20XX Vol. X No. XX, 000–000

11institutetext:  School of Physics and Astronomy, Sun Yat-sen University,
Zhuhai Campus, 2 Daxue Road, Xiangzhou District, Zhuhai, P. R. China;
22institutetext: CSST Science Center for Guangdong-Hong Kong-Macau Great Bay
Area, Zhuhai, China, 519082
33institutetext: School of Astronomy and Space Science, University of Chinese
Academy of Sciences, Beijing 100049, China;
44institutetext: National Astronomical Observatories, Chinese Academy of
Sciences, 20A Datun Road, Chaoyang District, Beijing 100012, China
Received 20XX Month Day; accepted 20XX Month Day

# Galaxy Spectra neural Networks (GaSNets). I. Searching for strong lens
candidates in eBOSS spectra using Deep Learning

Fucheng Zhong 1122 Rui Li E-mail<EMAIL_ADDRESS>Nicola R. Napolitano
E-mail<EMAIL_ADDRESS>
###### Abstract

With the advent of new spectroscopic surveys from ground and space, observing
up to hundreds of millions of galaxies, spectra classification will become
overwhelming for standard analysis techniques. To prepare for this challenge,
we introduce a family of deep learning tools to classify features in one-
dimensional spectra. As the first application of these Galaxy Spectra neural
Networks (GaSNets), we focus on tools specialized in identifying emission
lines from strongly lensed star-forming galaxies in the eBOSS spectra. We
first discuss the training and testing of these networks and define a
threshold probability, $P_{L}$, of 95% for the high-quality event detection.
Then, using a previous set of spectroscopically selected strong lenses from
eBOSS, confirmed with HST, we estimate a completeness of $\sim$80% as the
fraction of lenses recovered above the adopted $P_{L}$. We finally apply the
GaSNets to $\sim 1.3$M eBOSS spectra to collect the first list of $\sim$430
new high-quality candidates identified with deep learning from spectroscopy
and visually graded as highly probable real events. A preliminary check
against ground-based observations tentatively shows that this sample has a
confirmation rate of 38%, in line with previous samples selected with standard
(no deep learning) classification tools and confirmed by the Hubble Space
Telescope. This first test shows that machine learning can be efficiently
extended to feature recognition in the wavelength space, which will be crucial
for future surveys like 4MOST, DESI, Euclid, and the China Space Station
Telescope (CSST).

###### keywords:

gravitational lensing: strong — galaxies: fundamental parameters — surveys —
software: development

##  1 Introduction

Strong gravitational lensing (SGL) is a powerful tool to investigate a large
variety of open questions in cosmology. The formation of the distorted images
of background galaxies, the “sources”, depends on the total mass of the
foreground gravitational systems acting as “deflectors” or “lenses”. In case
this latter are galaxies, SGL provides us accurate constraints on different
properties correlated to their total mass, like the mass-to-light ratio (Ghosh
et al. 2021), the dark matter fraction (Auger et al. 2009; Tortora et al.
2010), the slope of the total density profile (Koopmans et al. 2006, 2009,
Auger et al. 2009) and its relation with other parameters (Bolton et al. 2012,
Shu et al. 2015; Li et al. 2018). SGL is also used to constrain the evolution
of galaxies via merging (Bolton et al. 2012, Sonnenfeld et al. 2013, 2014,
2015), the initial mass function in massive ellipticals (Spiniello et al.
2011; Barnabè et al. 2012), and study the dark substructures around large
galaxies (Gilman et al. 2018; Schuldt et al. 2019).

Moving to more cosmological constraints, SGL is used to measure the Hubble
constant($H_{0}$), and other cosmological parameters (Suyu et al. 2013, 2017;
Sluse et al. 2019; Rusu et al. 2020; Wong et al. 2020).

Strong lenses are generally searched in imaging data, where one can clearly
distinguish the lensing features in the form of arcs, or multiple images of
compact sources, like galaxies or quasars (Bolton et al. 2008; Brownstein et
al. 2012; Sonnenfeld et al. 2013; Suyu et al. 2013). Here, a great impulse to
lens hunting has been recently provided by automatized tools for lens finding
(Gavazzi et al. 2014). In particular, machine learning (ML) techniques have
been lately found to be very powerful in collecting hundreds of high quality
(HQ) candidates (Dark Energy Survey – DES: Jacobs et al. 2019, Kilo Degree
Survey – KiDS: Petrillo et al. 2019; Li et al. 2020, 2021b, Hyper Supreme-Cam
– HSC: Sonnenfeld et al. 2018).

After the identification of HQ candidates, a spectroscopical follow-up is
needed to confirm their gravitational lensing nature (Metcalf et al. 2019;
Witstok et al. 2021). In practice, one needs to collect the spectra of the
lens and the source and measure their relative redshift, confirming that the
lens is located in front of the source as expected from ray-tracing lensing
models (see Cornachione et al. 2018, Napolitano et al. 2020). This is a severe
bottleneck in the SGL studies and, so far, there have been only sparse
programs dedicated to these follow-up observations (Spiniello et al. 2019a, b;
Lemon et al. 2020; Nord et al. 2020). However, future large sky spectroscopic
surveys (e.g. Taipan: da Cunha et al. 2017 4MOST: de Jong et al. 2012, DESI:
DESI Collaboration et al. 2016) will provide an unprecedented opportunity for
massive follow-ups of lensing candidates, e.g. by reserving them dedicated
observing nieces in wide programs or by accommodating them as filler targets
in large-sky, multi-purpose surveys.

More interestingly, these large spectroscopic sky surveys will offer a unique
chance to be used as a playground for lens finding, e.g. by looking for
blended emission lines of background “lensed” galaxies, e.g. star-forming
systems, in the spectrum of a forward massive systems. This method has been
extensively used in the last years to produce tens of discoveries of new
unknown lens candidates.

The first example of a search of this kind was presented by Bolton et al.
(2004), within The Sloan Lens ACS (SLACS). They found 49 SGL candidates in 50
996 Sloan Sky Digital Survey (SDSS) spectra of luminous red galaxies (LRG).
They used the principal-component analysis to subtract the main components of
the foreground LRG spectrum and a Gaussian kernel to find the best emission
lines in the residual flux. They mainly focused on [OII] (3728Å), [OIII]
(4960Å, 5007Å), and $H_{\beta}$ (4863Å) lines, hence exploring a redshift
range of $z=(0.16-0.49)$ for the lenses and $z=(0.25-0.81)$ for the sources.
Later analyses increased the number of SLACS candidates to 131 (Bolton et al.
2008, SLACS hereafter). Within the BOSS Emission-Line Lens Survey (BELLS,
hereafter), Brownstein et al. (2012) extended the spectroscopic search,
previously performed in SLACS, to higher redshift, by looking for lenses up to
$z=0.7$ and the background sources up to $z=1.4$, with no color pre-selection.
This allowed them to finally find 45 SGL candidates in 133 852 SDSS galaxy
spectra. Along the same line of approaches, in the SLACS Survey for the Masses
(S4TM) project, Shu et al. (2015, 2017, S4TM hereafter) have extended the
search for SGL candidates to lower masses and found 118 new lens candidates.
On the other hand, Shu et al. (2016a, b, BELLS GALLERY) and Cao et al. (2020)
looked for high-redshift Ly$\alpha$ emitters as background sources and found
361 candidates.

The main disadvantage of these spectroscopy-selected samples is the missing
information from images. Indeed, even if spectra can provide the evidence of
two different emitting sources along the line of sight located at different
redshifts, they cannot guarantee that they represent an SGL event. Hence,
high-resolution imaging from space telescopes or adaptive optics is needed to
have a visual confirmation of the lenses. Currently, there are 135 confirmed
lenses with Hubble Space Telescope (HST) observations of the 294 selected
using optical lines (70/131 from SLACS, 25/45 from BELLS, 40/118 from S4TM),
and 17/21 Ly$\alpha$ candidates from BELLS GALLERY.

With the lesson learned from SDSS/BOSS, other experiments have combined the
spectroscopic selection and imaging: Chan et al. (2016) matched 45 spectra
from the Galaxy And Mass Assembly (GAMA) survey and confirmed 10 of them with
Hyper Suprime-Cam (HSC) imaging; Holwerda et al. (2022) selected lens
candidates in AAOmega spectra and followed up 56 of them with HST to find 9
confirmations.

The discovery power of this approach will be pushed to unprecedented limits by
future surveys combining spectroscopy and imaging from space (e.g. Euclid
mission and CSST) and produce a revolution in the lensing searches. However,
this revolution will stand on the ability to effectively analyze gigantic
spectroscopic data loads, which will imply the inspection of millions of
spectra and the identification of (sometimes very faint) emission lines from
background lensed systems. This is a prohibitive task for standard human-
driven analyses, unless one adopts severe selections to maximise the number of
detection but reduce the spectra to visually inspect.

Machine learning techniques can provide, instead, fast and efficient methods
to overcome these difficulties and systematically search for lensing features
in spectra. For instance, Convolutional Neural Networks (CNNs) have been
previously applied for lens searches (see Li et al. 2019, Li+19, hereafter).
In particular, they have focused on the identification of Ly$\alpha$ emitters
at higher redshift ($2<z<3$) in the spectra of lower redshift early-type
galaxies ($z<0.6$), and showed that these techniques can be efficiently used
as a classifier for galaxy spectra.

In this paper, we expand this approach and develop a new CNN tool to look for
SGL in the Baryon Oscillation Spectroscopic Survey (BOSS) spectroscopic
database (Dawson et al. 2016). Since these sources are usually star-forming
galaxies, we plan to use machine learning techniques to search for higher
redshift emission lines such as [OII], [OIII], $H_{\alpha}$, $H_{\beta}$ and
$H_{\delta}$ mixed in the foreground galaxy spectra. To do that, we build 3
CNN models: a classifier, to search for reliable emission lines in spectra,
and two regression models, to measure the foreground galaxy and the background
source redshifts, respectively. Then, we combine the predictions of the 3 CNNs
to provide a list of high probability events that we visually inspect to
select HQ candidates.

Finally, we compare this first deep learning spectroscopic-selected sample
with the most complete spectroscopic sample of SGL candidates in BOSS
observations from Talbot et al. (2021, T+21 hereafter), obtained with standard
cross-correlation techniques. This catalog consist of 838 likely, 448
probable, and 265 possible strong lens candidates, for a total of 1551
objects. They have also obtained a preliminary confirmation of 477 of them
with low-resolution imaging.

The paper is organized as follows. In §2, we will introduce the whole idea of
this project and the details of the new CNN models. In §3, we introduce the
modeled emission lines and the construction of training data. In §4, we show
the training and testing results of the new CNNs. In §5, we will apply the new
CNNs to the BOSS spectra and derive a list of candidates that we qualify via
visual inspection of their spectra, finally providing a catalog of HQ
candidates. In §6, we will discuss the results and estimate a tentative
confirmation rate based on the match with ground-based imaging. We also
discuss some avenues for improvement of future CNNs. In the final §7, we draw
some conclusions.

##  2  Methodology

In this work we want to apply ML techniques to spectroscopic data. In
particular, we want to use the ability of these techniques to perform feature
recognition and classification. ML has been widely used in astronomical data
analysis: 1) to find or classify different astronomical target candidates,
like AGN (Teimoorinia & Keown 2018; Zhu et al. 2021; Chang et al. 2021),
quasar (Khramtsov et al. 2019; Yang et al. 2021), star clusters (Jadhav et al.
2021; He et al. 2021) or 2) to measure or predict physical parameters of
astronomical targets, like redshifts (Ball et al. 2007; Han et al. 2021),
masses (Ntampaka et al. 2016; Bonjean et al. 2019), or velocity profiles
(MacBride et al. 2021). Here we want to test the possibility to use ML
techniques to efficiently search for strong lenses on vast amounts of spectra
and predict the redshift of their lenses and sources.

###  2.1 The challenge of searching for strong lenses in spectra

Next generation spectroscopic surveys will target tens of millions of galaxies
(Mandelbaum et al. 2019). These huge samples will allow us to systematically
search for high-probability candidates from integrated spectra, as the number
of expected events is noticeable, given the large number of background
galaxies potentially giving rise to lensing events.

Using the set of predictions from Collett
(2015)111https://github.com/tcollett/LensPop, we have estimated that the
number of lenses with a $1^{\prime\prime}$ Einstein radius, $R_{\rm E}$,
producing lensed images of the source, observable with a spectroscopic survey
with a 2′′ diameter fiber, over 15 000 deg2 of the sky, is of the order of 7
000. This is obtained assuming that the source is bright enough in some visual
band (e.g. Euclid visual mag$=24.5$) to make also the signal-to-noise ratio of
the emission lines high enough to be detected from the ground for typical
spectroscopic surveys (e.g. 4MOST or DESI). This estimate is subject to
different factors, including some flux loss, but it also excludes the
contribution from sources with slightly larger $R_{\rm E}$s that might
eventually scatter part of their light into a 2′′ fiber. Hence, combining all
these effects, this forecast is possibly not far from realistic. This is a
wealth of data extremely valuable because it provides, for free, the
information on the lens and the source redshifts, which are crucial for the
lensing modeling. Standard techniques based on sophisticated selection
criteria (T+21) still require rather time-consuming visual inspection. Hence,
a more practical solution to perform a systematic search of lens candidates in
these datasets is mandatory.

This is possibly true also for current spectroscopic surveys. For instance,
using the same set of predictions for the BOSS area ($\sim 10000$ deg2), and
assuming a fainter limiting magnitude for the sources, $r=$23.5, we get $\sim
920$ lenses within a 2′′ fiber, which become $\sim 1470$ within a 3′′ fiber
(e.g. the one available for SDSS releases earlier than 12). Currently, the
largest collection of candidate lenses with BOSS spectra consists of 477
objects with lensing evidence from low-resolution images (T+21). Taking this
sample as a bona fide high-completeness sample, this is rather far from the
expected number of discoverable lenses, meaning that there might be more
lenses to find in the full BOSS dataset. Given the full set of BOSS spectra
available, i.e. $\sim 2.6$M items (Ahumada et al. 2020), this means that we
should expect one real blended emission line object every $\sim$3500 spectra.

In this work, we want to tackle the problem of systematic searches of lens
candidates in spectra with deep learning and use the BOSS dataset to test the
efficiency of this approach.

Figure 1: The CNN model adopted for the GasNet-L1, L2, and L3. The network
structure is the same for the three GaSNets, except for the activation and
loss functions as reported in Table 1.

###  2.2 Convolutional Neural Networks as lens classifiers in 1D spectra

When searching for strong lens candidates in 1-dimension (1D) spectra, one
needs to identify two main features: 1) the potential emission lines from the
background sources, to determine the redshift of the source, and 2) the
absorption or emission lines of the foreground galaxies, to determine the
redshift of the lens and compare this with one of the putative sources to
possibly qualify the whole system as a lensing candidate. In most of the
current and planned surveys, the redshift of the main galaxy (the lens) is a
standard data product, hence this can be assumed to be a label of the
spectroscopic catalog. This can be either used as a first guess for the lens
classifier, to estimate the lens redshift itself or kept fixed, asking the CNN
to identify tentative background lines (see below).

###  2.3 Galaxy Spectra convolutional neural Networks (GaSNets)

In this work, we present the first set of Galaxy Spectra convolutional neural
Networks (GaSNets) for Lensing (-L). These are CNNs trained to identify strong
lensing event candidates in 1D galaxy spectra. To perform this task, we have
built three different GaSNet models:

  1. 1.

GaSNet-L1. This CNN is a classifier, trained to look for the presence of
emission lines blended in the features of the foreground galaxy and give the
probability to be a lens ($P_{L}$). In doing this, we do not assume any
specific morphology for the lens, which can be either a standard early-type
galaxy (ETG), dominated by absorption line features, or a late-type galaxy
(LTG), with ongoing star-formation. The GaSNet-L1 will learn whether, in the
spectra of either kind, there are higher-redshift emission lines, to finally
give the $P_{L}$.

  2. 2.

GaSNet-L2. This CNN is a regression algorithm, trained to identify potential
emission lines, among a list of standard features from star-forming galaxies,
overlapping a foreground galaxy spectrum and predict their redshift
($z_{PE}$).

  3. 3.

