# Using Convolutional Neural Networks to Search for Strongly Lensed Quasars in KiDS DR5

Zizhao He, Rui Li, Yiping Shu, Crescenzo Tortora, Xinzhong Er, Raoul Canameras, Stefan Schuldt, Nicola R Napolitano, Bharath Chowdhary N, Qihang Chen, et al.

► To cite this version:

Zizhao He, Rui Li, Yiping Shu, Crescenzo Tortora, Xinzhong Er, et al. Using Convolutional Neural Networks to Search for Strongly Lensed Quasars in KiDS DR5. The Astrophysical Journal, 2025, 981 (2), pp.168. 10.3847/1538-4357/adaf28. hal-04751894

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# Using Convolutional Neural Networks to Search for Strongly Lensed Quasars in KiDS DR5

Zizhao He<fnref n="1" />, Rui Li<fnref n="2" />, Yiping Shu<fnref n="1" />, Crescenzo Tortora<fnref n="3" />, Xinzhong Er<fnref n="4" />, Raoul Cañameras<fnref n="5" />,<fnref n="6" />,<fnref n="7" />, Stefan Schuld<fnref n="1" />,<fnref n="8" />,<fnref n="9" />, Nicola R. Napolitano<fnref n="10" />,<fnref n="11" />,<fnref n="12" />, Bharath Chowdhary N<fnref n="13" />, Qihang Chen<fnref n="14" />,<fnref n="15" />, Nan Li<fnref n="9" />,<fnref n="16" />, Haicheng Feng<fnref n="17" />, Limeng Deng<fnref n="1" />,<fnref n="18" />, Guoliang Li<fnref n="1" />, L. V. E. Koopmans<fnref n="13" />, and Andrej Dvornik<fnref n="19" />

Received 2024 September 23; revised 2024 December 11; accepted 2024 December 31; published 2025 March 6

## Abstract

Gravitationally strongly lensed quasars (SL-QSO) offer invaluable insights into cosmological and astrophysical phenomena. With the data from ongoing and next-generation surveys, thousands of SL-QSO systems can be discovered expectedly, leading to unprecedented opportunities. However, the challenge lies in identifying SL-QSO from enormous data sets with high recall and purity in an automated and efficient manner. Hence, we developed a program based on a convolutional neural network (CNN) for finding SL-QSO from large-scale surveys and applied it to the Kilo-degree Survey Data Release 5. Our approach involves three key stages: first, we preselected 10 million bright objects (with r-band MAG_AUTO < 22), excluding stars from the data set; second, we established realistic training and test sets to train and fine-tune the CNN, resulting in the identification of 4195 machine candidates, and the false-positive rate of ~1/2000 and recall of 0.8125 evaluated by using the real test set containing 16 confirmed lensed quasars; third, human inspections were performed for further selections, and then, 272 SL-QSO candidates were eventually found in total, including 16 high-score, 118 median-score, and 138 lower-score candidates, separately. Removing the systems already confirmed or identified in other papers, we end up with 229 SL-QSO candidates, including 7 high-score, 95 median-score, and 127 lower-score candidates, and the corresponding catalog is publicly available online (https://github.com/EigenHermit/H24). We have also included an excellent quad candidate in the Appendix, discovered serendipitously during the fine-tuning process of the CNN.

Unified Astronomy Thesaurus concepts: Gravitational lensing (670)

Materials only available in the online version of record: machine-readable tables

## 1. Introduction

Strongly lensed quasars serve as a crucial cosmological tool for investigating a wide range of astrophysical and cosmological phenomena. For instance, by studying the microlensing effect caused by stars in the lensing galaxies, one can uncover valuable information about the accretion disk properties of the background active galactic nuclei (AGN; T. Anguita et al. 2008; D. Sluse et al. 2011; V. Motta et al. 2012; E. Guerras

et al. 2013; L. Braibant et al. 2014; C. Fian et al. 2021; D. Hutsemékers & D. Sluse 2021). Lens modeling techniques allow researchers to constrain the distribution of luminous and dark matter within the lens galaxies (M. Oguri et al. 2014; S. H. Suyu et al. 2014; A. Sonnenfeld & M. Cautun 2021; L. Van de Vyvere et al. 2022). Additionally, by incorporating time-domain data, one can measure the time delay between the multiple images, which provides a direct measurement of the Hubble–Lemaître constant ($H_0$; S. H. Suyu et al. 2014, 2017; K. Liao et al. 2019; S. Zhu et al. 2023). This application is particularly important in addressing the recent Hubble tension (A. G. Riess et al. 2019; L. Verde et al. 2019; P. Shah et al. 2021), which refers to the discrepancy in $H_0$ values derived

<figure><img src="image_3.png" /></figure>

Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹ Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, Jiangsu, 210023, People's Republic of China; zzhe@pmo.ac.cn</footnote>

<footnote n="2">² Institute for Astrophysics, School of Physics, Zhengzhou University, Zhengzhou, 450001, People's Republic of China; liruiww@gmail.com</footnote>

<footnote n="3">³ INAF – Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, I-80131, Napoli, Italy</footnote>

<footnote n="4">⁴ Tianjin Astrophysics Center, Tianjin Normal University, Tianjin 300387, People's Republic of China</footnote>

<footnote n="5">⁵ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Straße 1, 85748 Garching, Germany</footnote>

<footnote n="6">⁶ Technical University of Munich, TUM School of Natural Sciences, Department of Physics, James-Franck-Straße 1, 85748 Garching, Germany</footnote>

<footnote n="7">⁷ Aix Marseille University, CNRS, CNES, LAM, Marseille, France</footnote>

<footnote n="8">⁸ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, I-20133 Milano, Italy</footnote>

<footnote n="9">⁹ INAF - IASF Milano, via A. Corti 12, I-20133 Milano, Italy</footnote>

<footnote n="10">¹⁰ School of Physics and Astronomy, Sun Yat-sen University, Zhuhai Campus, 2 Daxue Road, Xiangzhou District, Zhuhai, People's Republic of China</footnote>

<footnote n="11">¹¹ CSST Science Center for Guangdong-Hong Kong-Macau Great Bay Area, Zhuhai, 519082, People's Republic of China</footnote>

<footnote n="12">¹² INAF – Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, 80131 - Napoli, Italy</footnote>

<footnote n="13">¹³ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, NL-9700 AV Groningen, The Netherlands</footnote>

<footnote n="14">¹⁴ Department of Astronomy, Beijing Normal University, Beijing 100875, People's Republic of China</footnote>

<footnote n="15">¹⁵ Institute for Frontier in Astronomy and Astrophysics, Beijing Normal University, Beijing, 102206, People's Republic of China</footnote>

<footnote n="16">¹⁶ Key Laboratory of Space Astronomy and Technology, National Astronomical Observatories, CAS, Beijing 100101, People's Republic of China</footnote>

<footnote n="17">¹⁷ Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216, Yunnan, People's Republic of China</footnote>

<footnote n="18">¹⁸ School of Astronomy and Space Sciences, University of Science and Technology of China, Hefei 230026, People's Republic of China</footnote>

<footnote n="19">¹⁹ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing, 44780 Bochum, Germany</footnote>
from high and low redshift observations. A strong-lensing time delay offers an independent measurement that is not reliant on the cosmic microwave background (C. L. Bennett et al. 2013; Planck Collaboration et al. 2020) or the local distance ladder (see, e.g., A. G. Riess et al. 2016, 2018, 2019; W. Yuan et al. 2019; W. L. Freedman et al. 2019).

However, the limited number of known lensed quasars greatly restricts the ability to investigate these aforementioned topics. For instance, to achieve a 1% precision in constraining $H_0$, it is suggested that at least 40 quadruply imaged lensed quasars with wide separations and high-precision time-delay measurements are needed (A. J. Shajib et al. 2020). However, such systems are rare, with only around seven meeting these specific criteria out of the existing ~300 known lensed quasars.

