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Cited by 48Cosmology and Gravitation TheoriesGalaxies: Formation, Evolution, PhenomenaDark Matter and Cosmic Phenomena

Interpreting deep learning models for weak lensing

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Matilla, José Manuel Zorrilla, Sharma, Manasi, Hsu, Daniel, Haiman, Zoltán·2020·Physical Review D
DOI 10.1103/physrevd.102.123506
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Abstract

Deep neural networks (DNNs) are powerful algorithms that have been proven capable of extracting non-Gaussian information from weak lensing (WL) datasets. Understanding which features in the data determine the output of these nested, nonlinear algorithms is an important but challenging task. We analyze a DNN that has been found in previous work to accurately recover cosmological parameters in simulated maps of the WL convergence ($\ensuremath{\kappa}$). We derive constraints on the cosmological parameter pair $({\mathrm{\ensuremath{\Omega}}}_{m},{\ensuremath{\sigma}}_{8})$ from a combination of three commonly used WL statistics (power spectrum, lensing peaks, and Minkowski functionals), using ray-traced simulated $\ensuremath{\kappa}$ maps. We show that the network can improve the inferred parameter constraints relative to this combination by 20% even in the presence of realistic levels of shape noise. We apply a series of well-established saliency methods to interpret the DNN and find that the most relevant pixels are those with extreme $\ensuremath{\kappa}$ values. For noiseless maps, regions with negative $\ensuremath{\kappa}$ account for 69%--89%. of the attribution of the DNN output, defined as the square of the saliency in input space. In the presence of shape noise, the attribution concentrates in high-convergence regions, with 36%--68% of the attribution in regions with $\ensuremath{\kappa}>3{\ensuremath{\sigma}}_{\ensuremath{\kappa}}$.

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  • Matilla et al. (2020) found that in all cases, the most relevant pixels in input maps were the ones with extreme values.

    “They found that in all cases, the most relevant pixels in the input maps were the ones with extreme values.”

    From The Dawes Review 10: The impact of deep learning for the analysis of galaxy surveys (2023) · cites this paper as Matilla et al. (2020)

  • In noiseless maps, regions with negative convergence accounted for the majority of the attribution, while on realistically noisy maps, high value convergence regions (positive peaks) accounted for the majority of the attribution.

    “In noiseless maps, regions with negative convergence accounted for the majority of the attribution, while on realistically noisy maps, the high value convergence regions (positive peaks) account for the majority of the attribution.”

    From The Dawes Review 10: The impact of deep learning for the analysis of galaxy surveys (2023) · cites this paper as Matilla et al. (2020)

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Authors
Matilla, J. M. Z., Sharma, M., Hsu, D., & Haiman, Z.
Affiliations
Columbia University (US)
ORCID
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
2020-12-01
Volume
102
Issue
12
ISSN
  • 2470-0010 (ISSN-L)
  • 2470-0029
DOI
10.1103/physrevd.102.123506
OpenAlex
W3041488807
Cited by
48
References
45
Citations by year
2026: 6 · 2025: 7 · 2024: 9 · 2023: 5 · 2022: 11 · 2021: 9 · 2020: 1
FWCI
2.90
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. D/Physical review. D. (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Aeronautics and Space Administration (80NSSC18K1093)
  • National Science Foundation
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Dark Matter and Cosmic Phenomena
Keywords
weak gravitational lensing, deep neural network, model interpretability, saliency maps, cosmological parameter constraints, matter density parameter, amplitude of matter fluctuations, convergence maps, shape noise, Minkowski functionals, power spectrum

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