GaSNet-L3. This CNN is also a regression algorithm, trained to predict the
redshift of the foreground galaxy ($z_{PG}$) from the combination of continuum
plus a) classical absorption features from ETG spectra or b) emission lines of
LTGs. Having such an output will make the overall Network general enough to be
applied to spectroscopic databases, regardless these have gone through a
pipeline to estimate galaxy redshifts. In our analysis below, even though we
can assume that the redshift of the lenses is given (as they are provided with
the BOSS spectra, see Sect. 3.1), we opt to use the redshift predictions of
our GaSNet-L3 for the candidate selection and use the BOSS redshifts as ground
truth to assess the accuracy of the deep learning estimates.

The three CNN models have the same structure. They are built by 6 convolution
layers and 3 total connected layers (see Fig. 1), assembled by Python modules
TensorFlow and Keras. In the last layer in Fig. 1, due to the different tasks
to perform (classification vs. regression), for GaSNet-L1 we use a “sigmoid”
activation function (labeled as “my activation”), while for GaSNet-L2 and L3
we need no activation. For the same reason, we also use different loss
functions. For GaSNet-L1 we adopt a “binary cross-entropy” loss, which is
commonly used for a binary classifier. For GaSNet-L2 and GaSNet-L3, which are
two regression models, instead of the commonly used MAE and MSE loss
functions, we apply the “Huber” loss. This is defined as

$L_{\delta}(a)=\begin{cases}\dfrac{1}{2}(a)^{2},\ \ \ |a|\leq\delta\\\
\delta\cdot(|a|-\dfrac{1}{2}\delta),\ \ \ {\rm otherwise}.\end{cases}$ (1)

where $a=y_{\rm true}-y_{\rm pred}$, $y_{\rm true}$ is the real redshift,
$y_{\rm pred}$ is the predicted redshift by the CNNs , and $\delta$ is a
parameter that can be preset ($0.001$ in this work). The choice of the “Huber”
Loss has been made because, as shown in CNN regression models for galaxy light
profiles (i.e. the GaLNets, Li et al. 2021a), it can achieve higher accuracy
than MAE and MSE and better convergence. Both “activation” and “loss
functions” are summarized in Table 1.

Table 1: CNN “my activation” and “loss function”  | GaSNet-L1 | GaSNet-L2 | GaSNet-L3
---|---|---|---
my activation | sigmoid | - | -
loss function | binary crossentropy | huber_loss | huber_loss
Figure 2: Flow-chart describing the process to obtain the HQ candidates
combining the output of the three GaSNets. The final step is the visual
inspection of the candidates selected using the probability criterion,
$P_{L}>P_{\rm thresh}$, combined with the presence of background emission
lines, $z_{PE}>z_{PG}+0.1$.

From Fig. 1 we see that the CNNs all accept a 1D spectrum (i.e. a vector of
wavelength and fluxes) as input and produce as predicted parameters, either a
probability ($P_{L}$ for GaSNet-L1) or a redshift (i.e. $z_{PE}$ and $z_{PG}$
for GaSNet-L2 and GaSNet-L3, respectively).

###  2.4 Decomposing a complex CNN model

To conclude this section, we briefly discuss the choice to combine the outcome
of three CNNs to improve the accuracy of the identification of high-quality
(HQ) candidates and minimize the chance of false detection.

This task involves two steps: 1) the identification of different kinds of
features that can suggest the presence of a lensing event, i.e. the
coexistence of absorption and emissions lines from different objects along the
line-of-sight, and 2) the verification that (some of) the emission lines come
from the background system. This is a complex classification task that can be
more efficiently performed by combining different CNNs with different
specializations. Indeed, GaSNet-L1 is designed to identify a specific series
of emission lines at a higher redshift overlying a lower redshift spectrum
characterized either by a continuum plus absorption lines typical of ETGs or
continuum plus emission lines from LTGs. Even if the training sample is made
of real galaxy spectra, where the simulated emission lines from mock
background sources are randomly redshifted with respect to the main galaxy
(see §3), GaSNet-L1 can only give a probability of the coexistence of a lens
and a source at different redshifts, but cannot predict by how much the
emissions of the source are misplaced. Since this process can be uncertain, we
cannot exclude that GaSNet-L1 can confuse a lensing event with other “local”
emission processes (e.g. active galactic nuclei, ongoing star-formation, gas
outflows, etc.), and vice versa. On the other hand, the GaSNet-L2 and
GaSNet-L3 are able to predict the redshift of the tentative source and lens,
independently, meaning that they cannot predict, individually, if there is
another object at a different redshift, compatibly with a lensing event.

Only using the outputs of these three GaSNets together, we can both give a
“high probability” that there are two different systems contributing to the
spectrum and establish that the closer one is a galaxy, with redshift
$z_{PG}$, and the background one is a fainter line emitter, with redshift
$z_{PE}$. In particular, to qualify a spectrum as a candidate, we use the
following conditions: 1) $P_{L}>P_{\rm thresh}$, and 2) $z_{PE}>z_{PG}$, where
$P_{\rm thresh}$ is an appropriate lower probability threshold that will be
chosen later to define the high-probability candidates that will be further
visually investigated to assemble the list of candidates to pass to the visual
inspection, which finally produces the HQ candidate list. The full process for
the selection and grading of the HQ candidates is schematized in Fig. 2.

Figure 3: The redshift and SNR distribution of the DR16-predictive sample (see
text for details).

##  3  Data

The construction of the training sample is a critical step of any supervised
ML algorithm. Indeed, to avoid biased predictions and fictitious performances,
the training samples need to be as close as possible to real observations. In
our case, we build our training sample starting from real spectra from BOSS,
over which we simulate the presence of emission lines. Here below, we first
introduce the dataset we use for our analysis. Then, we describe the way we
have constructed the training set. This is constituted by two samples.

First, the negative sample, which represents a catalog of galaxy spectra with
no background sources blended in. As mentioned earlier, we do not make any
selection of galaxy types and we include ETGs and LTGs.

Second, the so-called positive sample, which represents a simulated sample of
spectra that emulates the presence of emission lines from a background source.
This is made of the same galaxy spectra of the negative sample, but with the
addition of artificial emission lines, redshifted with respect to the
“foreground” galaxies.

###  3.1 Data selection and predictive sample

The Sloan Digital Sky Survey (SDSS, see York et al. 2000) has observed over 10
000 deg2 of the sky, performing multi-band photometry and spectroscopy (Szalay
et al. 1999). In 2009, before the start of the Baryon Oscillation
Spectroscopic Survey (BOSS, Schlegel et al. 2009), in the third stage of the
project (SDSS-III), the spectrograph operating the observations has been
upgraded. Compared to SDSS-I/II, the number of fibers was increased from 640
to 1000, and the fiber diameter has been reduced from 3′′ to 2′′ (Ahn et al.
2012). The extended version of the BOSS survey, eBOSS (Dawson et al. 2016),
has overall produced spectra for around 2.6 million galaxies, in the
wavelength range 361–1014 nm. These are publicly available through the latest
data release 16 (DR16, Ahumada et al. 2020). This is the dataset we use in
this work222For convenience we will address this as eBOSS or DR16., over which
we operate a series of selections to ensure the quality of the spectra to
analyze. In particular, we select only: 1) plates labeled as “good” quality,
2) “Object” flags labeled as “galaxy”, 3) spectroscopic redshift between
$0.05-0.8$, 4) spectra with SNR$>2$, 5) wavelength range 3700–9200Å.

Table 2: Model parameters of equation 2. | $\lambda_{e,1}$ | $\lambda_{e,2}$ | $h_{e}$ | $z_{max}$
---|---|---|---|---
$[OII]^{1}$ | 3726.2 | 3728.9 | [2,10] | 1.44
[OIII] | 4959.0 | n/a | [1,5] | 0.82
[OIII] | 5007.0 | n/a | [1,15] | 0.82
$H_{\alpha}$ | 6562.8 | n/a | [1,15] | 0.39
$H_{\gamma}$ | 4340.5 | n/a | [1,5] | 1.10
$H_{\beta}$ | 4861.3 | n/a | [1,5] | 0.87

This latter criterion is applied to avoid a rather noisy region of the
spectra, at $\lambda>9200$Å, where the residuals from the telluric line
subtraction might be a source of spurious detections. This is a problem we
expect to deal with in future developments, but we wanted to avoid in this
first test. We stress, though, that the reduced wavelength range will allow us
to train tools that can be straightforwardly applicable to the SDSS-I/II
spectra, whose wavelength range is also limited to 3700-9200Å. Of course, this
makes our tools less sensitive to higher-$z$ systems, as many of the emission
lines we want to detect will fall out of the range at redshift z $>$$\sim$1.4
(see below).

Criterion 3 is dictated by the line observability. Indeed, we will assume that
typical sources in the SGL events are star-forming galaxies characterized by
emission lines as reported in Table 2. Here, for each line, we list the
central wavelength(s), the maximum redshift the emission line can reach below
9200Å, $z_{\rm max}$, and an intensity parameter, $h_{e}$, that will be used
in §3.3 for the simulated spectra. According to this list, for redshift
$z_{E}\leavevmode\nobreak\ \hbox to0.0pt{$>$\hss}{\lower
4.30554pt\hbox{$\sim$}}1.4$, all lines would fall out of the eBOSS wavelength
range, while with $z_{E}\mathrel{\hbox to0.0pt{\lower 3.5pt\hbox{\hskip
0.5pt$\sim$}\hss}\raise 0.5pt\hbox{$<$}}1.2$, we can still retain two emission
lines, i.e. [OII] and $H_{\gamma}$. In order to select lenses that are
compatible with the visibility of the background lines and with a reasonable
lens-source distance to guarantee an SGL event, we collect spectra in the
range $z_{G}=(0.05\sim 0.8)$.

Criterion 4, on the other hand, is an optimistic lower limit we have chosen to
increase the completeness. We have considered that the emission lines from
background sources have a SNR which is not necessarily correlated to the SNR
of the whole spectrum and, thus, can be seen also in a noisy galaxy spectrum.

The final selected sample consists of $1\,339\,895$ spectra: in the following,
we will refer to this as the DR16-predictive sample. In Fig. 3 we show the SNR
distribution of the selected spectra and the redshift of the central galaxy.

###  3.2 Construction of the negative sample

The first step to produce our training dataset is the selection of the
negative sample. This is chosen to make the CNN as general as possible, hence
assuming that every type of galaxy can work as a lens, with no particular
restrictions in luminosity or color, as it is typically done to contain the
predictive samples in imaging classifiers (see e.g. Petrillo et al. 2019, Li
et al. 2020).

For this purpose, we select 140 000 galaxies spectra from the DR16-predictive
sample, with a wavelength range of 3700-9200 Å. We take particular care that
the selected spectra uniformly cover, in number, the full $z_{G}$ range, by
counting the spectra in redshift bins of 0.05. This is crucial to avoid any
bias in the prediction of the $z_{G}$ from the poor sampling of one redshift
bin with respect to the close ones.

To mimic the presence of emission lines from local processes, for 1/5 of the
negative sample, we add artificial emission lines with the same redshift of
the galaxy, while the remaining 4/5 of the negative sample is left unchanged.
In particular, for this simulated “local emissions”, we use the same lines,
reported in Table 2, that will be used to simulate the background source
emissions, which we expect the GaSNets to distinguish from the local ones (if
any).

Figure 4: Detail of the line profiles of the simulated emissions. Artificial
Oxygen, OII (3727.1Å and 3729.9Å) lines (top) and Halpha (6562.8Å) lines
(bottom), as observed at different redshifts. The line fluxes are redshifted
and dimmed according to Eqs. 4-6.

Figure 5: Full spectrum of artificial emission lines added to the negative
sample (see Table 2 and text for details). The line fluxes are redshifted and
dimmed according to Eqs. 4-6.

###  3.3 Artificial emission line model

In this section, we give more details about the artificial emission lines we
want to add to the original eBOSS spectra to emulate both some local and
higher-$z$ emissions in the negative and positive samples, to be used for the
CNN training. Following Li+19, we use a 1-dimensional “double gaussian”
profile, defined as:

$F(\lambda)=h_{1}\exp\\{-\frac{(\lambda-\lambda_{e,1})^{2}}{2\sigma_{1}^{2}}\\}+h_{2}\exp\\{-\frac{(\lambda-\lambda_{e,2})^{2}}{2\sigma_{2}^{2}}\\}$
(2)

where $F$ is the flux, $\lambda_{e,1}$ and $\lambda_{e,2}$ are the central
wavelengths of the emission lines, and $h_{1}$, $h_{2}$, $\sigma_{1}$,
$\sigma_{2}$ are the four model parameters. The $\lambda_{e,1}$,
$\lambda_{e,2}$, $h_{1}$, and $h_{2}$ are listed in Table 2. These parameters
are further defined to satisfy the following conditions:

$\begin{cases}\sigma_{1}\in[0.8,1.6]\\\
\sigma_{2}\in\sigma_{1}+[0.5\sigma_{1},1\sigma_{1}]\\\
h_{1}=\frac{h_{e}}{(1+z_{E})^{2}}\\\
h_{2}=\frac{h_{e}}{4(1+z_{E})^{2}}\rm\leavevmode\nobreak\
if\leavevmode\nobreak\ \lambda_{e,2}\neq n/a;&=0\leavevmode\nobreak\ \rm
otherwise\\\ \end{cases}$ (3)

where the $\sigma_{1}$ is uniformly selected in the interval $[0.8,1.6]$, the
amplitude parameter, $h_{e}$, is given in Table 2, and $z_{E}$ is the redshift
of the emission line we want to simulate, assumed to be uniform in the range
[$z_{G}+0.1$, 1.2]333As we will discuss in §3.4, since $z_{G}$ is assumed to
be also uniform for the positive sample, this condition produces a final
$z_{E}$ distribution which is pseudo log-normal with a cut at 1.2. For the
negative sample, discussed in §3.2, this condition produces a $z_{E}$
distribution that follows the distribution of the $z_{G}$ as in Fig. 3.

The $\sigma_{1}$ range is determined under the assumption that the emission
lines from sources are enlarged by rotation. Hence, the line broadening in
wavelength can be written as $\Delta\lambda\approx 2\lambda_{0}v_{r}/c$, where
$\lambda_{0}$ is the central wavelength of the emission line, $v_{r}$ is the
max velocity along the line-of-sight, and $c$ is the speed of light. Then, we
can approximate $2\sigma_{1}\approx\Delta\lambda$, which, for a rotation
$v_{r}\sim 100$ km/s and $\lambda_{0}\approx 370$nm, gives $\sigma_{1}\approx
1.2$Å. Taking into account a larger wavelength range and rotation spectrum, we
can reasonably make $\sigma_{1}$ vary over a further $\pm 0.4$Å range, i.e.
the one we have assumed in Eqs. 3. Finally, we remark that the absolute
amplitude of the emission lines, depending on $h_{e}$, is not of major
importance, as the final SNR of the line strongly depends on the continuum of
the spectrum the lines are added to. On the other hand, two other important
features are 1) the relative distance of the line central wavelengths
($\lambda_{e,1}$ and $\lambda_{e,2}$) and 2) their relative full width half
maximum (FWHM), connected to the $\sigma_{1}$ and $\sigma_{2}$ parameters.

Figure 6: The spectra after adding artificial emission lines. We add the mock
emission lines in several different redshift positions ($z_{E}$) in the real
spectrum, in order to simulate the positive sample.

Simulated lines are first randomly generated at $z_{E}$=0 and then randomly
redshifted to $z_{E}>z_{G}+0.1$, where $z_{G}$ is the redshift of the negative
spectrum from which the positive is generated (see §3.4).

The flux at the redshift $z_{E}$ is then defined according to the standard
equation:

$F_{z_{E}}(\lambda)=F\left(\frac{\lambda}{1+z_{E}}\right)$ (4)

where the function $F$ is the rest frame emission line flux function (Eq. 2).