The search for lensed quasars in optical imaging surveys typically involves a two-step process: candidate identification followed by spectroscopic confirmation. Photometric surveys that currently exist or are planned for the future play a pivotal role in identifying a significant number of potential candidates (J. H. H. Chan et al. 2015, 2024; C. Spiniello et al. 2018, 2019; I. T. Andika et al. 2023; C. Dawes et al. 2023; Z. He et al. 2023), which can then undergo further scrutiny for verification (e.g., C. Lemon et al. 2022). Prominent surveys such as the Kilo-degree Survey (KiDS) offer extensive sky coverage, good image quality, and depth, rendering the discovery of numerous new lensed systems feasible (C. E. Petrillo et al. 2017, 2019; R. Li et al. 2020, 2021; N. R. Napolitano et al. 2020).

A dozen lensed quasar systems have been identified in KiDS in previous efforts (C. Spiniello et al. 2018, 2019; V. Khramtsov et al. 2019). However, the number is significantly below the theoretical prediction (M. Oguri & P. J. Marshall 2010). Moreover, with the forthcoming release of KiDS DR5, it is anticipated that more systems await detection. To enhance the process of candidate identification, we implemented a machine learning technique known as convolutional neural network (CNN). Our methodology involves training the CNN using a blend of simulated and real data.

Notably, within this field, numerous studies have trained CNNs specifically for detecting galaxy–galaxy strong lenses. These endeavors have led to the discovery of thousands of lens candidates (e.g., A. Sonnenfeld et al. 2018; C. E. Petrillo et al. 2019; R. Cañamas et al. 2020; Z. He et al. 2020; X. Huang et al. 2021; R. Li et al. 2021; K. Rojas et al. 2022), subsequently validated through investigations (e.g., K.-V. H. Tran et al. 2022; A. Cikota et al. 2023; F. Dux et al. 2024). In fact, in the strong-lensing finding challenge (R. B. Metcalf et al. 2019), CNN-based methods outperformed other techniques. Moreover, this approach has been extended to the search for lensed quasars (e.g., I. T. Andika et al. 2023; F. Dux et al. 2023), albeit with fewer studies compared to galaxy–galaxy lens detection.

In this study, we further advanced this methodology by developing a CNN as a lensed quasar-finder that can achieve a very low false-positive rate (FPR) while maintaining a high true-positive rate (TPR), aimed at detecting candidates within the KiDS DR5 data set.

The paper is structured as follows. Section 2 delineates the data sets utilized or compiled for this study, encompassing both the data analyzed for identifying lensed quasar candidates and the sets employed for training and testing purposes. Section 3 elaborates on the methodologies employed, including the Network architecture (hereafter, we use the capitalized

“Network” for our specific network) and the training process of the Network. Subsequently, Section 4 presents the human inspection and the obtained results, accompanied by a detailed catalog. The selection effect of the Network of several lensing parameters is delivered in Section 5. Finally, the summary and future plans are provided in Section 6. In this paper, a fiducial cosmological model with $\Omega_m = 0.26$, $\Omega_{DE} = 0.74$, $h = 0.72$, $w_0 = -1$, and $w_a = 0$ is assumed. Unless otherwise stated, all magnitudes quoted in this paper are in the AB system.

## 2. Data Sets

Here, we present three data sets compiled for our study. First, to establish a sample conducive to identifying lensed quasar candidates, we compiled the target data set, consisting of 9,958,196 objects (Section 2.1). Second, we introduce our training and validation set, comprising a total of 26,005 positives and 27,275 negatives (Section 2.2). Of this, 60% was used for training, and 10% was used for validation. Lastly, to evaluate the Network’s performance, we utilized two test sets (Section 2.3). The simulated test set contains the remaining 30% of the 26,005 positives and 27,275 negatives and was used to test the Network’s selection effect. The other, a real test set, comprises 16 × 6 lensed quasars and 50,000 nonlensed quasars, where “×6” denotes the data augmentation applied to the lensed quasar samples. Notably, we used gri three-band fits data as the input data for the Network.

### 2.1. Target Data Set

KiDS (J. T. A. de Jong et al. 2013) is a publicly available survey conducted by the European Southern Observatory. It utilizes five optical broadband filters: u, g, r, $i_1$, and $i_2$ using the Very Large Telescope Survey Telescope (M. Capaccioli & P. Schipani 2011). The near-infrared (NIR) data from KiDS is supplemented by data from the VISTA Kilo-Degree Infrared Galaxy Survey (A. Edge et al. 2013), which has completed observations in five NIR bands (Z, Y, J, H, and $K_s$) within the same sky region. The last data release, KiDS DR5 (A. H. Wright et al. 2024), includes all the survey tiles, totaling 1347 deg$^2$. The typical limiting magnitudes in each band ($u$, $g$, $r$, $i_1$, $i_2$, Z, Y, J, H, and $K_s$) are as follows: 24.17, 24.96, 24.79, 23.41, 23.49, 23.47, 22.72, 22.53, 21.94, and 21.75 (5σ in 2" aperture, A. H. Wright et al. 2024).

We defined the data set for analysis based on the KiDS DR5 catalogs and images (A. H. Wright et al. 2024), incorporating the star–quasar–galaxy classification from H.-C. Feng et al. (2024). In H.-C. Feng et al. (2024), probabilities $p_{Star}$, $p_{Galaxy}$, and $p_{QSO}$ represent the likelihood of a source being a star, galaxy, or quasar, respectively, derived using machine learning techniques that leverage both morphological and photometric information. This method achieved an impressive overall classification accuracy of 98.76% for objects with r-band $MAG\_AUTO < 22$.

The catalog from A. H. Wright et al. (2024) was subjected to the following selection criteria. First, we considered only sources with an r-band $MAG\_AUTO < 22$, as the star–quasar classification in H.-C. Feng et al. (2024) has higher uncertainty beyond this threshold. A similar cutoff was employed in V. Khramtsov et al. (2019). Second, we selected sources where $p_{Star}$ was the lowest of the three probabilities. Specifically, for stars, the method demonstrated a purity of 98.5% and a completeness of 98.62%, confirming its effectiveness in
accurately identifying and excluding stars. Additionally, our analysis was limited to sources with detections in all three bands: g, r, and i. After applying these selection criteria, we identified 9,958,196 relevant sources out of an initial 65,907,702.

In parallel to the aforementioned target data set, we identified 191,321 luminous red galaxies (LRGs) out of the 65,907,702 total sources, using the selection criteria outlined in Equations (1) and (2) in R. Li et al. (2021). This selection methodology aligns with that used in C. E. Petrillo et al. (2017), Z. He et al. (2020), and R. Li et al. (2020). Many studies that focus on searching for lensed galaxies use LRGs as their primary target data set, but this is not suitable for our purposes. The reason is that, according to images of spectroscopically confirmed lensed quasars, the lensing galaxies are invisible before the subtraction of quasar images in many systems (such as J0907+0003 and J1037+0018). These systems will not be selected when performing LRG selection. Nevertheless, a significant majority of the LRGs (191,101 out of 191,321) were already included within our target data set.

## 2.2. Training and Validation Sets

Our previous experience (e.g., Z. He et al. 2020; R. Li et al. 2021; R. Cañamas et al. 2023), as well as results from other researchers (e.g., X. Huang et al. 2021), indicates that the training set significantly influences the performance of the classifier. Thus, we concentrated on creating a realistic training set.

Furthermore, we decided to generate training sets only with very obvious strong-lensing features under KiDS observational conditions. Because of the seeing, we cannot identify systems with small separations or ambiguous multiple images. Consequently, some lensed quasars were inevitably missed under the current methodology and observational conditions. We anticipate using next-generation data sets such as the China Space Station Telescope (CSST; H. Zhan 2021), Euclid (R. Laureijs et al. 2011; Euclid Collaboration et al. 2024), and Roman (T. Eifler et al. 2021) to enhance observational capacity for those lensed quasars missed at this stage.

