[Paper Review] Selection functions of strong lens finding neural networks

Aniruddh Herle, Conor M. O’Riordan+1 more|arXiv (Cornell University)|Jul 19, 2023

Pulsars and Gravitational Waves ResearchPhysics and Astronomy3 citations

TL;DR

This paper systematically investigates the selection functions of convolutional neural networks (CNNs) used for strong gravitational lens finding, revealing that these models introduce significant biases toward systems with larger Einstein radii, more concentrated source light, and higher lens ellipticity—particularly for quasar-lens systems—while remaining insensitive to the lens mass profile slope. The findings highlight that neural network selection effects reinforce the intrinsic lensing cross-section bias, necessitating careful correction in upcoming wide-field surveys.

ABSTRACT

Convolution Neural Networks trained for the task of lens finding with similar architecture and training data as is commonly found in the literature are biased classifiers. An understanding of the selection function of lens finding neural networks will be key to fully realising the potential of the large samples of strong gravitational lens systems that will be found in upcoming wide-field surveys. We use three training datasets, representative of those used to train galaxy-galaxy and galaxy-quasar lens finding neural networks. The networks preferentially select systems with larger Einstein radii and larger sources with more concentrated source-light distributions. Increasing the detection significance threshold to 12$σ$ from 8$σ$ results in 50 per cent of the selected strong lens systems having Einstein radii $θ_\mathrm{E}$ $\ge$ 1.04 arcsec from $θ_\mathrm{E}$ $\ge$ 0.879 arcsec, source radii $R_S$ $\ge$ 0.194 arcsec from $R_S$ $\ge$ 0.178 arcsec and source Sérsic indices $n_{\mathrm{Sc}}^{\mathrm{S}}$ $\ge$ 2.62 from $n_{\mathrm{Sc}}^{\mathrm{S}}$ $\ge$ 2.55. The model trained to find lensed quasars shows a stronger preference for higher lens ellipticities than those trained to find lensed galaxies. The selection function is independent of the slope of the power-law of the mass profiles, hence measurements of this quantity will be unaffected. The lens finder selection function reinforces that of the lensing cross-section, and thus we expect our findings to be a general result for all galaxy-galaxy and galaxy-quasar lens finding neural networks.

Motivation & Objective

• To understand how neural network-based lens finders introduce selection biases in strong gravitational lens samples.
• To quantify the impact of training data and model architecture on the selection function of lens-finding CNNs.
• To assess whether these biases are independent of lens mass profile slope or dependent on source and lens morphology.
• To evaluate how detection significance thresholds affect the recovered lens population characteristics.
• To provide a foundation for correcting systematic biases in large-scale lens surveys using deep learning.

Proposed method

• Trained ResNet18-based CNNs on three synthetic datasets representative of galaxy-galaxy and galaxy-quasar lensing surveys.
• Simulated lensed images with controlled parameters: Einstein radius, source size, Sérsic index, lens ellipticity, and mass profile slope.
• Used a detection significance threshold of 8σ and 12σ to assess how threshold changes affect the selection of lens systems.
• Applied interpretability techniques to identify which lens and source parameters most influence the network's classification decisions.
• Compared selection functions across different training datasets to isolate the effects of source and lens morphology.
• Assessed the independence of selection bias from the lens power-law slope, a key cosmological parameter.

Experimental results

Research questions

• RQ1 How do lens-finding CNNs bias the selection of strong lens systems with respect to Einstein radius and source size?
• RQ2 What role does the lens ellipticity play in the selection function of quasar-lens versus galaxy-lens finding networks?
• RQ3 Does the selection function of CNN-based lens finders depend on the slope of the lens mass profile?
• RQ4 How do detection significance thresholds (e.g., 8σ vs. 12σ) influence the morphological characteristics of selected lens systems?
• RQ5 To what extent do training data characteristics (e.g., source light model complexity) affect the resulting selection bias?

Key findings

• Increasing the detection significance threshold from 8σ to 12σ increases the median Einstein radius of selected lenses from 0.879 arcsec to 1.04 arcsec.
• The median source radius increases from 0.178 arcsec to 0.194 arcsec, and the median Sérsic index from 2.55 to 2.62 under the same threshold increase.
• Neural networks trained to find lensed quasars show a stronger preference for higher lens ellipticity than those trained for galaxy-galaxy lenses.
• The selection function is independent of the lens mass profile power-law slope, meaning measurements of this parameter remain unbiased by the network.
• Larger Einstein radii and more concentrated source light distributions are the dominant drivers of selection, with the network favoring systems that are easier to detect visually.
• The selection bias reinforces the intrinsic lensing cross-section bias, indicating that these findings are generalizable across similar CNN-based lens finders.