The central wavelength of $F_{Z}$, $\lambda_{cz}$, is defined as

$\frac{\lambda_{cz}}{1+z_{E}}=\lambda_{c0}\ \to\
\lambda_{cz}=(1+z_{E})\lambda_{c0}.$ (5)

The interval of $\lambda$ is equal

$\frac{\mathrm{d}\lambda^{\prime}}{1+z_{E}}=\mathrm{d}\lambda\ \to\
\mathrm{d}\lambda^{\prime}=(1+z_{E})\mathrm{d}\lambda$ (6)

where $\lambda_{c0}$ is the central wavelength of the rest frame. According to
the equations above, $\lambda_{c0}$ shifted to $(1+z_{E})\lambda_{c0}$, and
the interval of $\lambda$ in the rest frame will broaden to
$(1+z_{E})\mathrm{d}\lambda$.

Figs. 4 and 5 show how typical simulated emission lines from Table 2 are
simulated according to the random parameters from Eqs. 3 and shifted to 0.5
and 1 redshifts.

###  3.4 Simulating the positive sample

The next step is to build a positive sample by adding simulated emission lines
to the negative sample. As anticipated, we use the same lines as in Table 2,
this time with lines redshifted to $z_{E}>z_{G}+0.1$, with the condition that
$z_{E}\mathrel{\hbox to0.0pt{\lower 3.5pt\hbox{\hskip 0.5pt$\sim$}\hss}\raise
0.5pt\hbox{$<$}}1.2$.

Figure 7: Spectra of confirmed gravitational lenses in Bolton et al. (2008),
the red line is the location of the identified emission lines.

In Fig. 6 we show three simulated positive spectra for a single moderate SNR
($\sim 7$) negative spectrum (SDSS-468-51912). Here, we have marked the
location of the simulated emission lines at different redshifts, on top of the
continuum of the real eBOSS galaxy spectrum. Looking at these spectra, one can
visually figure out what are the major challenges to identify the “ground
truth” emission lines in them. First, the SNR of the lines, as this depends
not only on the $h_{1}$ and $h_{2}$ but also on the intrinsic spectrum noise.
Second, the contamination from residual sky lines, e.g. at $\lambda>8000$ Å.
Third, the effect of the source redshift, which can shift most of the relevant
emission lines from Table 2 out of the spectral range (at $\lambda>9200$Å,
e.g. in Fig. 6-c). This latter issue could be in principle solved by including
more emission lines in our reference catalog. We will consider this option for
the next developments of GaSNets. However, we stress here that adding more
lines, which in most of the cases have much lower SNRs in real galaxies, might
introduce more uncertainties in the predictions of the GaSNet-L2, as they
might be easier confused with random noise, especially in low-SNR spectra.

As a comparison with real lensing events, in Fig. 7 we report some spectra of
confirmed lenses from Bolton et al. (2008, see also §3.5). Here the locations
of the emission lines of the background sources are marked, again, as red
vertical lines. In particular, in this figure,  we show spectra with different
SNRs to visualize the impact of the spectra quality on the recognisability of
the lines. In SDSS-393-51794 all lines are visible and show a pattern similar
to the simulated lines in Fig. 5. In SDSS-436-51883, despite the spectrum’s
SNR being comparable to the one above, the lower signal of the background
lines makes some of them embedded in the noise, although some others still
stick out rather clearly. Here, the number of visible lines is reduced by the
higher redshift of the source ($z_{E}=0.452$). Finally, in SDSS-391-51782, the
redshift of the source ($z_{E}=0.931$) permits the observations of only two
lines, which are yet rather easy to spot because of the decent SNR of the
spectrum and the high signal of the lines. Overall, these examples show the
kind of features the CNN needs to be trained on identifying in the spectra and
the impact of the spectra quality and SNR of the background emission on the
final line detection and redshift determination.

Similarly, these examples provide textbook cases of HQ candidates we will
visually grade among the high probability candidates provided from the GaSNets
(see §5.2).

###  3.5 Confirmed lenses from previous spectroscopic searches

As anticipated in the previous section, we also collect candidate/confirmed
lenses from previous spectroscopic searches in SDSS/BOSS, using standard
techniques, to be used as a real test sample for our deep learning tools. In
particular, we have collected 131 objects from Bolton et al. (2008), 45 from
Brownstein et al. (2012), and 118 from Shu et al. (2017), that have secure
confirmation based on HST follow-up. This “test sample” made of real systems
is useful for two main purposes: 1) to measure the completeness of our tool,
by checking how many of these lenses are recovered by GaSNet-L1; 2) to test
how accurate the GaSNet-L2 and GaSNet-L3 are in determining the $z_{E}$ and
$z_{G}$, respectively. We will also compare our final catalog of HQ candidates
vs. the latest highly complete sample of spectroscopic selected candidates in
eBOSS from T+21. This will allow us to check the presence of candidates missed
by standard techniques, and compare the different approaches.

Figure 8: Summary of the training data building process. After constructing
the negative and positive samples, they are labeled before they are fed into
the training process of the three GaSNets. In this scheme, we illustrate the
steps made to add the label to the two training samples.

##  4  Implementation

To proceed with the construction of the training and test samples, we collect
140 000 positives and the same number of negatives. These samples are further
split into the 3 datasets: 100 000 for training, 20 000 for validation, and 20
000 for testing. The first two samples are used to train the GaSNets and
evaluate how well the model predicts the ground truth targets based on the
unseen data during the training process. The last sample is used to qualify
the final performance of the GaSNets. Finally, we also test the performance
against real candidates from literature, as discussed in §3.5.

Figure 9: GasNets training results. Left panel: accuracy and the loss of
GasNets-L1, the training and evaluation curves both converge to the same
point, and show high accuracy. Middle panel: MAE and loss of GasNets-L2, which
show a worse but yet acceptable convergence, with a reasonably low MAE. Right
panel: MAE and loss of GasNets-L2, which well converge to the same values,
because $z_{G}$ is easier to predict than $z_{E}$.

Figure 10: ROC curve of training samples where the true-positive rate (TPR) is
plotted against the false-positive rate (FPR) (see text for details).

###  4.1 Training the Networks

According to the description in §2.3 and the tasks they are expected to
fulfill, during the training, the GaSNets are fed with the training spectra to
produce accurate predictions of the “target” quantities. For GaSNet-L1 the
inputs are the spectra of the positives and negatives as well as their labels
to give as output the probabilities ($P_{L}$) to be lens candidates. For
GaSNet-L2, the inputs are the simulated positive spectra with their labels,
while the outputs are the predicted redshifts of the emission lines $z_{E}$.
For GaSNet-L3, the inputs are the labeled spectra of positives and negatives
and the output are the redshifts of the foreground spectra ($z_{G}$). The full
process of the training sample building and labeling is summarized in Fig. 8.

Table 3: Statistical properties of the predicted parameters Sample | var. | $R^{2}$ | Out. fract. | NMAD | MAE | MSE
---|---|---|---|---|---|---
Test | $z_{PE}$ | $0.941$ | $0.0121$ | $0.0029$ | $0.0164$ | $0.0032$
Test | $z_{PG}$ | $0.998$ | $0.0003$ | $0.0009$ | $0.0017$ | $0.0001$
Real | $z_{PE}$ | $0.770$ | $0.0840$ | $0.0062$ | $0.0535$ | $0.0173$
Real | $z_{PG}$ | $0.989$ | $0.0047$ | $0.0012$ | $0.0033$ | $0.0004$
All | $z_{PG}$ | $0.988$ | $0.0012$ | $0.0009$ | $0.0020$ | $0.0002$

Regarding the training step, for GaSNet-L1 and GaSNet-L3 we use the 120 000
positive (traning+validation data) and 120 000 negative samples, i.e. a total
of 240 000 spectra. Since GaSNet-L2 only predicts the $z_{E}$, in this case
the training+validation sample is made by 120 000 spectra from the positive
sample only. For each GaSNet, we use the training data to train 30 epochs with
a learning rate of 0.0001 and use validation data to evaluate the performance.
We have found that this produces rather stable validation results. During the
training process, we optimize the 3 GaSNets with the Adam optimizer (Friedman
1999).

###  4.2 Testing on simulation data

Figure 11: GaSNets results on the test sample. Left: the $P_{L}$ distribution
from GaSNet-L1; Center: predicted emission line redshifts from GaSNet-L2,
$z_{PE}$, vs. ground truth values, $z_{E}$; Right: predicted lens galaxy
redshifts from GaSNet-L3, $z_{PG}$, vs. ground truth values, $z_{G}$.

After training, we first test the GaSNets’ performances using the simulated
“test” spectra. As anticipated, the test sample is made of 20 000 positive and
20 000 negative samples for GaSNet-L1 and GaSNet-L3 and 20 000 positive
samples for GaSNet-L2 .

In Fig. 9 we first show the results of the training run for the three GaSNets
to have a first evaluation of their performances. In particular, we plot the
first 30 training epochs. The solid lines in Fig. 9 represent the accuracy
reached on the training data as the average deviation of the predictions from
the ground truth (loss). The dot-dashed lines represent the same quantity on
the test data.

For each GaSNet, we set a different evaluation function: for GaSNet-L1, being
a classifier giving a probability as output, we use the “accuracy” (acc) as
loss variable; for GaSNet-L2 and GaSNet-L3 as they predict the $z_{E}$ and
$z_{G}$, we set the mean absolute error (MAE) as loss variable. From Fig. 9,
GaSNet-L1 and GaSNet-L3 both show good convergence at about the same epoch
toward the end of the training, while GaSNet-L2 shows a larger loss because of
the degeneracy between noise and emission lines (see comment above). One
possibility to improve this result might be the adoption of some spectra pre-
processing, e.g. via smoothing. However, this would imply an incursion on the
data characterization that is beyond the purposes of this paper, and we rather
plan to address this in next analyses. Here, we just stress that the accuracy
reached by GaSNet-L2 is high enough to separate the background emission lines
from the foreground spectral features in lens candidates, hence more than
sufficient for its actual purposes (see also §6.2).

In Table 3, we report some statistical estimators to measure the GaSNets’
performances. Besides the standard MAE and MSE, we add other three estimators.

First, the R-squared ($R^{2}$) is used to evaluate the linear relationship
between prediction and true values. It is defined as

$R^{2}=1-\frac{\sum_{i}(z_{P}-z_{T})^{2}}{\sum_{i}(z_{T}-\bar{z_{T}})^{2}}$

where $z_{P}$ is the predicted value and $z_{T}$ is the true value, and
$\bar{z_{T}}$ is the average value of $z_{T}$. The closer the $R^{2}$ is to 1,
the better the prediction. In Table 3 we see that for the test sample, $R^{2}$
is close to 1 for both $z_{PG}$ and $z_{PE}$, meaning that both GaSNet-L2 and
GaSNet-L3 are expected to produce accurate results.

Second, the outlier fraction, which is defined as the fraction of predicted
redshifts scattering more than 15% from the true values:

$\delta Z=\frac{\left|z_{P}-z_{T}\right|}{1+z_{T}}>0.15.$

For the test sample, in Table 3 we show that the outlier fractions are
$\mathrel{\hbox to0.0pt{\lower 3.5pt\hbox{\hskip 0.5pt$\sim$}\hss}\raise
0.5pt\hbox{$<$}}1\%$, implying a very small fraction of anomalous predictions.

Third, the normalized median absolute deviation (NMAD), which is defined as:

$NMAD=1.4826\times median(\left|\delta Z-median(\delta Z)\right|).$

It gives the absolute deviation of the predicted value from the central value
of $\delta Z$. As seen in Table 3, the NMAD for the test sample is close to
zero, meaning again a very small deviation from the true values, i.e. very
accurate predictions.

In Fig. 10 we also show the receiver operating characteristic (ROC) curve
where we plot the true-positive rate (TPR) against the false-positive rate
(FPR). The TPR is the fraction of lenses that are correctly classified with
respect to the total number of “ground truth” lenses, while the FPR is the
fraction of non-lenses that are misclassified as lenses with respect to the
total number of non-lenses. The ROC curve can be used to decide the
probability threshold to adopt as a trade-off between true detection and
contaminants from false positives. In the same figure, we report the TPR-FPR
for different $P_{L}$s. We can see that for a $P_{L}=0.95$, we almost reach
90% completeness with a negligible false positive rate. We stress here that
this result derived from simulated spectra is in rather ideal conditions.
Hence, both the TPR and, most of all, the FPR might be just an upper and lower
limit, respectively, as compared to the real cases. However, the $P_{L}=0.95$
occurs before the slope of the ROC becomes flatter, meaning that the gain in
the number of true detections, at lower thresholds, increases at the cost of a
larger number of contaminants. We will come back to these results later when
we will discuss the threshold to adopt to select HQ candidates in real data.

Finally, in Fig. 11 we detail the results obtained for the test sample. On the
left panel, we show the distribution of the $P_{L}$ from GaSNet-L1 for both
the negative and the positive samples. As expected the former tends to cluster
more toward a peak at $P_{L}=1$, but with a rather long tail toward the
$P_{L}=0$, meaning that, statistically, there is a significant fraction of
true positives to which GaSNet-L1 has given a low probability. We have checked
these latter cases and found no correlation with the overall SNR of the
spectra. Instead, we have found a correlation of the low $P_{L}$ objects with
the $z_{E}$, in the sense that the larger the $z_{E}$, the bigger the number
of the object with $P_{L}<0.5$. This suggests that either the lower number of
lines or the intrinsically lower SNR of the lines suppress the $P_{L}$ and
makes the classification of the lensing event more difficult at higher-$z$.

In the central panel of the same figure, we show the output of the GaSNet-L2
by comparing the predicted $z_{PE}$, against the ground truth values, $z_{E}$.
Overall, the majority of the predicted values are tightly distributed around
the one-to-one relation, as also quantified by the large $R^{2}$ values found
in Table 3 (Test/$z_{PE}$). Numerous predictions scatter quite largely from
the perfect correlation, because of the degeneracy of noise and background
emission lines, as mentioned above. However, these are statistically
irrelevant as the estimated outlier fraction in Table 3 is close to 1%.

Finally, in the right panel of Fig. 11, we show the predicted $z_{PG}$ from
GaSNet-L3 against the ground truth values, $z_{G}$. In this case, the
correlation is quite perfect and the outlier fraction is negligible ($<0.1\%$
see Table 3 – Test/$z_{PG}$), both for the positive and the negative sample.
Indeed, for this latter test, we have also input the negative sample to check
the performance of GaSNet-L3, as a pure automatic spectroscopic redshift tool,
in absence of artificial emission lines. This shows that the ability of
GaSNet-L3 to predict the galaxy redshift is not driven by the emission lines,
easier to spot, but by the overall features of the spectrum (i.e. continuum
and absorption/emission lines).

###  4.3 Test on HST confirmed samples

Previous analyses of the SDSS/BOSS spectra have brought to the collection of
294 strong lenses candidates: 131 from SLACS, 45 from BELLS, and 118 from S4TM
(see §1). Being candidates based on spectroscopic features, these samples
contain both real lenses and contaminants. Indeed, space imaging follow-ups
have confirmed 70/131 SLACS candidates (the Grade-A objects in Table 4 of
Bolton et al. 2008), 25/45 BELLS candidates (Grade-A objects in Table 3 of
Brownstein et al. 2012), and 40/118 S4TM (Grade-A in Table 1 of Shu et al.
2017). As also commented in §1 these correspond to an average confirmation
rate of 46%. Note, though, that the HST samples often tend to optimize the
confirmation rate by pre-selecting targets with low-resolution imaging (see
e.g. Bolton et al. 2004; Shu et al. 2016a), hence this can be considered an
optimistic upper limit estimate. These are the main statistical samples that
have been systematically followed up to collect space imaging confirmations of
spectroscopically selected SGL candidates, using optical lines. As such, these
represent the most secure sample to check our results against. These data can
be used for two main purposes: 1) to compare the classification of the GaSNets
against human selection and help us set a reasonable threshold to optimize the
chance of finding real lenses with the minimal contamination from false
positives; 2) to forecast the success rate we might expect from our set-up
since we have a reference sample of “candidates” and “confirmed” events. Being
this literature sample far from complete (see §2.1), it cannot be fully used
to draw firm conclusions about the completeness of the GaSNets, however, this
is the only sample we can use to benchmark the GaSNets’ performances, with a
necessary grain of salt. On the other hand, the large sample from T+21, having
no space observations cannot be used for the same purpose as the ones above.
As anticipated, we will use it for an a posteriori test to assess the
differences (if any) between standard and deep learning approaches.