More specifically, we generated the positive part of the training set by combining real LRGs (see Section 2.1) and mock lensed multiple images (C. E. Petrillo et al. 2017; R. Li et al. 2020, 2021; Z. He et al. 2020; I. T. Andika et al. 2023; B. C. Nagam et al. 2023). We selected 10,000 LRGs from a sample of 191,321 LRGs through visual inspection, choosing those with typical LRG morphology and without lensing features at random. We then estimated their velocity dispersion ($\sigma_v$) using the fundamental plane (FP) of elliptical galaxies.

$$ \log_{10} R_e = a_r \log_{10} \sigma_v + b_r \mu_r + c_r, \quad (1) $$

where the index r indicates that we used FP in r band and $a_r = 1.207$, $b_r = 0.315$, $c_r = -8.463$ (Y. Yoon & C. Park 2020). Furthermore, $\mu_r$ is given by

$$ \mu_r = m_r + 5 \log_{10} r_{e,r} + 2.5 \log_{10} 2\pi - 2.5 \log_{10}(1 + z_d)^3, \quad (2) $$

where $R_e$ is the physical half-light radius in the unit of kiloparsecs, while $r_e$ is in arcseconds. In this study, the redshifts of lensing LRG and background quasars were obtained by GaZNet (R. Li et al. 2022a). It is a CNN, which determines the redshift by using both morphological and

photometric information. Similarly, $r_e$ was obtained using the methodologies described in R. Li et al. (2022b), which is a CNN that can determine the parameters of the Sérsic profile.

After obtaining the velocity dispersion, we employed the singular isothermal ellipsoid (SIE; R. Kormann et al. 1994) profile to generate multiple images. The convergence of SIE is given by

$$ \kappa(x, y) = \frac{\theta_E}{2} \frac{1}{\sqrt{qx^2 + y^2/q}}, \quad (3) $$

where q is the axial ratio between the minor and major axes, which is assumed to be the same in the mock of the light distribution of lensing galaxy and its host halo; x, y are the coordinates in the lens plane. We assume the $\sigma_v$ estimated by Equation (1) is a good estimation of $\sigma_v$ of SIE halo; this is supported by previous works such as A. S. Bolton et al. (2008). Moreover, $\theta_E$ is the Einstein radius:

$$ \theta_E = 4\pi \left( \frac{\sigma_v}{c} \right)^2 \frac{D_{ds}}{D_s}, \quad (4) $$

where $D_{ds}$ is the angular diameter distance between lens and source while $D_d$ is the angular diameter distance between lens and the observer.

Utilizing these models and placing the pointlike source randomly in the source plane, we can calculate the positions and magnifications of the multiple images ($\mu_i$, where i represents the ith image). As background sources, we selected samples with a $p_{QSO}$ value greater than 0.9. There are 499,027 objects that satisfy this condition. The fluxes of the multiple images in gri bands are given by $\mu_i f_i$, where $f_i$ denotes the un lensed fluxes of the background sources in the simulated band. We used the methodologies outlined in R. Li et al. (2022a) to derive $z_{GaZ}$ of quasars, which are used to represent $z_s$.

We repeated these operations (randomly selecting the LRG and placing the quasar in the source plane) 1 million times. Consequently, the fluxes and positions of the multiple images were acquired and recorded into a catalog containing 1 million entries. We then applied selection criteria to isolate those with obvious strong-lensing features. The criteria are as follows: first, the Einstein radius ($\theta_E$) must be greater than 0.6, which is roughly the best FWHM of r-band seeing; second, the flux ratio between the brightest image and the foreground LRG must exceed 1. Here, we used the total fluxes of quasars and LRGs in the calculation. After applying these filters, a subset of 26,005 out of 1 million entries was selected. As a result, the mock lenses are generated, with six examples shown in Figure 1. The distributions of the mock lensed quasars in the training sample are shown in Figure 2, including the lens and source redshifts, the flux ratio between the brightest and second brightest image, the separation, and the magnitudes of the sources and lens. Moreover, the median $\sigma_v$ is 222.80 km s$^{-1}$, with a standard deviation of 42.92 km s$^{-1}$; the quad to pair ratio is approximately 1: 1.67.

Based on these selected samples, we generated high-resolution (0.05 pixel$^{-1}$) ideal lensed images in gri bands. We applied point-spread functions (PSFs) to the ideal image plane, assuming the PSF follows the Moffat distribution:

$$ I(r) = I_0 \left( 1 + \left( \frac{r}{\alpha} \right)^2 \right)^{-\beta} \quad (5) $$
<figure><img src="image_4.png" /><figcaption>Figure 1. Examples of the training samples used in this work, presented as gri three-band composite images. The left panel shows the mock lensed quasars (positives), while the right panel displays the nonlensed objects (negatives). Each cutout image has a size of 10" × 10".</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 2. Properties of the mock strong gravitational lensing systems in the training samples. Upper left panel: the i-band apparent magnitude distributions for the lens galaxies, background quasars, and brightest lensed images, respectively. Upper right panel: The maximum angular separations between the multiple lensed images. Note that the separation range is truncated at 3" in this plot. Lower left panel: the redshift distributions for the lens galaxies and background quasars. Lower right panel: the flux ratio between the brightest and second brightest lensed images.</figcaption></figure>

$I(r)$ is the intensity at a distance $r$ from the center of the distribution. $\alpha$ is the scale parameter related to the width of the distribution, and $\beta$ is the shape parameter, which determines the “heaviness” of the tails. Here, we fix $\beta$ at

2.2. Furthermore,

$$ \alpha = \frac{\text{FWHM}}{2 \cdot \sqrt{2\beta - 1}}. \qquad (6) $$
<table><caption>**Table 1**
The PSF Settings Used to Generate Mock Lensed Quasars for the Training and Validation Sets of the Network</caption><thead><tr><th>Parameter</th><th>Range</th><th>Units</th><th>Distribution</th></tr></thead><tbody><tr><td>FWHM-g</td><td>0.6-1.2</td><td>arcsec</td><td>normal (μ = 0.85, σ = 0.1)</td></tr><tr><td>FWHM-r</td><td>0.50-0.90</td><td>arcsec</td><td>normal (μ = 0.7, σ = 0.05)</td></tr><tr><td>FWHM-i</td><td>0.55-1.2</td><td>arcsec</td><td>normal (μ = 0.80, σ = 0.1)</td></tr><tr><td>β</td><td>2.20</td><td>...</td><td>fixed</td></tr><tr><td>Axis ratio</td><td>0.98-1.0</td><td>...</td><td>uniform</td></tr><tr><td>Position angle</td><td>0-180</td><td>degree</td><td>uniform</td></tr></tbody></table>

Note. Refer to Equations (5) and (6), as well as the relevant discussion, for the interpretation of the listed parameters. The distribution aligns with the realistic distribution in KiDS DR4 (K. Kuijken et al. 2019) and is consistent with those used in R. Li et al. (2021).

The detailed settings of the PSF are summarized in Table 1. Consequently, we reduced the resolution of our mock data to align with the KiDS observational conditions (0.2 pixel⁻¹).

We subsequently incorporated Poisson noise based on the low-resolution mocks of multiply imaged quasars. The noise value *x* obeys the Poisson distribution:

$$f(x) = \frac{\lambda^x}{x!}e^{-\lambda}, \qquad (7)$$

where λ is the ADU at a certain pixel position of the noiseless image. The ADUs can be calculated by Gain * Flux * Exp_time, where Gain, a factor that converts the number of electrons into the number of ADUs, can be obtained from the FITS header file of KiDS observation images. The exposure time varies across different bands<fnref n="20" /> (1800 s for the *r* band, 900 s for the *g* band, and 1200 s for the *i* band). Note that the Poisson noise was not added to the lensing galaxy, since their images were taken from observations and the noise already included.

