref{['ratio']}. Left panels correspond to CMB E-modes, right panels to CMB B-modes. We compare two CNNs tested on a third foreground model.
  • Figure 5: Median and 68% Probability Interval (PI) of the ratio defined in Eq. \ref{['ratio']}. Left panels correspond to E-modes, right panels to B-modes. We compare the three CNNs with two fixed models that were not used during training.
  • ...and 2 more figures