Figure 12: Results of the GaSNets applied to spectra of strong gravitational
lens candidates (in blue) and HST-confirmed events (in red) from SLACS, BELLS,
and S4TM samples (see text for details). Left: the $P_{L}$ distribution from
GaSNet-L1; Center: predicted emission line redshifts from GaSNet-L2, $z_{PE}$,
vs. literature redshifts, $z_{E}$, for the candidate objects (top) and the HST
confirmed (bottom); Right: predicted lens redshifts from GaSNet-L3, $z_{PG}$,
vs. literature redshifts, $z_{G}$, for the candidate objects (top) and the HST
confirmed (bottom).

Figure 13: Predictions of the three GaSNets on the DR16-predictive sample
($\sim 1.3M$ objects): the $P_{L}$ from GaSNet-L1 (left), the $z_{PE}-z_{PG}$
(center) and the $z_{PG}$ (right), from GaSNet-L2 and GaSNet-L3 outputs, vs.
$z_{G}$, the galaxy redshift from eBOSS/DR16 catalog (see text for the
details). In the center and right panels we show the $P_{L}>0.95$ sample (in
red) and the $P_{L}<0.95$ in blue.

To proceed with the test of the HST confirmed catalogs against GaSNets, we
first select the literature spectra that are located in the predictive range
of our CNNs (i.e. $0.05<z_{G}<0.8$ and $0.15<z_{E}<1.2$). These are 264/294
candidates and 121/135 confirmed objects. In Fig. 12 we show the probability
predicted from the GaSNet-L1 (left panel), the redshift of the source
predicted from GaSNet-L2 (central panel), and the redshift of the lens
galaxies predicted by the GaSNet-L3 (right panel), for the candidates and
confirmed literature objects face-to-face.

In particular, we see that GaSNet-L1 predicts high probabilities for most of
the lenses: e.g., 69% of the candidates and 80% of the confirmed objects have
$P_{L}>0.95$, which becomes 81% of the candidates and 90% of the confirmed
objects for $P_{L}>0.8$.

More importantly, the ratio of the confirmed/candidates increases dramatically
from $0.8<P_{L}<0.95$ to $P_{L}>0.95$, as we have 12/33, i.e. 36% for the
former and 97/182, i.e. 53%, for the latter, vs. the overall 46% estimated for
the full sample (see above). On the other hand, for $P_{L}<0.8$ the
confirmation rate drops to 12/49, i.e. 24%, which is too low for successful
space observations and still anti-economical for lens search in spectra.
Indeed, as discussed in §4.2, at $P_{L}<0.8$ the FPR becomes prohibitive,
producing massive false detections in large samples that should be cleaned
with tedious visual inspections. Interestingly enough, for $P_{L}>0.95$ the
fraction of true SGL events recovered (80%) is rather close to the TPR ($\sim
89\%$) predicted by the ROC curve (Fig. 10) for an idealized mock population
of strong lenses. This means that the performances of the GaSNets on the real
data might be not far from the expectations from simulated data.

However, In Fig. 12 (left) a misalignment between the deep learning and human
filtered selections is further demonstrated by the fact that some confirmed
lenses have received a small probability by GaSNet-L1. As discussed in the
previous section, these are mainly low-SNR emission line spectra or higher-$z$
systems that, even if accounted for in the training sample, are difficult to
be highly scored by GaSNet-L1 but might have been picked by the human eye with
higher confidence. Hence, we conclude that a $P_{L}=0.95$ threshold is very
likely to produce effective completeness higher than the 80% obtained above
over a complete and unbiased true SGL sample.

Figure 14: HQ candidate spectra. The SDSS/BOSS spectra are plotted with
highlighted their main spectral features. Red vertical lines indicate the
emission lines of the background source at the redshift $eyez_{E}$ (i.e. the
one corrected during the visual inspection). Blue vertical lines indicate the
spectral features of the lens at redshift $z_{G}$. Green lines show the
location at rest frame ($z=0$) of the emission lines from sky). On the top of
each spectrum from left to right, we report the probability from GaSNet-L1,
the average SNR of the spectrum, the cataloged redshift of the galaxy from
SDSS/BOSS, the predicted redshift from GaSNet-L3, the corrected redshift from
visual inspection, the predicted redshift from GaSNet-L2, and finally, the RA,
DEC, and ID of the target.

The middle and the right panel of Fig. 12 show that both GaSNet-L2 and
GaSNet-L3 can make good predictions on the redshift of the emission lines and
the lens galaxies. In general, GaSNet-L3 performs better than GaSNet-L2 (see
Table 2), possibly because the spectra of the lens galaxies can provide more
information, both from the continuum and the absorption or emission lines,
while GaSNet-L2 relies only on a few emission lines, which provide
intrinsically less information. We also see that the confirmed objects
generally show a smaller scatter and outlier fraction than the candidates,
especially in $z_{PE}$, and also that the highest probability objects show
tighter one-to-one predictions. This demonstrates that misclassifications of
SGL events might be related to uncertainties on the redshift of the background
sources, which tend to be placed further away than sometimes they are, i.e.
confusing “local” emissions with background ones. However, the chance of such
misclassification is reduced for $P_{L}>0.95$ systems.

All in all, Fig. 12 indicates that the $P_{L}>0.95$ sample is accurate enough
to produce reliable lens candidates from the DR16-predictive sample.

##  5 Results

In this section, we apply the trained GaSNets to the DR16-predictive sample,
introduced in §3.1. This is made of 1 339 895 galaxy spectra and represents
the sample among which we want to find new strong lens candidates and, for
them, determine the redshift of the background source, $z_{E}$.

###  5.1 Predictions on the eBOSS spectra

According to the workflow described in Fig. 2, the first step to perform is
the classification of candidates using GaSNet-L1. In Fig. 13 (left) we report
the probability $P_{L}$ distribution obtained from GaSNet-L1 for the
DR16-predictive sample. From this histogram, we see that using a $P_{L}>0.8$,
which, according to the ROC curve, would return almost 95% of the true lenses,
would produce a list of about 10 000 candidates. This is a sample hard to
handle for two main reasons: 1) it is time-consuming to visually inspect and
2) it is foreseen to be severely contaminated from false detections. This
latter case has been confirmed by randomly inspecting $100$ candidates with
$0.8<P_{L}<0.95$ to find that about 90% are very poor candidates. On the other
hand, choosing $P_{L}>0.95$, which, for the true lens cases, allowed to
recover of $80\%$ of the confirmed lens known in SDSS/BOSS, would produce a
more manageable sample of $\sim 4000$ candidates. Hence, at the cost of some
acceptable incompleteness, for this first test, we decide to adopt a more
conservative approach and search for high-quality candidates among the ones
with $P_{L}>0.95$. We can now look into the predictions of the GaSNet-L2 and
GaSNet-L3 to finalize the sample to visually inspect. In Fig. 13 (center) we
report the redshift gap between the lens and the source, $\Delta
Z=z_{PE}-z_{PG}$ as a function of the lens redshift $z_{G}$ for the full
predictive sample. Here we highlight the objects with $P_{L}>0.95$, from all
the other spectra in the predictive sample. We can distinguish a few features:
1) the upper limit imposed on the $z_{E}$ produces a zone of avoidance on the
up-right side of the image; 2) there is a crowded sequence of high $P_{L}$ in
the box defined by $z_{G}$=[0.5,0.6] and $\Delta z$=[0.4,0.6]. This is due to
the presence of rather redundant residual emission lines from sky subtraction
in the SDSS pipeline at $\lambda\sim 5600$Å (see Fig. 14) that is very often
ignored by GaSNet-L2 but that in many cases is confused as a real emission. As
we will see later, this sequence is easily filtered out by the visual
inspection, but it has to be better accounted for in the training sample to
reduce its impact in future analyses.

A similar effect is produced by the residual sky lines at $\lambda>8000$Å,
which also produce a sequence of spurious $z_{E}$ predictions (see $z_{G}\sim
0.2$ and $\Delta Z\sim 0.9$). These have a small $P_{L}$, according to
GaSNet-L1, and thus they do not bother, as they are excluded by the following
analysis.

Overall, the $P_{L}>0.95$ sample looks rather unbiased, as seen by the $z_{G}$
estimates from GaSNet-L3 in the right panel of Fig. 13, where the predicted
$z_{PG}$ is extremely tightly correlated to the eBOSS catalog values (see also
the statistical estimators in Table 3).

However, before proceeding with the visual inspection of the background
emissions estimated by the GaSNet-L2, to minimize the heterogeneity in the
human grading, we pre-select the spectra that show an average SNR, computed at
the expected positions of the reference lines from Table 2,
$\langle$SNR${}_{\rm lines}\rangle$, to be larger than one. This further
selection gives us 931 potential candidates pass to the visual inspection.

###  5.2 Visual inspection of spectra

The 931 candidates are visually inspected by the three authors, according to
an ABCD ranking scheme, being A=“sure positive”, B=“maybe positive”, C=“maybe
not a positive” and D=“sure negative”. To combine the human grading with the
$P_{L}$, we have turned the ranking above into a score according to the
conversion A=10, B=7, C=3, D=0 (see also Li+21). We finally select the spectra
for which we have obtained an average score $\geq$7, as the final high-quality
candidate sample. This is made of 497 objects in total.

Some spectra of this “high quality” sample are plotted in Fig. 14. Here we
clearly see the emission lines, marked as red vertical lines, from background
lensed star-forming galaxies.

During the visual inspection process, besides grading, we also check that the
predicted values, $z_{PE}$ and $z_{PG}$, given by GaSNets, are perfectly
aligned with visible spectral features. This is not often the case as the
prediction process has some intrinsic uncertainty. For instance, the two
GaSNets need to interpolate across a grid of training spectra that have been
shifted with a coarse sampling (i.e. 0.05 in redshift, see Sect. 3.2).
However, other sources of errors are possibly causing even more significant
shifts, as we will discuss in more detail in Sect. 6.2. Using an interactive
GUI developed by one of us (ZF), we then determine by eye the needed shift to
obtain a perfect visual alignment and a “corrected” redshift for the $z_{PE}$,
assuming the $z_{G}$ from the eBOSS catalog as an unbiased estimate of the
main galaxy redshift.

Finally, to qualify a spectrum as a lensed galaxies candidate we check that 1)
the emission lines do not belong to the sky lines (green lines in Fig. 14) and
2) that the identified emission lines, i.e. red lines in Fig. 14, having
redshift $z_{PE}$ from GaSNet-L2, do not correspond to any line from the
galaxy (i.e. blue lines in Fig. 14 at redshift $z_{PG}$ from GaSNet-L3). In
other words, the $\Delta Z=z_{PE}-z_{PG}$ has to be larger than 0.1, as shown
in Fig. 15, where it is plotted as a function of the estimated $z_{PG}$. Here
we also see that the $\Delta z$ is decreasing with the $z_{PG}$ because the
further the lenses, the smaller the difference in redshift with the background
source. From Fig. 15 it is clear that this is mainly a selection effect due to
our condition on the $z_{PE}<1.2$, however, since the high-quality candidates
do not cluster toward the upper bound of the zone of avoidance, we conclude
that the candidate distribution becomes incomplete when the $z_{PE}\sim 1.2$.
This is consistent with the correlation of the low $P_{L}$ with the
higher-$z_{PE}$ we have discussed in §4.2. An encouraging feature, in the same
figure, is that the combination of the $\langle$SNR${}_{\rm lines}\rangle>1$
and the visual inspection, allows us to drop the stripe of spurious detection
from residual sky lines discussed in §5.1.

Figure 15: $z_{PE}-z_{PG}$ vs. $z_{PG}$ distribution of visual inspection 497
good potential candidates and all $P_{L}>0.95$ spectra

###  5.3 Deep learning vs. traditional methods

We end this section by comparing our HQ catalog, based on deep learning, with
the catalog of 1551 candidates selected with the rest-frame optical bands from
T+21, using traditional selection methods. They used the complete eBOSS/DR16
database and applied the standard spectroscopic detection method introduced in
the eBOSS Emission-Line Lens Survey (BELLS) and added Gaussian fit
information, grading, additional inspection observables, and additional
inspection methods to improve the BELLS selection method. They used a total of
2 million objects with no selection on the redshift of the lenses.
Furthermore, they used a larger database of reference lines, including also
[NII]a/b and [SII]a/b: these are best suited for low-redshift detections being
all placed at $\lambda>6500$Å, leaving the only [OII] doublet as a feature for
the identification of background sources at $z\leavevmode\nobreak\ \hbox
to0.0pt{$>$\hss}{\lower 4.30554pt\hbox{$\sim$}}1.2$. As such, their predictive
sample is wider in the parameter space than the DR16-predictive we have
adopted. For a proper comparison, we have selected the T+21 candidates that
fall in the GaSNets predictive space (i.e. $z_{G}=0.05-0.8$, spectra SNR$>2$,
$z_{E}\mathrel{\hbox to0.0pt{\lower 3.5pt\hbox{\hskip 0.5pt$\sim$}\hss}\raise
0.5pt\hbox{$<$}}1.2$, $z_{E}=z_{G}+0.1$) and finally obtain 778 “compatible”
candidates ($\sim 50\%$ of the original sample). We have checked the excluded
773 and found that 739 detections are, indeed, based on a single line
(generally in spectra with SNR$>2$) and 29/5 are based on 2/3 lines (all with
spectra SNR$<2$), according to the T+21 catalog. Hence, the majority of these
“known candidates” would have been missed anyways in our HQ catalog because of
the conservative selection in the number of lines to use for the
classification, either in the deep learning training or visual ranking.

We have, then, matched the compatible 778 candidates with our HQ sample of 497
entries and, surprisingly, we have found a match for only 68 objects.

The positive note is that GaSNets have found $\sim 430$ new HQ candidates that
have been missed by standard techniques. The negative note is that the GaSNets
seem to have missed $710$ candidates from T+21.

Is this true? To answer this question we need to first check how many of these
objects are lost by the GaSNets according to the criteria imposed on their
outputs, i.e. they do not fall in the criteria $P_{L}>0.95$ and
$z_{E}-z_{G}>0.1$. These are 327, i.e. $42\%$ of the compatible sample. This
is larger than the fraction of lost objects found in the test against the real
systems in §4.3 (i.e. $100-69=31$% of “candidates” and $100-80=20$% confirmed
ones, having $P_{L}<0.95$). One explanation of this excess of lost objects
with low $P_{L}$ can be that these are mainly optimistic candidates in T+21,
for which the GaSNets have given low reliability. To confirm this we have
checked that 215/327 are single line detections, according to T+21, and only
87/327 have scored A+ or A in their check against low-resolution imaging444As
we will comment later, the image quality of the low-resolution DES imaging
used by T+21 does not consent a firm classification, except for very clear
features. Hence, we have conservatively assumed the A+ and A scores sufficient
to preliminary quantify the confirmation rate.. Hence, we can fairly conclude
that this sample of lost candidates is overall low-valuable, having a tiny
(albeit insecure) confirmation rate. This also implies that the fraction of
lost SGL “real” events in our catalog is in line with the one estimated in
§4.3, reported above (i.e. 20%).

Going to the remaining lost candidates ($710-327=383$), in Fig. 16 we show the
spectra (not line) SNR vs. the estimated redshift of the background lines from
T+21, color-coded by the number of detected lines. From this figure, we
observe that:

Figure 16: Sample of missing candidates in the HQ catalog from GaSNets+ visual
inspection. In this figure, we show the distribution of the missing candidates
in the parameter space adopted for the training of the GaSNets (i.e. spectra
SNR$>2$ and $z_{E}<1.2$). Each candidate is color-coded by the number of
detected lines in their spectra (according to T+21). Most of the missed
candidates are 1-line and did not qualify in our HQ sample.

Figure 17: Sample of missing candidates in the HQ catalog from GaSNets +
visual inspection and found in T+21. The red vertical lines are the features
identified as multi-lines in T+21, but that have been excluded by us because
either too faint or embedded in noisy regions, making them poorly reliable to
qualify as HQ candidates.