For the negative part of the training set, we randomly selected objects in the predictive data set, ensuring that no known lenses were included in this process. To balance the negative samples with the positive ones, we made the volume of each set approximately the same. Thus, 27,275 negative examples were selected.

In summary, we constructed the training and validation sets by focusing on the portion of the mock catalog that exhibits the most distinct strong-lensing features of lensed quasars. In total, we created 26,005 mock lensed quasars as the positive set, complemented by 27,275 real nonlenses as the negative set. We allocated 60% of these data sets for training the Network, 10% for validation purposes, and reserved the remaining 30% for testing the selection effect of the Network (named as simulated testing set).

## 2.3. Testing Set

To evaluate the efficacy of our classifier, we created two testing data sets incorporating both positive and negative instances. The first data set, referred to as the simulated testing data, was introduced in Section 2.2; the second data set, named the real test set, included negatives directly sourced from the target data set and positives from known lensed quasars with applied data augmentation.

For the real test set, the negative subset comprised 50,000 samples randomly drawn from the target data, with rigorous visual scrutiny confirming the absence of any strong-lensing features. The positive subset was identified by crossmatching the target data with the SLED database,<fnref n="21" /> resulting in 22 known lensed quasars and lensed compact galaxies. Figure 3 displays all the cutouts from our crossmatching, while Table 2 lists the names of these lensing systems alongside their respective references. Notably, we used the lensed quasars as our positive subset, excluding lensed galaxies due to their more extended nature (J1244+0106, J2329-3409) or significantly different color (J1224+0050) compared to lensed quasars. Additionally, three systems (J1359+0129, J2201+3201, J2218-3322) with atypical image features in KiDS imaging were eliminated. Thus, 6 out of the 22 strong lenses were excluded, leaving 16 systems for the test set. These 16 systems underwent the following data augmentation process to better evaluate performance.

Each image in the real test set was subjected to a series of transformations, including vertical flipping, horizontal flipping, diagonal flipping, and random rotation within the range of 0°–360° (applied twice). Consequently, each image was enhanced through five repetitions of these operations, with the fourth operation applied twice. This process increased the data set’s volume sixfold, encompassing both the original images and their augmented counterparts. As a result, we constructed a test set comprising 50,000 negatives and 96 positives (16 original positives augmented sixfold). Notably, in this work, the data augmentation process was only used in the real test set and not applied during the training process.

## 3. Methodology

In Section 3.1, we present the Network architecture and elaborate on its evaluation metrics. Using the aforementioned training and test sets (Sections 2.2 and 2.3), the Network was trained, and the Network parameters are fine-tuned to achieve the best performance in the real test set. This is detailed in Section 3.2.

### 3.1. Network and Evaluation Metric

We used a ResNet-18 (K. He et al. 2016) as our classifier. This Network has been adopted by plenty of lens-finding works (e.g., F. Lanusse et al. 2018; R. Li et al. 2020, 2021; X. Huang et al. 2021). The inputted data are three-band *gri* fits with a square root applied to it; the normalization is applied in each band separately. The shape of the inputted data is 50 pixel × 50 pixel × 3 channels. The Network was trained from scratch, with no pretraining process applied. The detailed Network architecture can be found at this link.<fnref n="22" />

Classic metrics were used for evaluating the performance of Networks. First, the TPR (or recall) is defined by

$$TPR = \frac{TP}{TP + FN}, \qquad (8)$$

where TP represents the lensed quasars correctly picked out by the classifier. *FN* represents the lensed quasars mistakenly classified by the Network. Thus, *TP*+*FN* is the overall number

<footnote n="20">²⁰ https://kids.strw.leidenuniv.nl/DR4/index.php</footnote>

<footnote n="21">²¹ C. Lemon, private communication; SLED (Vernardos et al. 2025, in preparation).</footnote>

<footnote n="22">²² https://github.com/EigenHermit/H24/blob/main/Network-structure</footnote>
<figure><img src="image_6.png" /><figcaption>Figure 3. The confirmed lensed quasars and lensed compact galaxies in KiDS footprint. The ones marked by red frames were not included in the test set. The ones marked by yellow frames were missed by the Network. The cutout size is 8.8 × 8.8. The detailed information is given in Table 2. Left is east; up is north.</figcaption></figure>

of lensed quasars that exist in the testing data set. TPR measures how well the classifier can recover the lensed quasars. Second, the FPR is defined by

$$FPR = \frac{FP}{TN + FP}, \qquad (9)$$

where FP means the nonlensed quasars incorrectly labeled as lensed quasars by the Network, and TN represents the nonlensed quasars correctly labeled. Last but not least, the accuracy measures the overall performance of our classifier:

$$accuracy = \frac{TP + TN}{TP + FP + TN + FN}, \qquad (10)$$

Furthermore, the receiver operating characteristic (ROC) curve was also adopted in this work to measure the capacity of the Network when choosing different thresholds ($p_{th}$) of the Networks. The x, y-axes of the ROC curve are TPR and FPR. The data points on the curve represent the Network's TPR and FPR when choosing different thresholds of the Networks.

## 3.2. Training and Testing of the Network

With the training and validation sets obtained in Section 2.2 and the Network described in Section 3.1, we proceeded to train the Network. The training loss was computed on the training set, while the validation loss was computed on the validation set. Subsequently, we fine-tuned the number of epochs ($ep$) and learning rate ($lr$) based on two key criteria.

First, it is crucial for both the training loss and validation loss to converge at a similar pace. Second, we assessed the Network's performance on the real test set, focusing particularly on the TPR at an FPR of approximately 1/2000. We chose this FPR because, given the volume size of the data to be applied (approximately 10 million), an FPR of around 1/2000 corresponds to a candidate size of roughly 5000, which we found suitable for subsequent human inspection. The Network's performance under the tested parameters is depicted in Figure 4. If not labeled in the figure, the $ep$ was set to 200. Notably, when trained with longer epochs, the TPR at 1/2000 shows a decrease; see the $ep$ = 300 and $ep$ = 400 lines for this result, which may be contributed by the overfitting.