1) The majority (286/383, i.e. 75%) of the missing candidates have 1-line
detection, thus they are lost from our HQ catalog because we excluded them in
our filtering (both because of the $\langle$SNR${}_{\rm lines}\rangle$ or the
visual inspection, see §5.1 and 5.2). According to the T+21 low-resolution
grading, 164/286 of the 1-line detections have A or A+ scores, which implies a
rather large confirmation rate, $\sim$60%, if confirmed by higher-quality
imaging. This is a sample we can easily intercept with GaSNets, by simply
releasing the conservative criterion of the 1-line. From Fig. 16, we see that
above $z\leavevmode\nobreak\ 1.05$ we lose some 2-line candidates, which
supports further the conclusion in §5.2 that we are incomplete at
$z_{E}\mathrel{\hbox to0.0pt{\lower 3.5pt\hbox{\hskip 0.5pt$\sim$}\hss}\raise
0.5pt\hbox{$<$}}1.2$.

2) The remaining 97 multi-line objects, in Fig. 16, majorly concern us, as
according to their $P_{L}$ and number of lines should have been picked by the
GaSNets + visual inspection. First, we have found 10/97 objects classified as
quasar or unknown in DR16, so these could not be in our catalog. For all the
other 87 we have visually inspected the spectra and found that despite they
being classified as multi-lines in T+21, no line, except the [OII] doublet,
had an acceptable SNR. Hence, these are all candidates that have been
substantially treated as 1-line from us or given a rather poor visual grade.
We give some examples of these spectra in Fig. 17. Since 60/97 have received A
or A+ scores from the low-resolution confirmation in T+21, i.e. 60%, this is a
sample that is likely to be valuable and should not be missed. However, we
need to point out that this sample was not lost by the GaSNets but by human
selection.

###  5.4 First catalog of new HQ strong lensing candidates in eBOSS from Deep
Learning

After having subtracted the 68 candidates already found in T+21, we obtain a
final catalog of 429 new HQ candidates in eBOSS, the first fully derived using
deep learning. The full catalog is reported in Appendix A. This includes
information about 1) RA/DEC coordinates; 2) plate ID; 3) MJD (Modified Julian
Day), the observation date; 4) the GaSNet-L1 probability, $P_{L}$; 5) the
redshift of the galaxy from the eBOSS catalog; 6) the predicted redshift of
the galaxy from GaSNet-L3; 7) the predicted redshift of the background source
from GaSNet-L2; 8) the corrected redshift of the source from the visual
inspection (see Sect. 6.2); the total probability, $P_{T}=P_{L}\times 0.1$
visual scores, i.e. combining the GaSNets and human probabilities to be a
lens.

##  6 Discussion

In the previous section, we have presented the final list of 429 new strong
galaxy lensing candidates, obtained by applying the three GaSNets to the
latest eBOSS database (DR16), and further cleaning the sample via visual
inspection.

Figure 18: Some examples of ground-based color cutouts
($20^{\prime\prime}\times 20^{\prime\prime}$) of GaSNet candidates. Top row:
match with HSC known candidates, re-graded as in the bottom-left corner.
GaSNets have found them as HQ candidates independently. Bottom 4 rows: A, B, C
and D ranked HSC counterparts of GaSNet candidates from the HQ sample in §5.4.

Strictly speaking, the GaSNets’ candidates consist of systems where, in the
spectrum of a foreground galaxy, we have found emission lines that are
incompatible with belonging to the same galaxy. We have assumed, so far, that
all these lines come from lensing events. In reality, they can be emitted by
other kinds of sources, like overlapping galaxies along the line of sight,
outflows in late-type galaxies, interacting systems, etc., although we have
set a redshift gap, $\Delta z$, that might have prevented the confusion with
some “local” phenomena. Hence, to fully assess the new catalog, we need to
estimate a fiducial confirmation rate based on space observations or high-
quality ground-based imaging. Such a confirmation rate is important 1) to
compare with the one from standard techniques, to see whether Deep Learning
can outperform them in terms of reliability of the candidates; 2) to check
whether the large spectroscopically selected samples accumulated so far, are
compatible with expected numbers of SGL events from theoretical predictions
(see e.g. 2.1), or we might expect to find more events with more refined
tools.

Besides the confirmation rate, in this section, we also discuss the
possibility to use the GaSNet-L2 and GaSNet-L3 as automatic tools for redshift
estimates and spectra classification. We will conclude this discussion with
some perspective on the next improvements of the GaSNets.

###  6.1 Confirmation rate via ground based imaging

To properly derive a fiducial confirmation rate for the 429 HQ candidates in
§5.4, we have checked the HST archive observations to look for serendipitous
matches with our newly discovered candidates but found no matches. Hence, the
only remaining check we can perform is inside archive observations from the
ground. There are three datasets potentially useful for the test: 1)
DECaLS555https://portal.nersc.gov/cfs/cosmo/data/legacysurvey/dr7/; 2)
KiDS666https://kids.strw.leidenuniv.nl/DR4/access.php and 3)
HSC777https://hsc-release.mtk.nao.ac.jp/das_cutout/pdr3/. We have found 279
matches with DECaLS, 16 with KiDS, and 63 with HSC, however: 1) the quality of
the DECaLS grz color images from the public data is rather poorer than other
surveys and made the identification of the lensing features extremely
uncertain (see Appendix B); 2) the number of KiDS matches is too small to have
a fair statistics and we decided to leave the few convincing candidates for
future analyses; 3) the HSC sample is the one with sufficient large
statistics, image quality, and uniformity to make a fair estimate of the
fraction of convincing lenses without strong biases.

Looking at this latter sample, we find that 7 candidates have corrupted color
images or are too close to some bright source to be used with sufficient
confidence. Hence, we finally inspect 56 systems. Of these, our HQ candidates
match 8 known lens candidates from HSC 888http://www-
utap.phys.s.u-tokyo.ac.jp/ oguri/sugohi/ (e.g., Sonnenfeld et al. 2018, 2019),
although they are all C-graded by the imaging only in their catalogs. We have
visually inspected them again and, applying the ABCD scheme as in §5.2 and
taking into account the spectroscopic evidence, we have reclassified 3 of them
with A-grade and 5 with B-grade.

Of the remaining 49 matches, we have classified 7 candidates as A-grade and 17
as B-grade systems. Taking the A-grade as bona fide confirmed lenses and
weighting the B-grade ones by a 0.5 factor to account that they may be not
lenses, we conclude that the lens confirmation rate is 21/56 or 38%, which is
lower than the confirmation rate estimated in §4.3 using space imaging.

In Fig. 18 we show a gallery of the “confirmed” lens and, as a comparison, the
“unconfirmed” ones (i.e. the ones C- and D-graded). In the first row, we
report some of the lenses previously found in the HSC imaging and confirmed
and re-graded by us, in the second and third rows some examples of new
GaSNets’ confirmed lenses with A-grade, and B-grade, respectively. In the
final two rows the unconfirmed C and D cases. These clearly show the variety
of potential contaminants, including arc-like features of unclear nature,
blue/faint background galaxies similar to other objects in the field-of-view,
interacting systems, and large late-type or lenticular galaxies. In these
latter examples, especially the large galaxies, if we exclude the cases where
it is likely that the background emissions found in the spectra come from
unlensed faint background systems as they can be seen in field-of-view, it is
difficult to identify any other potential high-$z$ emitters. This leaves the
nature of these emissions unresolved. In principle we cannot exclude that,
given the small area covered by the fibers in eBOSS ($2^{\prime\prime}$, see
also Fig. 18) there is some very low separation arc, embedded in the bright
foreground galaxy light, remaining undetected in the seeing-confused images
from HSC. In this case, we can argue that the confirmation rates estimated
above (38%) might represent a lower limit.

If this conclusion is correct, we can attempt to derive a prediction of the
total number of true SGL events in eBOSS, based on the current candidates from
T+21 and this work. Put together they are 1551+429=1980. Assuming a
pessimistic confirmation rate of 38%, they make $752$ real SGL events, while
for a more optimistic $46\%$ conformation rate of SLACS+BELLS+S4TM, it makes
$911$ real SGL. If we add the other candidates found in BOSS from BELLS (25)
and BELLS GALLERY (17999Note that more can be still found on their sample of
remaining 155 candidates remaining unconfirmed. Assuming $\sim 50\%$
confirmation rate they can be $\sim 70$.) we reach 794 and 953 real SGL, which
nicely bracket the expected number we have estimated in §2.1 for BOSS ($\sim
920$). This suggests that we have possibly reached the full completeness of
the lens population accessible by the largest spectroscopic database currently
available.

###  6.2 Statistical errors of GaSNet-L2 and GaSNet-L3

GaSNet-L2 and GaSNet-L3 are two CNNs that can perform the generic task to
estimate the redshift of given features in 1D spectra. As such, they can be
applied to spectroscopic databases regardless of the specific task of looking
for strong gravitational lenses.

Certainly, the search for lenses requires a much lower accuracy in the
$z_{PG}$ and $z_{PE}$, because the only condition to ring the bell for
potential events is $\Delta z=z_{PE}-z_{PG}>0.1$, which is rather higher than
typical spectroscopic redshift errors based on the human measurements.
However, this condition is physically meaningful if $\Delta z$ is larger than
the combination of the typical errors on $z_{PE}$ from GaSNet-L2 and $z_{PG}$
from GaSNet-L3, which also include the uncertainties that a deep learning
process might introduce (activation, loss, training, etc.).

Hence, if on one hand, the assessment of the “bias” and typical “statistical
errors” of the two GaSNets (L2 and L3) is needed to validate the pre-condition
for the HQ candidates, on the other hand, they can also quantify the accuracy
of the individual CNN as “automatic tools” for redshift measurements. In this
latter case, we can possibly require the typical errors to be of the order of
$<1\%$, and systematics smaller than this precision. At the same time, we
should expect a negligible fraction of outliers/catastrophic events.

Figure 19: $Eyez_{E}$ vs. $z_{PE}$ and $eyez_{E}$, $z_{PE}$ distribution of
visual inspected 429 HQ candidates.

As mentioned in §5.2, during the visual inspection we had the chance to check
the accuracy of the $z_{PE}$ estimates and correct them by hand. This process
is not error-free itself, as the resulting $eyez_{E}$ is a combination of a
subjective identification of the line center and the accuracy in the line
alignment by eye. However, we can confidently use these corrections, together
with the nominal $z_{G}$ given in the SDSS catalogs, to compute the scatter of
the GaSNet-L2 and GaSNet-L3 predictions and derive systematics and statistical
errors for $z_{PE}$ and $z_{PG}$. For the $z_{PG}$ we can use all the galaxies
in the predictive catalog as shown in Fig. 13 (right), for which $z_{G}$ is
known, to determine the $\delta_{z_{PG}}=z_{PG}-z_{G}$. The scatter in this
case is $\sigma(\delta_{z_{PG}})=0.015$. The outliers, defined as the spectra
for which the $(|z_{PG}-z_{G}|)/(1+z_{G})>$0.15, are about 0.113%.

For the $z_{PE}$ we can use the spectra that we have visually inspected and
for which we have collected the average $eyez_{E}$ estimated by the three of
us. These are shown against the $z_{PE}$ in Fig. 19 and used to estimate the
$\delta_{z_{PE}}=z_{PE}-eyez_{E}$. In this case, we have estimated the scatter
$\sigma(\delta_{z_{PE}})=0.046$, while the outliers are about 1.21%.

In both cases, the scatter and accuracy are reasonably good, and so it is the
outlier fraction. This result confirms that the adoption of the $\Delta z>0.1$
is conservative enough to account for the nominal statistical errors of the
predicted redshifts. Furthermore, if we consider that the SNR is generally
poor for the majority of the emission lines of the background galaxies, then
we believe that both GaSNets (L2 and L3) are a very promising start and can be
possibly be already used to automatically provide a first accurate guess of
the redshift of galaxies in large surveys, while a more dedicate training
would possibly improve the overall accuracy. We will dedicate future analyses
to the GaSNets on this latter and more applications, including specialized
tasks for spectra classification (e.g. starburst galaxies, active galactic
nuclei, irregular systems, etc.).

Figure 20: A possible scheme for increasing the interplay between the three
GaSNets. Here, we foresee input GaSNet-L1 with the outputs of GaSNet-L2 and
-L3, as shown in the yellow line show, to improve the $P_{L}$.

###  6.3 Improvements of CNN model

In this work we have used 3 independent CNN models and combined their outputs
according to some physically meaningful conditions (see Fig. 2), to identify
strong lens candidates. In fact, because of the physics of the SGL, which
involves the position of the source and lens with respect to the observer, the
properties of the projected potential, etc., the 3 outputs of the GaSNets are
not fully independent. Rather, they must be connected via the ray-tracing
equation of the SGL. For instance, one can define a more meaningful
probability for spectra to have caught a lens candidate, by looking at the
relative distance of the $z_{PG}$ and $z_{PE}$, or at the absolute value of
$z_{PG}$ (e.g. giving a lower $P_{L}$ if the galaxy is a very low redshift),
etc. One possible future development is to connect different individual CNN
networks (just like the neurons in our brain), for example, as in Fig. 20, to
make a more educated probability for a spectrum to be an SGL system.

In this figure, we suggest using the prediction of $z_{PG}$ as conditional
information for the prediction of $P_{L}$, then using the prediction of
$z_{PG}$ and $P_{L}$ as auxiliary information for the prediction of $z_{E}$.
If, on one hand, this architecture can help to improve the accuracy, the cost
to pay is the model complexity, including a larger correlation among the
different branches with some large back-propagation. This would make the
overall model more time-consuming in terms of training and prediction, but
likely more accurate and false detection free.

##  7 conclusions

In this paper, we have presented a novel deep learning tool to search for
strong gravitational lensing (SGL) events in 1D galaxy spectra. This is the
first attempt to use multiple emission lines after Li+19 used Ly$\alpha$ only.

The new algorithm is made of different CNNs, dubbed Galaxy Spectra
convolutional neural Networks (GaSNets). These are optimized to work together
to provide SGL candidates, but can also perform classification and regression
tasks independently. As such, they are extremely suitable for further
applications in large databases of tens to hundreds of millions of spectra,
like the ones expected from the next generation spectroscopic surveys (4MOST,
DESI, EUCLID, CSST).

In this paper, we have started by applying these new tools to the strong
lensing search in the eBOSS/DR16 database (Ahumada et al. 2020). To this aim
we have introduced: 1) GaSNet-L1 giving to each eBOSS spectrum the probability
to be an SGL event ($P_{L}$); 2) GaSNet-L2 estimating the redshift of
background sources ($z_{PE}$) from a series of pre-selected emission lines
(see Table 2); and 3) GaSNet-L3 estimating the redshift of the galaxy itself
($z_{PG}$), using the information it learns from the continuous spectrum,
including local absorption/emission features. Only working together, the three
GaSNets efficiently pinpoint SGL candidates combining a high $P_{L}$ with the
condition that the $z_{PE}>z_{PG}$, as expected for typical strong lensing
configurations.

In particular, by testing the GaSNets on a list of known spectroscopically
selected gravitational lenses in SDSS/BOSS (from Bolton et al. 2008,
Brownstein et al. 2012, and Shu et al. 2017) we have found that using a
$P_{L}>0.95$ we can recover about 80% of the strong lenses confirmed by HST.
This very conservative probability threshold provided a reasonable trade-off
between significant completeness and a reasonably small sample to visually
inspect, with low contamination from false-positive detection.

Using this set-up, with the condition that $z_{PE}>z_{PG}+0.1$, we have
applied the GaSNets to $\sim 1.3$ million spectra from the SDSS-DR16, after
having imposed some appropriate cuts to guarantee a good spectrum quality and
the visibility of at least two emission lines from the putative sources
(namely, [OII] and $H_{\gamma}$), assumed to be star-forming galaxies.

We have collected $\sim 930$ candidates that have been further cleaned by
misclassified SGL events, via visual inspection. The final sample of visual HQ
candidates is made of 497 spectroscopic selected objects. This catalog has
been a posteriori compared to the most extended catalog of spectroscopic
selected lens candidates from T+21 and found an overlap of only 68 candidates,
meaning that 429 of our candidates are newly found. On the other hand, we have
demonstrated that GaSNets did not recover the remaining T+21 sample because of
the conservative constraints we have adopted for the number of lines to be
detected ($>2$). Releasing them, half of the sample from T+21 (i.e. the one
for which GaSNets has $P_{L}>0.95$) remains under the GaSNets discovery reach.

For the new HQ catalog, we provide RA, DEC, the probability, $P_{L}$, the
redshift of the galaxy from the eBOSS catalog, the predicted redshift of the
galaxy from GaSNet-L3, the predicted redshift of the background source from
GaSNet-L2, the corrected redshift of the source from the visual inspection, in
Appendix A.

To estimate a tentative confirmation rate of these candidates, we have matched
the coordinates with archive HST observations and found no matches. Instead,
we have found optical counterparts in DECaLS, KiDS, and HST observations, but
only HSC has provided sufficient statistics and image quality to confidently
confirm the first sample of GaSNets’ candidates. Among these, we have
independently confirmed 8 SGL candidates from previous HSC lens imaging
searches, thus providing spectroscopic evidence of lensing events, even though
for only 3 of them we have found convincing features in the imaging to be
“sure lens”. Besides these “known” lenses, we have found a preliminary optical
confirmation of a further 24 GaSNet HQ candidates, although, also in this
case, for 17 of them the HSC images allowed only a “maybe lens” B-grade, and
only 7 have a “sure lens” A-grade. Taking the A-grade as bona fide lenses and
giving a 0.5 weight to the B-grade candidates, we have estimated a
confirmation rate of $38\%$ for our HQ catalog.

Some examples of the HSC matched are shown in Fig. 18, where we also show low-
graded imaging of GaSNet candidates. The possible contaminants are higher
redshift galaxies, overlapping in the fiber spectra, or maybe local phenomena
mimicking an SGL event. For example, local gas outflows, with typical
velocities of $3\times 10^{3}$ kms-1, will introduce asymmetric velocity
distribution along the ejection direction (Veilleux et al. 2020), which would
shift the wavelength of some characteristic emission lines. Among these the
[OIII] line could deviate from the $z_{G}$ by $\sim 50$Å and produce a false
positive.

In this paper, we have demonstrated that Deep Learning represents a very
efficient method to search for strong lenses in galaxy spectra. This can be
applied to next generation spectroscopic surveys in a fast and automated way.
This first application to the eBOSS database has confirmed that the
spectroscopic selection of SGL candidates is complementary to the imaging-
based SGL searches. For instance, of the 32 A/B grade candidates from the
GaSNets matching with HSC imaging, only 8 were found previously on HSC images.
This over-performance of the spectroscopic searches with respect to imaging is
particularly evident for ground-based observations, where the typical seeing
has no impact on emission lines of background sources in spectra but makes it
hard to resolve low-separation gravitational arcs of the same sources.

For this first application, we have made conservative choices regarding 1) the
number of features to use for the training of the GaSNets; 2) the overall
Network architecture, e.g. limiting the interconnections between the three
GaSNets 3) the probability threshold to optimize the sample to visual inspect
and keep the false positive under control. These are all directions to
consider for future improvements. As a final positive note, we have discussed
that the GaSNet-L3, in particular, has reached an accuracy and scatter of its
predictions, sufficient to be used to automatically measure galaxy redshifts
in large spectroscopic surveys.

## Acknowledgements

We thank Dr. C. Tortora and Dr. Y. Shu for useful comments on the manuscripts.
RL acknowledges the science research grants from the China Manned Space
Project (No CMS-CSST-2021-B01,CMS-CSST-2021-A01). NRN acknowledges financial
support from the “One hundred top talent program of Sun Yat-sen University”
grant N. 71000-18841229.

## Data Availability

The data that support the findings of this study are available at the URLs
provided in the text and the Table in Appendix A. All other data that are not
provided in the paper can be requested from the authors.

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##  Appendix A HQ catalog from GaSNets

In this appendix we list the HQ candidates obtained with the GaSNets and
described in §5. The table content is listed in §5.4.

New HQ candidates from GaSNets
---
| RA | DEC | PLATE | MJD | FIBER | $P_{L}$ | z | $z_{PG}$ | $z_{PE}$ | $mean_{eyeZE}$ | $P_{T}$
1 | 27.6755 | -7.1667 | 7164 | 56597 | 275 | 1.0 | 0.126 | 0.125 | 0.322 | 0.297 | 1.0
2 | 356.6865 | 34.8954 | 7143 | 56572 | 678 | 1.0 | 0.095 | 0.096 | 0.291 | 0.276 | 1.0
3 | 124.173 | 18.6976 | 4486 | 55588 | 218 | 1.0 | 0.221 | 0.221 | 0.636 | 0.641 | 1.0
4 | 139.3617 | 31.157 | 5808 | 56325 | 434 | 1.0 | 0.239 | 0.238 | 0.823 | 0.82 | 1.0
5 | 205.2421 | 18.6312 | 5862 | 56045 | 110 | 1.0 | 0.244 | 0.244 | 0.638 | 0.645 | 1.0
6 | 233.5735 | 3.4663 | 4805 | 55715 | 326 | 1.0 | 0.291 | 0.288 | 0.707 | 0.708 | 1.0
7 | 22.0923 | 22.3834 | 5107 | 55940 | 409 | 1.0 | 0.277 | 0.275 | 0.7 | 0.695 | 1.0
8 | 356.4175 | -2.1613 | 4356 | 55829 | 729 | 1.0 | 0.294 | 0.294 | 0.659 | 0.658 | 1.0
9 | 9.4789 | 17.8124 | 6193 | 56237 | 298 | 1.0 | 0.298 | 0.297 | 0.695 | 0.695 | 1.0
10 | 4.8287 | 26.2703 | 6276 | 56269 | 26 | 1.0 | 0.262 | 0.262 | 0.6 | 0.604 | 1.0
11 | 244.2444 | 59.9424 | 6976 | 56448 | 830 | 1.0 | 0.257 | 0.258 | 0.509 | 0.507 | 1.0
12 | 221.3814 | 60.9204 | 6982 | 56444 | 516 | 1.0 | 0.258 | 0.257 | 0.501 | 0.511 | 1.0
13 | 228.0721 | 14.4225 | 5486 | 56030 | 270 | 1.0 | 0.327 | 0.327 | 0.706 | 0.708 | 1.0
14 | 143.3092 | 22.088 | 5770 | 56014 | 842 | 1.0 | 0.35 | 0.35 | 0.694 | 0.694 | 1.0
15 | 352.9407 | 29.3635 | 6581 | 56540 | 976 | 1.0 | 0.313 | 0.312 | 0.68 | 0.678 | 1.0
16 | 202.7383 | 47.6651 | 6743 | 56385 | 86 | 1.0 | 0.349 | 0.35 | 0.662 | 0.662 | 1.0
17 | 145.3751 | 1.865 | 4736 | 55631 | 264 | 1.0 | 0.353 | 0.354 | 0.719 | 0.722 | 1.0
18 | 212.4583 | 58.3783 | 6804 | 56447 | 957 | 1.0 | 0.36 | 0.36 | 0.744 | 0.742 | 1.0
19 | 189.6944 | 51.0158 | 6674 | 56416 | 262 | 1.0 | 0.388 | 0.387 | 0.762 | 0.766 | 1.0
20 | 358.2568 | 32.3241 | 6498 | 56565 | 550 | 1.0 | 0.367 | 0.366 | 0.729 | 0.731 | 1.0
21 | 215.0974 | 30.7816 | 3866 | 55623 | 45 | 1.0 | 0.466 | 0.47 | 0.813 | 0.814 | 1.0
22 | 127.2466 | 6.7193 | 4866 | 55895 | 335 | 1.0 | 0.47 | 0.471 | 0.878 | 0.877 | 1.0
23 | 176.7038 | 31.9488 | 4614 | 55604 | 299 | 1.0 | 0.478 | 0.479 | 0.845 | 0.846 | 1.0
24 | 322.7388 | -1.587 | 4384 | 56105 | 873 | 1.0 | 0.506 | 0.509 | 0.81 | 0.814 | 1.0
25 | 338.7334 | 15.1238 | 5038 | 56235 | 231 | 1.0 | 0.514 | 0.513 | 0.822 | 0.825 | 1.0
26 | 118.3424 | 11.0724 | 4511 | 55602 | 755 | 1.0 | 0.565 | 0.558 | 0.82 | 0.824 | 1.0
27 | 189.7042 | 24.9656 | 5984 | 56337 | 333 | 1.0 | 0.559 | 0.558 | 0.826 | 0.828 | 1.0
28 | 153.3944 | 25.7594 | 6465 | 56279 | 537 | 1.0 | 0.616 | 0.619 | 0.825 | 0.828 | 1.0
29 | 321.1025 | 1.1421 | 4193 | 55476 | 665 | 1.0 | 0.7 | 0.7 | 0.875 | 0.878 | 1.0
30 | 358.3876 | -8.6495 | 7166 | 56602 | 784 | 1.0 | 0.167 | 0.167 | 0.653 | 0.657 | 1.0
31 | 253.2719 | 50.6749 | 6311 | 56447 | 56 | 1.0 | 0.095 | 0.093 | 0.57 | 0.575 | 1.0
32 | 321.5421 | 1.9777 | 5143 | 55828 | 640 | 1.0 | 0.152 | 0.151 | 0.772 | 0.78 | 1.0
33 | 150.7402 | 6.319 | 4874 | 55673 | 82 | 1.0 | 0.225 | 0.225 | 0.781 | 0.781 | 1.0
34 | 17.3453 | 18.7404 | 5124 | 55894 | 36 | 1.0 | 0.226 | 0.226 | 0.645 | 0.644 | 1.0
35 | 207.8211 | -1.7923 | 4041 | 55361 | 522 | 1.0 | 0.208 | 0.208 | 0.77 | 0.774 | 1.0
36 | 31.4846 | -2.3339 | 4347 | 55830 | 156 | 1.0 | 0.283 | 0.281 | 0.462 | 0.462 | 1.0
37 | 181.6564 | 37.855 | 4700 | 55709 | 242 | 1.0 | 0.263 | 0.262 | 0.607 | 0.609 | 1.0
38 | 26.7007 | 22.0027 | 5108 | 55888 | 811 | 1.0 | 0.267 | 0.266 | 0.745 | 0.745 | 1.0
39 | 128.9045 | 8.3751 | 5285 | 55946 | 510 | 1.0 | 0.259 | 0.258 | 0.555 | 0.558 | 1.0
40 | 42.3078 | -2.8227 | 4342 | 55531 | 112 | 1.0 | 0.292 | 0.29 | 0.459 | 0.459 | 1.0
41 | 18.952 | 5.1636 | 4425 | 55864 | 376 | 1.0 | 0.337 | 0.336 | 0.607 | 0.606 | 1.0
42 | 173.7037 | 54.187 | 6697 | 56419 | 386 | 1.0 | 0.302 | 0.301 | 0.614 | 0.613 | 1.0
43 | 134.3035 | 19.7311 | 5175 | 55955 | 804 | 1.0 | 0.377 | 0.379 | 0.632 | 0.629 | 1.0
44 | 145.78 | 55.292 | 5710 | 56658 | 116 | 1.0 | 0.355 | 0.356 | 0.607 | 0.609 | 1.0
45 | 258.3841 | 42.9416 | 6062 | 56091 | 91 | 1.0 | 0.352 | 0.354 | 0.713 | 0.714 | 1.0
46 | 242.464 | 37.8714 | 5200 | 56091 | 151 | 1.0 | 0.448 | 0.448 | 0.648 | 0.648 | 1.0
47 | 176.8551 | 35.8301 | 4646 | 55622 | 879 | 1.0 | 0.473 | 0.473 | 0.658 | 0.658 | 1.0
48 | 199.5047 | 14.466 | 5425 | 56003 | 820 | 1.0 | 0.478 | 0.481 | 0.826 | 0.825 | 1.0
49 | 203.1219 | 19.9543 | 5861 | 56069 | 347 | 1.0 | 0.494 | 0.496 | 0.831 | 0.835 | 1.0
50 | 189.5541 | 23.2605 | 5983 | 56310 | 25 | 1.0 | 0.48 | 0.48 | 0.849 | 0.85 | 1.0

| RA | DEC | PLATE | MJD | FIBER | $P_{L}$ | z | $z_{PG}$ | $z_{PE}$ | $mean_{eyeZE}$ | $P_{T}$
---|---|---|---|---|---|---|---|---|---|---|---
51 | 248.9654 | 17.222 | 4064 | 55366 | 77 | 1.0 | 0.497 | 0.496 | 0.715 | 0.714 | 1.0
52 | 189.5441 | 46.0467 | 6635 | 56370 | 501 | 1.0 | 0.492 | 0.493 | 0.822 | 0.823 | 1.0
53 | 219.7836 | 54.8809 | 6710 | 56416 | 27 | 1.0 | 0.461 | 0.462 | 0.722 | 0.722 | 1.0
54 | 214.9087 | 19.692 | 5895 | 56046 | 973 | 1.0 | 0.528 | 0.527 | 0.883 | 0.883 | 1.0
55 | 331.1801 | 30.5522 | 5961 | 56460 | 545 | 1.0 | 0.538 | 0.552 | 0.83 | 0.832 | 1.0
56 | 6.3176 | 28.2843 | 6274 | 56550 | 455 | 1.0 | 0.501 | 0.502 | 0.816 | 0.816 | 1.0
57 | 240.6962 | 7.4048 | 4893 | 55709 | 858 | 1.0 | 0.622 | 0.623 | 0.869 | 0.874 | 1.0
58 | 115.6977 | 25.8798 | 4462 | 55600 | 271 | 1.0 | 0.441 | 0.441 | 0.682 | 0.684 | 1.0
59 | 160.3564 | 43.6801 | 4690 | 55653 | 424 | 1.0 | 0.238 | 0.236 | 0.439 | 0.439 | 1.0
60 | 180.9566 | 23.4359 | 5969 | 56069 | 846 | 1.0 | 0.263 | 0.263 | 0.612 | 0.619 | 1.0
61 | 177.6002 | 19.2965 | 5881 | 56038 | 604 | 1.0 | 0.289 | 0.288 | 0.476 | 0.474 | 1.0
62 | 139.0009 | 21.6609 | 5771 | 56011 | 574 | 1.0 | 0.322 | 0.322 | 0.511 | 0.508 | 1.0
63 | 30.0581 | 3.8889 | 4270 | 55511 | 7 | 1.0 | 0.429 | 0.427 | 0.776 | 0.754 | 1.0
64 | 133.0317 | 40.5817 | 4607 | 56248 | 711 | 1.0 | 0.447 | 0.446 | 0.842 | 0.844 | 1.0
65 | 129.9769 | 59.5436 | 5148 | 56220 | 583 | 1.0 | 0.475 | 0.474 | 0.821 | 0.822 | 1.0
66 | 164.8521 | 11.0051 | 5356 | 55979 | 881 | 1.0 | 0.473 | 0.473 | 0.832 | 0.834 | 1.0
67 | 189.5441 | 46.0467 | 6667 | 56412 | 1 | 1.0 | 0.491 | 0.493 | 0.822 | 0.822 | 1.0
68 | 154.1187 | 9.2856 | 5334 | 55928 | 953 | 1.0 | 0.545 | 0.544 | 0.859 | 0.86 | 1.0
69 | 354.6202 | 27.6904 | 6516 | 56571 | 543 | 1.0 | 0.549 | 0.547 | 0.846 | 0.848 | 1.0
70 | 118.5745 | 16.4872 | 4495 | 55566 | 811 | 1.0 | 0.607 | 0.607 | 0.812 | 0.814 | 1.0
71 | 152.2575 | 38.1894 | 4567 | 55589 | 235 | 1.0 | 0.648 | 0.648 | 0.828 | 0.828 | 1.0
72 | 337.6706 | -1.1175 | 4203 | 55447 | 368 | 1.0 | 0.33 | 0.33 | 0.526 | 0.531 | 1.0
73 | 251.7678 | 29.8492 | 4189 | 55679 | 752 | 1.0 | 0.375 | 0.374 | 0.59 | 0.591 | 1.0
74 | 137.8548 | 16.6327 | 5301 | 55987 | 328 | 1.0 | 0.394 | 0.394 | 0.693 | 0.698 | 1.0
75 | 18.8537 | -1.4834 | 4353 | 55532 | 663 | 1.0 | 0.438 | 0.438 | 0.802 | 0.805 | 1.0
76 | 144.1259 | 17.0156 | 5317 | 56000 | 579 | 1.0 | 0.403 | 0.404 | 0.819 | 0.821 | 1.0
77 | 6.512 | 9.7381 | 6195 | 56220 | 424 | 1.0 | 0.246 | 0.244 | 0.391 | 0.39 | 1.0
78 | 160.1055 | 3.5501 | 4773 | 55648 | 290 | 1.0 | 0.439 | 0.438 | 0.642 | 0.643 | 1.0
79 | 213.0731 | 46.9419 | 6751 | 56368 | 355 | 1.0 | 0.402 | 0.405 | 0.657 | 0.653 | 1.0
80 | 215.0974 | 30.7816 | 3867 | 55652 | 579 | 1.0 | 0.466 | 0.465 | 0.813 | 0.814 | 1.0
81 | 137.8928 | 43.2083 | 4687 | 56369 | 409 | 1.0 | 0.497 | 0.495 | 0.837 | 0.84 | 1.0
82 | 135.5464 | 1.2383 | 3816 | 55272 | 61 | 1.0 | 0.514 | 0.513 | 0.831 | 0.833 | 1.0
83 | 143.9865 | 53.3553 | 5724 | 56364 | 508 | 1.0 | 0.198 | 0.198 | 0.424 | 0.424 | 1.0
84 | 28.2369 | -2.3081 | 4348 | 55559 | 155 | 1.0 | 0.534 | 0.536 | 0.669 | 0.665 | 1.0
85 | 350.6051 | 34.2495 | 7139 | 56568 | 687 | 1.0 | 0.292 | 0.29 | 0.612 | 0.612 | 1.0
86 | 224.9773 | -2.6469 | 4020 | 55332 | 247 | 1.0 | 0.511 | 0.509 | 0.824 | 0.83 | 1.0
87 | 6.2129 | -2.6018 | 4367 | 55566 | 263 | 1.0 | 0.583 | 0.584 | 0.85 | 0.852 | 1.0
88 | 156.6438 | 37.2146 | 4559 | 55597 | 409 | 1.0 | 0.484 | 0.484 | 0.636 | 0.639 | 1.0
89 | 185.1209 | 10.9196 | 5399 | 55956 | 433 | 1.0 | 0.507 | 0.507 | 0.707 | 0.712 | 1.0
90 | 140.0093 | 36.1607 | 4644 | 55922 | 855 | 1.0 | 0.595 | 0.594 | 0.882 | 0.883 | 1.0
91 | 201.2076 | 5.5061 | 4839 | 55703 | 339 | 1.0 | 0.58 | 0.581 | 1.018 | 1.018 | 1.0
92 | 184.1385 | 35.6992 | 4613 | 55591 | 234 | 0.999 | 0.347 | 0.347 | 0.728 | 0.73 | 1.0
93 | 22.0924 | -3.7932 | 7047 | 56572 | 878 | 0.999 | 0.395 | 0.394 | 0.598 | 0.654 | 1.0
94 | 7.5599 | 24.7932 | 6281 | 56295 | 145 | 0.999 | 0.405 | 0.402 | 0.874 | 0.876 | 1.0
95 | 180.5188 | 55.022 | 6688 | 56412 | 521 | 0.999 | 0.512 | 0.512 | 0.83 | 0.832 | 1.0
96 | 9.2422 | 10.4302 | 5656 | 55940 | 264 | 0.999 | 0.178 | 0.178 | 0.357 | 0.361 | 1.0
97 | 336.5143 | 28.8703 | 6586 | 56485 | 471 | 0.999 | 0.507 | 0.502 | 0.825 | 0.829 | 1.0
98 | 39.6814 | -5.6274 | 4399 | 55811 | 917 | 0.999 | 0.358 | 0.358 | 0.726 | 0.724 | 1.0
99 | 333.8121 | 13.4517 | 5041 | 55749 | 103 | 0.999 | 0.605 | 0.608 | 0.941 | 0.944 | 1.0
100 | 5.8983 | -6.5602 | 7151 | 56598 | 634 | 0.999 | 0.292 | 0.291 | 0.541 | 0.534 | 1.0