Upon evaluation, setting save_best = True ensures that the training program continuously saves the model with the lowest validation loss as the final model, rather than relying on the model from the last epoch. The optimal parameters identified were a learning rate of $1 \times 10^{-7}$ and a total of 186 epochs. The loss value for this Network is illustrated in Figure 5. With these settings, the achieved TPR is 0.8125, using a threshold of $p_{th}$ = 0.94. This threshold will be used in subsequent stages of the application process. It is important to note that the limited number of known lensed quasars in the real test set introduces Poisson noise into the evaluation, despite the application of data augmentation. Nevertheless, performance with real data is preferable to that obtained from a simulated test set, as the Network tends to perform exceptionally well on simulated data. Additionally, results based on real data are more meaningful
<table><caption>**Table 2**
The Detailed Information of the Cutouts in Figure 3 Is Provided above</caption><thead><tr><th>Name</th><th>R.A. (J2000)</th><th>Decl. (J2000)</th><th>Image Separation (arcsec)</th><th>z<sub>s</sub></th><th>z<sub>d</sub></th><th>n<sub>img</sub></th><th>Rediscovered</th><th>In Testing Set</th><th>References</th></tr></thead><tbody><tr><td>J0030-3358</td><td>7.674</td><td>-33.9767</td><td>2.03</td><td>1.58</td><td>0.715</td><td>2</td><td>Y</td><td>Y</td><td>X. Huang et al. (2021); C. Lemon et al. (2023)</td></tr><tr><td>J0156-2751</td><td>29.1039</td><td>-27.8562</td><td>1.5</td><td>2.97</td><td>...</td><td>2</td><td>Y</td><td>Y</td><td>C. Dawes et al. (2023); Z. He et al. (2023); C. Lemon et al. (2023)</td></tr><tr><td>J0907+0003</td><td>136.7937</td><td>0.0559</td><td>1.32</td><td>1.299</td><td>...</td><td>2</td><td>Y</td><td>Y</td><td>C. Spiniello et al. (2019)</td></tr><tr><td>SDSSJ0924+0219</td><td>141.23246</td><td>2.32358</td><td>1.34</td><td>1.685</td><td>0.393</td><td>4</td><td>Y</td><td>Y</td><td>N. Inada et al. (2003)</td></tr><tr><td>CXCOJ100201.50 +020330.0</td><td>150.5063</td><td>2.0581</td><td>0.85</td><td>2.016</td><td>0.439</td><td>2</td><td>N</td><td>Y</td><td>A. T. Jaelani et al. (2021)</td></tr><tr><td>J1037+0018</td><td>159.3665</td><td>0.3057</td><td>1.25</td><td>2.462</td><td>...</td><td>2</td><td>Y</td><td>Y</td><td>C. Lemon et al. (2022)</td></tr><tr><td>KIDS1042+0023</td><td>160.6553</td><td>0.3839</td><td>1.45</td><td>2.26</td><td>...</td><td>2</td><td>Y</td><td>Y</td><td>C. Spiniello et al. (2019)</td></tr><tr><td>SDSSJ1138+0314</td><td>174.51554</td><td>3.24939</td><td>1.44</td><td>2.438</td><td>0.445</td><td>4</td><td>Y</td><td>Y</td><td>N. Inada et al. (2008)</td></tr><tr><td>J1224+0500</td><td>186.233403</td><td>0.846681</td><td>...</td><td>1.10</td><td>0.2372</td><td>4</td><td>Y</td><td>N</td><td>N. R. Napolitano et al. (2020)</td></tr><tr><td>SDSSJ1226-0006</td><td>186.5334</td><td>-0.10061</td><td>1.21</td><td>1.125</td><td>...</td><td>2</td><td>Y</td><td>Y</td><td>N. Inada et al. (2008); Z. He et al. (2023)</td></tr><tr><td>J1233-0227</td><td>188.4219</td><td>-2.4604</td><td>1.76</td><td>1.598</td><td>0.345</td><td>2</td><td>Y</td><td>Y</td><td>C. Dawes et al. (2023); C. Lemon et al. (2023)</td></tr><tr><td>J1244+0106</td><td>191.21402</td><td>1.111979</td><td>...</td><td>1.069</td><td>0.388</td><td>4</td><td>Y</td><td>N</td><td>D. P. Stark et al. (2013)</td></tr><tr><td>SDSSJ1332+0347</td><td>203.09425</td><td>3.79442</td><td>0.99</td><td>1.685</td><td>0.191</td><td>2</td><td>Y</td><td>Y</td><td>T. Morokuma et al. (2007)</td></tr><tr><td>J1335+0118</td><td>203.894979</td><td>1.301553</td><td>1.62</td><td>1.57</td><td>0.44</td><td>2</td><td>Y</td><td>Y</td><td>N. Inada et al. (2008)</td></tr><tr><td>J1359+0129</td><td>209.9332</td><td>1.47053</td><td>1.05</td><td>1.096</td><td>...</td><td>2</td><td>N</td><td>N</td><td>V. Khramtsov et al. (2019)</td></tr><tr><td>SDSSJ1458-0202</td><td>224.6982</td><td>-2.03497</td><td>2.15</td><td>1.724</td><td>...</td><td>2</td><td>N</td><td>Y</td><td>A. More et al. (2016)</td></tr><tr><td>ULASJ1527+0141</td><td>231.8338</td><td>1.69433</td><td>2.55</td><td>1.439</td><td>0.3</td><td>2</td><td>Y</td><td>Y</td><td>N. Jackson et al. (2012)</td></tr><tr><td>CY2201-3201</td><td>330.38667</td><td>-32.02889</td><td>0.83</td><td>3.9</td><td>0.32</td><td>2</td><td>N</td><td>N</td><td>F. J. Castander et al. (2006)</td></tr><tr><td>J221849.86-332243.6</td><td>334.7075</td><td>-33.3787</td><td>0.6</td><td>2</td><td>...</td><td>4</td><td>N</td><td>N</td><td>Y.-C. Chen et al. (2022)</td></tr><tr><td>KIDS2307-3039</td><td>346.8287</td><td>-30.6547</td><td>...</td><td>2.64</td><td>0.46</td><td>2</td><td>Y</td><td>Y</td><td>C. Spiniello et al. (2019)</td></tr><tr><td>J2329-3409</td><td>352.417763</td><td>-34.156397</td><td>...</td><td>1.59</td><td>0.3810</td><td>4</td><td>Y</td><td>N</td><td>N. R. Napolitano et al. (2020)</td></tr><tr><td>WISE 2344-3056</td><td>356.0708</td><td>-30.9405</td><td>...</td><td>2.18</td><td>1.298</td><td>4</td><td>N</td><td>Y</td><td>P. L. Schechter et al. (2017)</td></tr></tbody></table>

Note. J1224+0500, J1244+0106, and J2329-3409 are lensed galaxies. “Rediscovered” indicates whether this system had earned a *p*<sub>CNN</sub> larger than the threshold of 0.94. “In Testing Set” indicates whether this system was used in the test set, denoted by “Y” for yes and “N” for no.

(This table is available in machine-readable form in the online article.)

due to potential discrepancies between actual lensed quasars and their simulated counterparts.

During the fine-tuning process, we serendipitously encountered a nice quad candidate, which is detailed in the Appendix.

## 4. Results

We applied the best-performance Network (Section 3.2) to the target data set (Section 2.1). The Network identified 4,195 candidates assuming a $p_{th} = 0.94$. Following this, the first author Z.H. inspected them, discerning and eliminating 1,057 highly improbable objects, including clearly bright stars, extended objects, leaving us with the remaining candidates undergoing thorough human scrutiny involving 10 individuals (Section 4.1). Finally, the final candidates are selected and categorized into high-, median-, lower-score candidates (Section 4.2) based on their average scores received in the human inspection process. We also compared our results with other candidate lists in SLED.

### 4.1. Human Inspection

Ten authors were involved in the scoring process, which contained three rounds. The adopted scheme is as follows:

1. *Score 3.* The object has clear multiple pointlike images and a central galaxy, and a lens model can easily reproduce their configuration.

2. *Score 2.* Case 1 includes clear multiple pointlike (with similar color) images but without a clear central galaxy. Case 2 includes multiple pointlike images and a central galaxy, but the configuration is atypical.

3. *Score 1.* Case 1 is likely to be multiple pointlike images without a clear central galaxy, while the color is less similar (compared to the color similarity of Case 1 in “Score 2”). Case 2 has a clear central elliptical galaxy and one pointlike source located near the galaxy but lacking other counter images.

4. *Score 0.* For Case 1, the color of two pointlike sources differs largely, or they are located distantly. Case 2 includes everything else (like bright stars, disk galaxies, mergers, artifacts, etc.).

In the first round, or the calibration round, 200 common objects, including 12 known lensed quasars and 4 lensed compact galaxies that were successfully rediscovered by the Network (see Figure 3), were graded by 10 authors. We used $S_{av}$ to denote the average scores an object received, and $var(S_{av})$ to denote the variance of $S_{av}$. When the systems received different opinions (the $var(S_{av}) > 0.8$) and the
<figure><img src="image_7.png" /><figcaption>**Figure 4.** The figure shows the fine-tuning process of Network. “lr” represents the learning rate; “ep” stands for the total number of epochs that were used in the training processes. The blue solid vertical line shows the FPR equals 1/2000.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 5.** Loss value evaluated on the training and validation samples respectively. We set the save_best = True, which means the model with lowest validation loss will be saved, rather than the model from the last epoch. Thus, the epoch = 186 model was used. See more discussion in Section 3.2.</figcaption></figure>

confirmed systems received at least one zero score, they were discussed to cross-calibrate our grading criteria and then achieve a consensus of the grading criteria for the second and third round grading. Final adopted criteria have been listed above. Here, we choose 0.8 to select the most controversial candidates and control the sample size that we need to discuss.