| RA | DEC | PLATE | MJD | FIBER | $P_{L}$ | z | $z_{PG}$ | $z_{PE}$ | $mean_{eyeZE}$ | $P_{T}$
---|---|---|---|---|---|---|---|---|---|---|---
101 | 9.2422 | 10.4302 | 6201 | 56186 | 264 | 0.999 | 0.178 | 0.178 | 0.361 | 0.361 | 1.0
102 | 236.1196 | 19.2834 | 3937 | 55352 | 191 | 0.999 | 0.468 | 0.469 | 0.831 | 0.834 | 1.0
103 | 135.0759 | 24.7684 | 5179 | 55957 | 95 | 0.999 | 0.476 | 0.477 | 0.803 | 0.807 | 1.0
104 | 177.0745 | 26.108 | 6411 | 56331 | 427 | 0.999 | 0.291 | 0.289 | 0.74 | 0.742 | 1.0
105 | 134.2845 | 35.8839 | 4602 | 55644 | 841 | 0.999 | 0.538 | 0.54 | 0.679 | 0.675 | 1.0
106 | 3.0886 | 2.5671 | 4298 | 55511 | 759 | 0.999 | 0.414 | 0.413 | 0.691 | 0.688 | 1.0
107 | 251.1692 | 50.6684 | 6311 | 56447 | 334 | 0.999 | 0.182 | 0.183 | 0.702 | 0.712 | 1.0
108 | 255.5705 | 36.1605 | 4988 | 55825 | 645 | 0.998 | 0.552 | 0.553 | 0.73 | 0.731 | 1.0
109 | 353.1292 | 21.7432 | 6115 | 56237 | 979 | 0.998 | 0.369 | 0.368 | 0.627 | 0.629 | 1.0
110 | 200.5318 | 26.3394 | 5996 | 56096 | 706 | 0.998 | 0.304 | 0.303 | 0.626 | 0.63 | 1.0
111 | 1.4434 | 15.5096 | 6177 | 56268 | 906 | 0.998 | 0.295 | 0.294 | 0.4 | 0.4 | 1.0
112 | 339.6335 | 29.3202 | 6585 | 56479 | 719 | 0.998 | 0.482 | 0.482 | 0.68 | 0.68 | 1.0
113 | 5.6359 | -0.3464 | 4220 | 55447 | 481 | 0.998 | 0.498 | 0.5 | 1.037 | 0.632 | 1.0
114 | 208.6658 | 51.3517 | 6740 | 56401 | 11 | 0.998 | 0.491 | 0.49 | 0.683 | 0.684 | 1.0
115 | 337.2294 | 24.2962 | 6300 | 56449 | 292 | 0.998 | 0.309 | 0.308 | 0.434 | 0.432 | 1.0
116 | 195.0441 | 9.6711 | 5417 | 55978 | 646 | 0.998 | 0.297 | 0.297 | 0.565 | 0.564 | 1.0
117 | 203.5244 | 53.5181 | 6757 | 56416 | 275 | 0.998 | 0.49 | 0.49 | 0.739 | 0.739 | 1.0
118 | 243.9984 | 51.2459 | 6316 | 56483 | 834 | 0.998 | 0.359 | 0.36 | 0.482 | 0.478 | 1.0
119 | 197.2786 | 11.4382 | 5422 | 55986 | 379 | 0.998 | 0.525 | 0.524 | 0.719 | 0.721 | 1.0
120 | 175.9948 | 45.3268 | 6645 | 56398 | 264 | 0.997 | 0.44 | 0.441 | 0.548 | 0.544 | 1.0
121 | 185.4293 | 40.7285 | 6633 | 56369 | 164 | 0.997 | 0.216 | 0.216 | 0.507 | 0.501 | 1.0
122 | 156.8435 | 46.1132 | 6659 | 56607 | 299 | 0.997 | 0.521 | 0.52 | 0.749 | 0.75 | 1.0
123 | 124.7393 | 29.6162 | 4447 | 55542 | 81 | 0.997 | 0.579 | 0.576 | 0.757 | 0.756 | 1.0
124 | 137.5782 | 34.9972 | 5811 | 56334 | 583 | 0.997 | 0.52 | 0.521 | 0.666 | 0.666 | 1.0
125 | 1.4434 | 15.5096 | 6172 | 56269 | 69 | 0.996 | 0.295 | 0.294 | 0.399 | 0.4 | 1.0
126 | 161.1167 | 13.2743 | 5348 | 55978 | 957 | 0.996 | 0.349 | 0.348 | 0.472 | 0.474 | 1.0
127 | 7.3882 | 29.8282 | 6274 | 56550 | 757 | 0.996 | 0.496 | 0.497 | 0.761 | 0.767 | 1.0
128 | 0.7136 | 15.5908 | 6177 | 56268 | 744 | 0.995 | 0.427 | 0.428 | 0.756 | 0.756 | 1.0
129 | 202.3971 | 16.0299 | 5434 | 56033 | 376 | 0.995 | 0.296 | 0.295 | 0.491 | 0.475 | 1.0
130 | 340.6461 | 5.7733 | 4411 | 56164 | 113 | 0.994 | 0.436 | 0.437 | 0.684 | 0.685 | 0.99
131 | 171.6804 | 23.9861 | 6421 | 56274 | 577 | 0.994 | 0.566 | 0.564 | 0.791 | 0.794 | 0.99
132 | 21.4969 | 19.6116 | 5135 | 55862 | 850 | 0.993 | 0.101 | 0.102 | 0.579 | 0.584 | 0.99
133 | 256.4372 | 30.4618 | 4997 | 55738 | 389 | 0.993 | 0.553 | 0.551 | 0.809 | 0.814 | 0.99
134 | 224.4952 | 18.075 | 5902 | 56042 | 203 | 0.993 | 0.47 | 0.483 | 0.914 | 0.912 | 0.99
135 | 172.253 | 20.7167 | 5879 | 56047 | 630 | 0.992 | 0.208 | 0.209 | 0.439 | 0.44 | 0.99
136 | 246.2337 | 28.3755 | 5007 | 55710 | 53 | 0.99 | 0.453 | 0.452 | 0.553 | 0.557 | 0.99
137 | 188.5778 | 57.148 | 6832 | 56426 | 591 | 0.99 | 0.432 | 0.433 | 0.797 | 0.798 | 0.99
138 | 350.4799 | 34.3269 | 7139 | 56568 | 640 | 0.99 | 0.292 | 0.291 | 0.403 | 0.398 | 0.99
139 | 185.5842 | 9.6532 | 5396 | 55947 | 939 | 0.989 | 0.465 | 0.477 | 0.718 | 0.72 | 0.99
140 | 15.5525 | 29.6444 | 6257 | 56274 | 28 | 0.989 | 0.359 | 0.359 | 0.472 | 0.474 | 0.99
141 | 328.2786 | 25.191 | 5960 | 56097 | 96 | 0.989 | 0.201 | 0.201 | 0.553 | 0.555 | 0.99
142 | 13.899 | 11.3643 | 5706 | 56165 | 718 | 0.988 | 0.082 | 0.083 | 0.727 | 0.717 | 0.99
143 | 20.6702 | 24.4333 | 5693 | 56246 | 139 | 0.988 | 0.542 | 0.541 | 0.731 | 0.724 | 0.99
144 | 125.5973 | 32.6817 | 4446 | 55589 | 756 | 0.987 | 0.553 | 0.553 | 0.805 | 0.806 | 0.99
145 | 178.7055 | 4.095 | 4765 | 55674 | 115 | 0.986 | 0.443 | 0.444 | 0.65 | 0.649 | 0.99
146 | 139.9778 | 0.8461 | 3821 | 55535 | 955 | 0.986 | 0.433 | 0.432 | 0.587 | 0.587 | 0.99
147 | 322.6555 | -0.5033 | 4193 | 55476 | 21 | 0.985 | 0.47 | 0.471 | 0.754 | 0.757 | 0.98
148 | 342.6829 | 31.1553 | 6508 | 56535 | 998 | 0.982 | 0.425 | 0.426 | 0.69 | 0.696 | 0.98
149 | 221.893 | 16.5992 | 5474 | 56036 | 341 | 0.98 | 0.53 | 0.53 | 0.771 | 0.771 | 0.98
150 | 249.4794 | 33.6617 | 5188 | 55803 | 146 | 0.98 | 0.335 | 0.333 | 0.535 | 0.534 | 0.98