For the second round, the 3172 candidates were evenly distributed among the authors. Each member scored 386 candidates, which contains ~69 systems from 200 objects that were already inspected in the first round to check the consistency.

In Figure 6, we compare the distribution of S<sub>av</sub> for the 200 common objects with the first-round results. For objects that

<figure><img src="image_9.png" /><figcaption>**Figure 6.** The S<sub>av</sub> vs. average variance of S<sub>av</sub> in respective bin of 200 common objects; the bin size is 0.5. Those objects were used to check the consistency of inspectors in the first and second rounds of human grading.</figcaption></figure>

are clearly nonlenses, with low S<sub>av</sub>, the inspectors agree, and the scatter in the scores is small (around 0.2). Similarly, for the most obvious lenses, with high S<sub>av</sub>, all inspectors tend to agree, and the scatter is again small, around 0.1–0.2. A different story emerges for the remaining inspected objects, those around a score of 1, which are more uncertain and show greater variability in the inspectors’ decisions.

Overall, we observe that the var(S<sub>av</sub>) is reduced in this round. We then recorded the scores for each candidate, and for the 200 systems that received multiple scores, we calculate the average scores. Based on these (average) scores, we eliminate the objects that received a zero score. This resulted in the rejection of 1297 candidates.

In the third round, the remaining 1,879 objects were evenly distributed to the 10 inspectors, with each member responsible for inspecting 374 or 376 objects. Combining the grades from the second and third rounds, each of the 1,879 objects received at least three ratings.

After the inspection process, the S<sub>av</sub> for each object was determined. The interval selections were established with reference to Y. Shu et al. (2022). Objects scoring between [2.33, 3] were designated as high-score candidates. Those scoring between [1.67, 2.33] were categorized as median-score candidates, while objects with S<sub>av</sub> between [1.33, 1.67] were classified as lower-score candidates. Any S<sub>av</sub> below 1.33 resulted in the candidate being disqualified. Among the 12 known lensed quasars and 4 lensed compact galaxies that underwent human inspection, 8 were classified as high-score systems, while the remaining 8 were classified as median-score systems. The average score of the 16 systems is 2.44.

It is worth noting that we decided not to use the Grade A, B, and C classifications commonly employed in galaxy–galaxy lensing studies. This is because, when identifying strongly lensed quasars candidates, it is challenging to eliminate star contaminants in the candidates, especially in doubles. In contrast, in the case of lensed galaxies, the distorted galaxies are easier to distinguish from other possible contaminants, such as ring galaxies and mergers.
<caption>Table 3</caption>

Descriptions of the Properties Provided for Each Lensed Quasar Candidate in Our Final Catalog

<table><thead><tr><th colspan="2">All Candidates</th></tr><tr><td colspan="2">This Catalog Contains Candidates Identified in This Work</td></tr><tr><th>Columns</th><th>Description</th></tr></thead><tbody><tr><td>Name</td><td>Name of this system, generated automatically by its R. A., decl.</td></tr><tr><td>R.A.</td><td>R.A. (J2000)</td></tr><tr><td>Decl.</td><td>decl. (J2000)</td></tr><tr><td>Grade</td><td>Grades of lensed quasar candidates (high, median, lower scores)</td></tr><tr><td>n<sub>img</sub></td><td>Number of images</td></tr><tr><td>Separation</td><td>The image (maximum) separation of this system</td></tr><tr><td>SLED label</td><td>Crossmatch label from with SLED database</td></tr><tr><td></td><td>There are three kinds of labels: confirmed, contaminant, or candidates.</td></tr><tr><td>References</td><td>Relevant references for this system</td></tr><tr><td>S<sub>av</sub></td><td>The average score received in human inspection</td></tr><tr><td>p<sub>Network</sub></td><td>The probability given by the Network</td></tr><tr><td>isKnownLenses</td><td>Whether this object exists in Table 2</td></tr></tbody></table>

Note. The catalog contains new candidates and includes rediscovered confirmed systems. The full catalog is available online (see https://github.com/EigenHermit/H24).

(This table is available in its entirety in machine-readable form in the online article.)

## 4.2. Final Candidates

Following the human inspection process outlined in Section 4.1, we find 272 candidates that have received a score higher than 1.33; thus, they were selected by our study.

To illustrate them, we build two catalogs. The first one provides a comprehensive overview of the catalog's contents, including the following information: R.A., decl., grade by human inspection, number of images, maximum separation, SLED crossmatching results, the average scores from human inspection, and a flag indicating whether the system is in the test set. The detailed explanations about those columns can be found at Table 3. On the other hand, Table 4 offers a more detailed breakdown of each image. This detailed table includes the R.A. and decl. of each image, spectroscopic redshifts and their sources, astrometric information such as PM\_SIG and PLX\_SIG, the *u*, *g*, *r*, and *i* magnitudes provided by KiDS, and the *photo-z* of each image as determined by GaZNet (R. Li et al. 2022a).

According to the classification standards defined in Section 4.1, our catalog includes 16 high-score candidates, 118 median-score candidates, and 138 lower-score candidates. After excluding systems confirmed through spectroscopy, the revised counts are 8 high-score, 110 median-score, and 138 lower-score candidates. The color images of these candidates are presented in Figures 7, 8, and 9. Median-score and lower-score candidates will undergo PSF subtraction to determine if any lensing galaxies are visible, which is crucial for further assessing their potential as lenses. The results will be presented in a separate publication.

Crossmatching with SLED revealed that some candidates and contaminants had been previously reported. Candidates that were reported earlier without further spectroscopic confirmation are highlighted with white frames, while systems that have undergone spectroscopic observation and were

<caption>Table 4</caption>

Descriptions of the Properties Given for Each Image of Each Candidate Lensed Quasar in the Detailed Catalog

<table><thead><tr><th colspan="2">Candidates in Detail</th></tr><tr><td colspan="2">This Catalog Describes Every Image of Each Candidate</td></tr><tr><th>Columns</th><th>Description</th></tr></thead><tbody><tr><td>Name</td><td>Name of this candidate system that this image belongs to</td></tr><tr><td>R.A.</td><td>R.A. (J2000) of the center of this image</td></tr><tr><td>Decl.</td><td>decl. (J2000) of the center of this image</td></tr><tr><td>specz</td><td>Spectroscopy redshift from public available data sets</td></tr><tr><td>specz_cite</td><td>Sources of "specz" of this object from SLED database</td></tr><tr><td>PM\_SIG</td><td>Proper-motion significance defined in C. A. Lemon et al. (2018)</td></tr><tr><td>PLX\_SIG</td><td>Parallax motion significance defined in C. A. Lemon et al. (2018)</td></tr><tr><td>u</td><td>u-band magnitude of this image</td></tr><tr><td>g</td><td>g-band magnitude of this image</td></tr><tr><td>r</td><td>r-band magnitude of this image</td></tr><tr><td>i</td><td>i-band magnitude of this image</td></tr><tr><td>photo-z</td><td>The quasar machine learning redshift obtained using GaZNet (R. Li et al. 2022a)</td></tr></tbody></table>

Note. The full catalog is available online (see https://github.com/EigenHermit/H24).

(This table is available in its entirety in machine-readable form in the online article.)

confirmed as nonlenses are marked with orange frames. After excluding these candidates and contaminants, the final counts are as follows: 7 high-score candidates, 95 median-score candidates, and 127 lower-score candidates, resulting in a total of 229 candidates. Specifically, the high-score candidates have only one overlap, which has not yet been subjected to spectroscopic observation. The median-score candidates exhibit 15 overlaps with SLED, of which 7 are contaminants, yielding a contaminant rate of approximately 47%. For the lower-score candidates, there are 11 overlaps, with 8 identified as contaminants, resulting in a contaminant rate of roughly 73%. This suggests that the purity of the median-score candidate list is higher than that of the lower-score candidates, although the statistics are affected by significant Poisson noise due to the small number of overlaps. More precise purity assessments can be made once spectroscopic observations are conducted.

We found that 40 out of 272 systems have at least one spectroscopic redshift detection by other spectroscopic surveys like Sloan Digital Sky Survey (SDSS; M. R. Blanton et al. 2017) and Dark Energy Spectroscopic Instrument Early Data Release (DESI Collaboration et al. 2024) and targeted observations like those from C. Lemon et al. (2022). In the final catalog, these redshifts are recorded in the "specz" column, with the sources of the spectroscopic redshifts indicated in the "cite_z" column (Table 4).

In Figure 10, we show the distributions of various parameters: the quasar spectroscopy redshift of 40 systems that have spectroscopic detections, *i*-band magnitudes, image (maximum) separation (*sep*), and *g* − *r* versus *r* − *i*. Note that the *i*-band magnitudes and *g* − *r* versus *r* − *i* plots pertain to the quasar images, excluding the lensing galaxies.

The 272 candidate lensed quasars in the study span a redshift range of [0.422, 3.57], with a peak around 1.5. Their *i*-band apparent magnitudes range from $16 \le i \le 22$, with a peak around *i* ~ 20. This distribution reveals that the luminosity distribution of the quasars in this work deviates from the
<figure><img src="image_10.png" /><figcaption>**Figure 7.** Cutouts of the identified high-score systems (excluding confirmed lenses, which are displayed in Figure 3) are presented here. The left side represents east, while the top indicates north. A white frame signifies that the system has been identified in other studies, as detailed in Table 3, under the column labeled SLED\_xmatch. Each cutout measures 8.8 × 8.8 arcsec².</figcaption></figure>

power-law trend given by M. Oguri & P. J. Marshall (2010) around $i=20$, indicating that the method tends to select samples at lower redshifts (<2.0) and misses high-redshift lensed quasars. This is likely due to the training sample being dominated by lower redshift quasars, as shown in Figure 2. Furthermore, the spectroscopic redshifts are primarily from SDSS, which is limited by its own selection effects.

The image (maximum) separation ranges from $0.8 \le sep \le 2.75$, peaking at approximately $1.5$. This is largely due to the training sample setting, in which sep peaks at $1.3$. The $g-r$ versus $r-i$ color–color plot shown in Figure 10 reveals that high-score candidates are more consistent with known lensed quasars, while the ones circled by the pink circle have a higher risk of being star contamination.

According to M. Oguri & P. J. Marshall (2010), by selecting an $i$-band limit magnitude of 23.6 and considering the 1,347 deg² survey area of KiDS DR5, approximately 170 lensed quasars are expected to be found within KiDS DR5, with a predicted quad-to-pair ratio of about 1/6. Previous studies have identified 19 lensed quasars, suggesting that around 151 systems are still yet to be discovered. In our study, we identified 229 new candidates that can contribute to the pool. As shown in Figure 10, our sample is expected to contribute significantly to the $i$-band magnitude range of 20–21.

Taking both the rediscovered lenses and candidates into consideration, our findings reveal a quad-to-pair ratio of 1/66, significantly lower than the ratio in the training set, which is approximately 1/1.67, and also lower than the predicted ratio of 1/6 by M. Oguri & P. J. Marshall (2010). This discrepancy can be attributed to two factors. First, based on known lensed quasars and the Network’s predictions, it appears that about half of the quads are missed, while approximately one-quarter of known pairs are overlooked. This suggests that quads are more likely to be missed by the Network. Second, the FPR for pair candidates is expected to be higher than that for quads, as pairs are more prone to being mimicked by stars, dual quasars, and projected quasars.

## 5. The Selection Effect of CNN

We evaluated the Network’s selection effects of four parameters (image separation, flux ratio between the first and second brightest image, magnitude of the second brightest image, and flux ratio between the brightest image and the lensing LRG) using the lenses in simulated test set. Every tested parameter was divided into four or five bins, ensuring each bin has at least 100 simulated lensed quasars.

The shaded areas with different colors in Figure 11 illustrate the range of different bins. On the left y-axis, the green vertical lines indicate the range (maximum and minimum values) of $p_{CNN}$, which is the probability given by the Network, versus the tested parameters. The TPRs calculated in different bins are depicted using a red line, with values shown on the right y-axis, also in red. We evaluated the variation of TPR due to changes in a tested parameter by comparing the highest and lowest TPRs across all tested bins:

$$V_{TPR} = \frac{\max(\text{TPRs}) - \min(\text{TRPs})}{\max(\text{TPRs})} \qquad (11)$$

Regarding image separation, the Network performs best in the separation bin (1.3, 1.7). This aligns with the training set, which has the most samples near this separation (see the top right panel of Figure 2). The worst performance occurs in the (2.1, 2.5) bin, resulting in $V_{TPR} = 2.2\%$.

For the flux ratio between the first and second brightest images, the TPR generally decreases as the flux ratio increases, with a sharp decline observed when the flux ratio exceeds 10. The $V_{TPR}$ for this parameter is 4.5%. Regarding the magnitude of the second brightest image, the TPR generally decreases as the magnitude becomes fainter, with a sharp decline observed when the magnitude is fainter than 22. The $V_{TPR}$ for this parameter is 6.4%. For the flux ratio between the brightest image and the LRG, performance improves as the flux ratio increases, with $V_{TPR}$ approximately 1.3%.

Overall, performance varies across all tested parameters. The magnitude of the second brightest image has the largest $V_{TPR}$
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Cutouts of identified lower-score systems are presented. The color scheme of the labels, the direction, and cutout size remain consistent with those in Figure 8.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure 10.** The distribution of $z_s$, i-band magnitude, image (maximum) separation, and $g-r$ vs. $r-i$ colors for our candidates is compared with known lensed quasars in the test set (see details in Table 2). The theoretical predictions from M. Oguri & P. J. Marshall (2010) are also plotted, denoted as OM10 in the legend. In this plot, we focus on the color and magnitude of the quasars, excluding the magnitude and color of the lensing galaxies.</figcaption></figure>

missed due to the very faint magnitude of one of its multiple images (approximately 24.5 in the *r* band). J2344-3056, however, was missed due to its small image separation. The $\theta_E$ of this system is approximately 0.5, which falls below the training sample's selection criterion for $\theta_E$.

It is worth noting that our Network can recover three lensed galaxies (J2329-3409, J1224+0500, J1244+0106) listed in Table 2, even though the training set does not include such types of samples. This suggests that the Network possesses a degree of extrapolation capability.

## 6. Summary

We developed a ResNet-18 classifier (R. Li et al. 2020) to identify strongly lensed quasar candidates in three-band (*gri*) combined images from the KiDS Data Release 5. Simulated lensed quasars were generated using a mock catalog of lensed quasars with parameters reflecting realistic distributions. Based on the catalog, the images were created by combining real images of LRGs and simulated noisy multiply imaged quasars. Negative samples in the training and validation sets were collected from real nonlenses. 60% of the negative and positive samples are used for training, 10% are used for validation, and 30% are used for constructing a simulated test set. Besides, a real test set made by spectroscopically confirmed lensed quasars and nonlenses from KiDS observations is also prepared

to better understand the performance and fine-tune the Network.

After the training and fine-tuning process, the Network was applied to target data, identifying 4,229 candidates. These candidates were visually inspected by first author Z.H. to eliminate the most unlikely ones. The remaining 3,172 objects were then evaluated by 10 inspectors, ultimately resulting in the selection of 272 candidates. The *i*-band magnitude distribution of the lensed quasar candidates predominantly ranges from 18 to 21, peaking at approximately 20. The maximum separation between images varies from 1.0 to 2.5, with a peak at 1.5. The redshift distribution of quasars, assessed from a subset of samples with spectroscopic redshifts (comprising 40 systems), spans from 0.422 to 3.57, with a peak near 1.5. According to M. Oguri & P. J. Marshall (2010), approximately 170 lensed quasars remain to be discovered within the KiDS DR5 footprints. After excluding known systems previously identified in earlier studies from the initial pool of 272 candidates, the total is reduced to 229. This reduction will help fill the pool of undiscovered quasars, particularly for *i* magnitudes exceeding 20.5. During the fine-tuning process, a promising quad candidate was identified; see Figure 12 in the Appendix for details.

The Network demonstrated strong performance in rediscovering known systems, as evaluated by a real test set. It successfully rediscovered 81.25% of known systems in the test
<figure><img src="image_13.png" /><figcaption>**Figure 11.** The $p_{CNN}$ and TPR in different parameter spaces are depicted. The green lines represent the range of $p_{CNN}$ in different bins, with the color beneath indicating various bin ranges. Each of the bin contains at least 100 data points. The TPR is indicated by the red lines, with corresponding numerical values also displayed in red on the right y-axis. The upper left plot corresponds to image separation, followed by (upper right) the flux ratio between the brightest image and the second brightest image. The bottom left plot represents the magnitude of the second brightest image, while the bottom right one illustrates the flux ratio between the second brightest image and the lensing galaxy.</figcaption></figure>

set. Simultaneously, the FPR was only approximately 1/2000. Furthermore, a crossmatch with SLED revealed the following: Among the high-score candidates, there was one overlap and no contaminants. Among the median-score candidates, there were 15 overlaps, with 7 out of 15 being contaminants. Among the lower-score candidates, there were 11 overlaps, with 8 out of 11 being contaminants. This indicates that lower-score candidates are more likely to be polluted nonlenses compared to median-score ones. More precise purity assessments will be possible once spectroscopic follow-ups are conducted.

Through testing and analysis, we observed stable performance of our classifier across four parameters (see the details at Section 5). The largest degradation (~6%) of TPR is observed when the magnitude of second brightest quasars exceed $r \sim 23$. The flux ratio between two images also has an influence: when exceed ~10, the TPR will decrease to ~0.95 from 1, corresponding to a ~5% degradation. The image separation and the flux ratio between LRG and brightest quasar image have ~2% influence. The selection bias of image separation has also been observed in other works (e.g., A. Herle et al. 2024). Furthermore, analysis of real test sets revealed identifiable reasons for the classifier's omission of three spectroscopically confirmed lensed quasars, attributed to factors such as large flux ratio between images, faintness of the second brightest quasar image, or small image separations. Notably, our classifier demonstrated the ability to rediscover

three lensed compact galaxies, despite their exclusion from the training data, showcasing its robustness and adaptability.

The lensed quasar candidates discovered in this paper will be analyzed in more details in the future. First, image decomposition will be performed to check whether any lensing galaxies can be detected. Second, the color and astrometric information will be analyzed to further eliminate star contaminants. Based on the results of image decomposition, color, and astrometric analysis, the follow-up spectroscopy will be conducted to confirm the most promising candidates. In this work, we focused on the discovery of the systems with $\theta_E$ larger than 0.6, which is expected to have clear multiple images in KiDS survey. As one of our future plans, the methodology will also be improved to search for smaller image separation systems (for instance, maximum separation larger than 0.6) by constructing targeted training and testing samples. Those lensed quasars are harder to identify, but still possible.

In summary, we constructed a CNN classifier to identify strongly lensed quasar candidates in KiDS DR5 imaging data, resulting in the discovery of 229 new candidates. The training set preparation pipelines and fine-tuning methodologies developed in this work can be applied to further lensed quasar identification efforts in other wide-field imaging surveys, such as Euclid (R. Laureijs et al. 2011; Euclid Collaboration et al. 2024), CSST, Wide-Field Survey Telescope (T. Wang et al. 2023), and Dark Energy Spectroscopic Instrument Legacy
Imaging Surveys (A. Dey et al. 2019). It has been predicted that numerous strong lenses will be identified from those surveys (T. E. Collett 2015; X. Cao et al. 2024). Future large-scale spectroscopic surveys, such as DESI and the 4 m Multi-Object Spectrograph telescope (R. S. de Jong et al. 2019), will help confirm a portion of these candidates. Additionally, targeted observations using telescopes like P200 and New Technology Telescope will also assist in confirming some candidates. The confirmed systems from this work can potentially be used to study the circumgalactic medium (Z. Cai et al. 2019; M. W. Lau et al. 2022), the accretion disks of background AGN (D. Sluse et al. 2017; C. Fian et al. 2021), and the Hubble constant (S. H. Suyu et al. 2017; K. Liao et al. 2019; K. C. Wong et al. 2020).

## Acknowledgments

We thank the referee in the KiDS internal review process for detailed comments, which helped improve the quality of this paper. We gratefully acknowledge Dr. C. Lemon for assisting us in crossmatching our candidate list with the SLED database, which we have found immensely helpful for our study. Additionally, Dr. Lemon provided valuable suggestions regarding some of the candidates. We also extend our thanks to Dongxu Zhang, Ran Li, Xiaoyue Cao, and Zuhui Fan for their constructive discussions.

Z.H. acknowledges that this work is supported by the Postdoctoral Fellowship Program of CPSF under grant No. GZC20232990. R.L. acknowledges the support of the National Nature Science Foundation of China (No 12203050). Y.S. acknowledges the support from the China Manned Space Program through its Space Application System. S.S. has received funding from the European Union's Horizon 2022 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 101105167 - FASTIDIoUS. C.T. acknowledges the INAF grant 2022 LEMON. G.L. acknowledges the support of the National Nature Science Foundation of China Manned Spaced Project (CMS-CSST-2021-A12). N.L. acknowledges the support of the CAS Project for Young Scientists in Basic Research (No. YSBR-062), the science research grants from the China Manned Space Project (No. CMS-CSST-2021-A01), and the hospitality of the International Centre of Supernovae (ICESUN), Yunnan Key Laboratory at Yunnan Observatories, Chinese Academy of Sciences. A.D. acknowledges the Grant of ERC Consolidator (No. 770935).

## Appendix
One Quad Candidate

As shown in Figure 12, the quad candidate at R.A. = 12.626° and decl. = -30.630° is detected as a single source in TILE KIDS_12.7_-30.2, with magnitudes of $u = 20.798 \pm 0.017$, $g = 20.025 \pm 0.003$, $r = 19.698 \pm 0.002$, $i = 19.570 \pm 0.008$, $z = 19.511 \pm 0.010$, $Y = 19.432 \pm 0.020$, $J = 19.337 \pm 0.017$, $H = 19.340 \pm 0.027$, $K_s = 19.198 \pm 0.044$.

<figure><img src="image_14.png" /><figcaption>**Figure 12.** The quad candidate in the southern sky was accidentally discovered during the network fine-tuning process. The image size is 20" by 20", and its orientation and plotting scheme are consistent with the ones that were used in Figure 3.</figcaption></figure>

## ORCID iDs

Zizhao He https://orcid.org/0000-0001-8554-9163
Rui Li https://orcid.org/0000-0002-3490-4089
Yiping Shu https://orcid.org/0000-0002-9063-698X
Crescenzo Tortora https://orcid.org/0000-0001-7958-6531
Xinzhong Er https://orcid.org/0000-0002-8700-3671
Raoul Cañameras https://orcid.org/0000-0002-2468-5169
Stefan Schuldt https://orcid.org/0000-0003-2497-6334
Nicola R. Napolitano https://orcid.org/0000-0003-0911-8884
Qihang Chen https://orcid.org/0009-0006-9345-9639
Haicheng Feng https://orcid.org/0000-0002-1530-2680
L. V. E. Koopmans https://orcid.org/0000-0003-1840-0312

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