| RA | DEC | PLATE | MJD | FIBER | $P_{L}$ | z | $z_{PG}$ | $z_{PE}$ | $mean_{eyeZE}$ | $P_{T}$
---|---|---|---|---|---|---|---|---|---|---|---
151 | 137.5782 | 34.9972 | 4645 | 55623 | 95 | 0.979 | 0.519 | 0.522 | 0.667 | 0.667 | 0.98
152 | 169.6515 | 11.6851 | 5368 | 56001 | 392 | 0.979 | 0.504 | 0.506 | 0.617 | 0.615 | 0.98
153 | 17.4289 | 30.2485 | 6263 | 56279 | 445 | 0.976 | 0.385 | 0.384 | 0.689 | 0.69 | 0.98
154 | 141.3097 | 23.3655 | 5774 | 56002 | 235 | 0.975 | 0.575 | 0.573 | 0.768 | 0.769 | 0.98
155 | 353.682 | 30.3667 | 6501 | 56563 | 228 | 0.973 | 0.079 | 0.079 | 0.534 | 0.544 | 0.97
156 | 123.0994 | 38.6284 | 3805 | 55269 | 423 | 0.972 | 0.5 | 0.502 | 0.726 | 0.723 | 0.97
157 | 209.103 | 36.1326 | 3853 | 55268 | 951 | 0.966 | 0.555 | 0.558 | 0.764 | 0.756 | 0.97
158 | 13.3108 | 1.9039 | 4308 | 55565 | 439 | 0.966 | 0.494 | 0.493 | 0.675 | 0.675 | 0.97
159 | 206.6969 | 4.1721 | 4785 | 55659 | 610 | 0.966 | 0.414 | 0.416 | 0.623 | 0.623 | 0.97
160 | 225.1194 | 61.5364 | 6982 | 56444 | 843 | 0.963 | 0.506 | 0.506 | 0.793 | 0.797 | 0.96
161 | 15.3889 | 20.9285 | 5703 | 56190 | 896 | 0.959 | 0.403 | 0.402 | 0.762 | 0.764 | 0.96
162 | 197.0164 | 28.3228 | 6483 | 56341 | 63 | 0.953 | 0.582 | 0.58 | 0.764 | 0.764 | 0.95
163 | 136.6796 | 30.4776 | 5809 | 56353 | 409 | 0.953 | 0.512 | 0.513 | 0.73 | 0.73 | 0.95
164 | 169.6424 | 18.8327 | 5878 | 56033 | 391 | 0.953 | 0.439 | 0.439 | 0.637 | 0.634 | 0.95
165 | 334.2061 | 5.2761 | 4319 | 55507 | 547 | 0.952 | 0.512 | 0.514 | 0.671 | 0.67 | 0.95
166 | 150.7027 | 20.8144 | 5784 | 56029 | 104 | 0.951 | 0.372 | 0.371 | 0.492 | 0.492 | 0.95
167 | 172.5368 | 12.4397 | 5372 | 55978 | 709 | 0.95 | 0.492 | 0.491 | 0.777 | 0.781 | 0.95
168 | 114.5797 | 22.8478 | 4470 | 55587 | 420 | 1.0 | 0.205 | 0.205 | 0.624 | 0.623 | 0.9
169 | 22.4308 | 7.8777 | 4553 | 55584 | 393 | 1.0 | 0.437 | 0.438 | 0.838 | 0.838 | 0.9
170 | 5.0461 | 32.0964 | 7128 | 56567 | 584 | 0.999 | 0.162 | 0.162 | 0.325 | 0.319 | 0.9
171 | 152.2732 | 40.8465 | 4562 | 55570 | 557 | 0.999 | 0.512 | 0.51 | 0.668 | 0.667 | 0.9
172 | 317.5483 | 5.4372 | 4078 | 55358 | 620 | 0.999 | 0.414 | 0.416 | 0.721 | 0.721 | 0.9
173 | 211.6158 | 15.8081 | 5451 | 56010 | 815 | 0.999 | 0.476 | 0.475 | 0.812 | 0.815 | 0.9
174 | 234.0938 | 51.1223 | 6722 | 56431 | 735 | 0.999 | 0.596 | 0.595 | 0.736 | 0.735 | 0.9
175 | 208.9611 | 32.3567 | 3861 | 55274 | 229 | 0.999 | 0.487 | 0.488 | 0.695 | 0.696 | 0.9
176 | 220.9617 | 1.3445 | 4021 | 55620 | 106 | 0.999 | 0.526 | 0.527 | 0.674 | 0.671 | 0.9
177 | 223.3063 | 6.3302 | 4857 | 55711 | 393 | 0.999 | 0.566 | 0.571 | 0.696 | 0.694 | 0.9
178 | 8.9715 | 5.6913 | 4419 | 55867 | 498 | 0.999 | 0.365 | 0.366 | 0.674 | 0.669 | 0.9
179 | 356.9756 | 20.0522 | 6126 | 56269 | 845 | 0.999 | 0.411 | 0.412 | 0.741 | 0.741 | 0.9
180 | 237.5934 | 52.8266 | 6715 | 56449 | 938 | 0.999 | 0.442 | 0.443 | 0.731 | 0.733 | 0.9
181 | 16.4021 | 28.2601 | 6259 | 56565 | 461 | 0.999 | 0.486 | 0.486 | 0.884 | 0.781 | 0.9
182 | 176.2923 | 0.7391 | 3841 | 56016 | 957 | 0.999 | 0.53 | 0.524 | 0.642 | 0.642 | 0.9
183 | 127.3317 | 54.1993 | 5156 | 55925 | 574 | 0.999 | 0.361 | 0.36 | 0.678 | 0.675 | 0.9
184 | 216.0698 | 4.4967 | 4781 | 55653 | 660 | 0.999 | 0.309 | 0.309 | 0.565 | 0.563 | 0.9
185 | 346.7121 | 22.9308 | 6591 | 56535 | 991 | 0.998 | 0.194 | 0.195 | 0.586 | 0.587 | 0.9
186 | 343.2212 | 15.6879 | 5040 | 56243 | 734 | 0.998 | 0.273 | 0.272 | 0.674 | 0.419 | 0.9
187 | 191.5569 | 12.2667 | 5409 | 55957 | 966 | 0.997 | 0.633 | 0.633 | 0.826 | 0.827 | 0.9
188 | 191.3409 | 17.2785 | 5856 | 56090 | 427 | 0.997 | 0.559 | 0.557 | 0.726 | 0.726 | 0.9
189 | 233.1948 | -0.6518 | 4010 | 55350 | 236 | 0.997 | 0.342 | 0.343 | 0.686 | 0.685 | 0.9
190 | 40.7073 | -3.6349 | 7053 | 56564 | 664 | 0.997 | 0.28 | 0.278 | 0.445 | 0.44 | 0.9
191 | 325.0915 | 4.4258 | 4083 | 55443 | 908 | 0.996 | 0.509 | 0.509 | 0.633 | 0.637 | 0.9
192 | 146.7165 | 58.7815 | 5715 | 56598 | 782 | 0.996 | 0.349 | 0.349 | 0.577 | 0.649 | 0.9
193 | 0.7136 | 15.5908 | 6172 | 56269 | 232 | 0.996 | 0.427 | 0.428 | 0.754 | 0.757 | 0.9
194 | 232.7971 | 52.0507 | 6722 | 56431 | 545 | 0.995 | 0.482 | 0.487 | 0.784 | 0.785 | 0.9
195 | 332.4037 | 31.2179 | 5954 | 56462 | 521 | 0.995 | 0.481 | 0.479 | 0.836 | 0.836 | 0.9
196 | 13.8325 | 3.9522 | 4307 | 55531 | 699 | 0.994 | 0.664 | 0.666 | 0.835 | 0.827 | 0.9
197 | 211.0407 | 40.2749 | 6630 | 56358 | 67 | 0.993 | 0.51 | 0.506 | 0.629 | 0.626 | 0.89
198 | 220.7873 | 35.7258 | 4718 | 56014 | 659 | 0.993 | 0.557 | 0.556 | 0.761 | 0.764 | 0.89
199 | 174.6345 | 15.131 | 5378 | 56011 | 392 | 0.993 | 0.254 | 0.253 | 0.493 | 0.436 | 0.89
200 | 161.1167 | 13.2743 | 5350 | 56009 | 284 | 0.992 | 0.349 | 0.349 | 0.466 | 0.473 | 0.89

| RA | DEC | PLATE | MJD | FIBER | $P_{L}$ | z | $z_{PG}$ | $z_{PE}$ | $mean_{eyeZE}$ | $P_{T}$
---|---|---|---|---|---|---|---|---|---|---|---
201 | 233.7202 | 30.6619 | 4722 | 55735 | 603 | 0.992 | 0.546 | 0.544 | 0.669 | 0.67 | 0.89
202 | 23.0487 | 25.9812 | 5694 | 56213 | 919 | 0.992 | 0.494 | 0.495 | 0.704 | 0.678 | 0.89
203 | 163.2455 | 40.0812 | 4629 | 55630 | 852 | 0.991 | 0.302 | 0.303 | 0.638 | 0.583 | 0.89
204 | 191.086 | -2.7746 | 3793 | 55214 | 203 | 0.991 | 0.55 | 0.55 | 0.713 | 0.716 | 0.89
205 | 238.0017 | 12.4111 | 4882 | 55721 | 634 | 0.99 | 0.107 | 0.108 | 0.486 | 0.483 | 0.89
206 | 163.8696 | 31.3152 | 6445 | 56366 | 883 | 0.99 | 0.453 | 0.451 | 0.802 | 0.816 | 0.89
207 | 178.0232 | 21.705 | 6407 | 56311 | 543 | 0.99 | 0.618 | 0.619 | 0.772 | 0.775 | 0.89
208 | 339.1266 | 9.5256 | 5054 | 56191 | 495 | 0.989 | 0.424 | 0.425 | 0.74 | 0.74 | 0.89
209 | 29.6199 | 1.0778 | 4234 | 55478 | 548 | 0.988 | 0.325 | 0.324 | 0.781 | 0.781 | 0.89
210 | 176.0852 | 30.9175 | 6433 | 56339 | 930 | 0.987 | 0.076 | 0.076 | 0.623 | 0.695 | 0.89
211 | 228.2038 | 53.9555 | 6713 | 56402 | 396 | 0.985 | 0.441 | 0.44 | 0.621 | 0.624 | 0.89
212 | 336.7086 | 5.148 | 4428 | 56189 | 98 | 0.984 | 0.09 | 0.09 | 0.401 | 0.406 | 0.89
213 | 174.3192 | 32.0515 | 4616 | 55617 | 283 | 0.984 | 0.456 | 0.461 | 0.641 | 0.641 | 0.88
214 | 157.7968 | 28.1283 | 6456 | 56339 | 122 | 0.983 | 0.312 | 0.311 | 0.549 | 0.555 | 0.88
215 | 233.2035 | 26.8323 | 3959 | 55679 | 69 | 0.982 | 0.523 | 0.524 | 0.668 | 0.664 | 0.88
216 | 186.9392 | 5.4132 | 4833 | 55679 | 266 | 0.979 | 0.47 | 0.47 | 0.634 | 0.625 | 0.88
217 | 336.3138 | 6.0182 | 4428 | 56189 | 199 | 0.979 | 0.498 | 0.5 | 0.736 | 0.734 | 0.88
218 | 174.0321 | 12.571 | 5376 | 55987 | 258 | 0.977 | 0.486 | 0.487 | 0.727 | 0.731 | 0.88
219 | 21.6396 | 14.2556 | 5140 | 55836 | 213 | 0.976 | 0.423 | 0.418 | 0.648 | 0.648 | 0.88
220 | 252.8827 | 36.6409 | 5198 | 55823 | 396 | 0.973 | 0.603 | 0.605 | 0.712 | 0.718 | 0.88
221 | 252.9652 | 35.5515 | 5198 | 55823 | 372 | 0.964 | 0.412 | 0.414 | 0.71 | 0.708 | 0.87
222 | 25.5021 | 31.3093 | 6601 | 56335 | 413 | 0.961 | 0.5 | 0.502 | 1.068 | 0.572 | 0.86
223 | 118.0482 | 15.4782 | 4495 | 55566 | 310 | 0.96 | 0.282 | 0.282 | 0.622 | 0.623 | 0.86
224 | 345.3411 | -1.4885 | 4362 | 55828 | 827 | 0.959 | 0.434 | 0.435 | 0.73 | 0.734 | 0.86
225 | 221.6961 | 7.9757 | 4858 | 55686 | 786 | 0.955 | 0.269 | 0.268 | 0.711 | 0.568 | 0.86
226 | 232.7992 | 10.7432 | 5493 | 56009 | 967 | 0.954 | 0.563 | 0.56 | 0.823 | 0.825 | 0.86
227 | 23.8523 | 14.5389 | 5137 | 55833 | 167 | 0.954 | 0.449 | 0.449 | 0.719 | 0.72 | 0.86
228 | 149.5008 | 10.1101 | 5324 | 55947 | 843 | 0.951 | 0.49 | 0.491 | 0.803 | 0.807 | 0.86
229 | 8.8946 | 9.0665 | 4540 | 55863 | 69 | 1.0 | 0.214 | 0.213 | 0.799 | 0.805 | 0.85
230 | 204.6975 | 5.1005 | 4786 | 55651 | 678 | 1.0 | 0.271 | 0.271 | 0.561 | 0.559 | 0.85
231 | 27.2466 | 21.0868 | 5108 | 55888 | 99 | 1.0 | 0.277 | 0.276 | 0.753 | 0.752 | 0.85
232 | 11.5709 | 25.3449 | 6286 | 56301 | 265 | 1.0 | 0.428 | 0.429 | 0.822 | 0.828 | 0.85
233 | 190.6792 | -0.3908 | 3793 | 55214 | 663 | 1.0 | 0.454 | 0.452 | 0.815 | 0.818 | 0.85
234 | 246.8241 | 19.5842 | 4061 | 55362 | 499 | 1.0 | 0.462 | 0.463 | 0.848 | 0.848 | 0.85
235 | 200.1508 | 12.4425 | 5427 | 56001 | 700 | 1.0 | 0.528 | 0.529 | 0.818 | 0.821 | 0.85
236 | 28.1217 | 9.5832 | 4530 | 55564 | 308 | 1.0 | 0.557 | 0.555 | 0.841 | 0.845 | 0.85
237 | 11.9627 | 31.0756 | 6872 | 56540 | 443 | 1.0 | 0.643 | 0.643 | 0.844 | 0.847 | 0.85
238 | 170.9226 | 13.9839 | 5370 | 56003 | 683 | 1.0 | 0.521 | 0.52 | 0.888 | 0.886 | 0.85
239 | 207.1491 | 9.5015 | 5442 | 55978 | 711 | 1.0 | 0.578 | 0.577 | 0.812 | 0.812 | 0.85
240 | 159.9814 | 8.136 | 5349 | 55929 | 379 | 1.0 | 0.617 | 0.619 | 0.873 | 0.875 | 0.85
241 | 169.8367 | 65.4877 | 7110 | 56746 | 833 | 1.0 | 0.529 | 0.527 | 0.826 | 0.826 | 0.85
242 | 182.5102 | 3.7887 | 4749 | 55633 | 381 | 1.0 | 0.596 | 0.597 | 0.885 | 0.885 | 0.85
243 | 150.4387 | 37.4688 | 4637 | 55616 | 705 | 1.0 | 0.677 | 0.677 | 0.847 | 0.848 | 0.85
244 | 248.9092 | 49.4879 | 8056 | 57186 | 769 | 1.0 | 0.671 | 0.672 | 0.89 | 0.891 | 0.85
245 | 338.5431 | 32.4454 | 6509 | 56486 | 788 | 1.0 | 0.422 | 0.422 | 0.84 | 0.842 | 0.85
246 | 195.6242 | 5.7652 | 4838 | 55686 | 467 | 1.0 | 0.492 | 0.493 | 0.879 | 0.883 | 0.85
247 | 154.1187 | 9.2856 | 5336 | 55957 | 321 | 1.0 | 0.545 | 0.542 | 0.86 | 0.86 | 0.85
248 | 160.0284 | 63.5812 | 7097 | 56667 | 865 | 1.0 | 0.528 | 0.528 | 0.836 | 0.836 | 0.85
249 | 143.962 | 15.6466 | 5315 | 55978 | 623 | 1.0 | 0.605 | 0.608 | 0.86 | 0.86 | 0.85
250 | 204.0295 | 33.6021 | 3985 | 55320 | 773 | 0.999 | 0.484 | 0.486 | 0.917 | 0.92 | 0.85

| RA | DEC | PLATE | MJD | FIBER | $P_{L}$ | z | $z_{PG}$ | $z_{PE}$ | $mean_{eyeZE}$ | $P_{T}$
---|---|---|---|---|---|---|---|---|---|---|---
251 | 226.5216 | 40.6238 | 6054 | 56089 | 256 | 0.999 | 0.483 | 0.481 | 0.628 | 0.628 | 0.85
252 | 171.3643 | 41.4413 | 4699 | 55684 | 447 | 0.999 | 0.487 | 0.485 | 0.914 | 0.912 | 0.85
253 | 24.3379 | 16.7282 | 5130 | 55835 | 545 | 0.999 | 0.471 | 0.472 | 0.651 | 0.65 | 0.85
254 | 154.1552 | 54.3047 | 6696 | 56398 | 487 | 0.999 | 0.487 | 0.488 | 0.859 | 0.862 | 0.85
255 | 159.2973 | 10.5324 | 5346 | 55955 | 829 | 0.998 | 0.199 | 0.618 | 1.109 | 1.111 | 0.85
256 | 38.4525 | -7.1342 | 4388 | 55536 | 88 | 0.998 | 0.335 | 0.335 | 0.638 | 0.642 | 0.85
257 | 180.8803 | 13.5498 | 5390 | 56002 | 607 | 0.997 | 0.52 | 0.517 | 0.993 | 0.994 | 0.85
258 | 320.9945 | 5.4038 | 4081 | 55365 | 185 | 0.997 | 0.608 | 0.61 | 1.099 | 1.095 | 0.85
259 | 327.7053 | 3.4418 | 4090 | 55500 | 539 | 0.996 | 0.571 | 0.567 | 0.687 | 0.685 | 0.85
260 | 22.2645 | 3.9838 | 4310 | 55508 | 314 | 0.992 | 0.196 | 0.196 | 0.909 | 0.914 | 0.84
261 | 353.3421 | 15.6571 | 6137 | 56270 | 267 | 0.992 | 0.378 | 0.379 | 0.687 | 0.69 | 0.84
262 | 236.7188 | 40.2551 | 6051 | 56093 | 405 | 0.988 | 0.658 | 0.655 | 0.816 | 0.818 | 0.84
263 | 4.8287 | 26.2703 | 6279 | 56243 | 741 | 1.0 | 0.262 | 0.262 | 0.604 | 1.013 | 0.8
264 | 22.0923 | 22.3834 | 5115 | 55885 | 56 | 1.0 | 0.277 | 0.275 | 0.698 | 0.696 | 0.8
265 | 32.8873 | 0.125 | 4235 | 55451 | 893 | 1.0 | 0.213 | 0.213 | 0.823 | 0.824 | 0.8
266 | 155.9018 | 15.7562 | 5337 | 55987 | 126 | 1.0 | 0.368 | 0.368 | 0.762 | 0.762 | 0.8
267 | 207.704 | 65.7459 | 6986 | 56717 | 439 | 1.0 | 0.376 | 0.376 | 0.706 | 0.705 | 0.8
268 | 198.9484 | 46.7589 | 6624 | 56385 | 965 | 1.0 | 0.466 | 0.463 | 0.807 | 0.81 | 0.8
269 | 205.3212 | 36.1224 | 3986 | 55329 | 887 | 1.0 | 0.555 | 0.555 | 0.68 | 0.679 | 0.8
270 | 349.6495 | 26.6599 | 6587 | 56537 | 438 | 0.999 | 0.434 | 0.435 | 0.771 | 0.774 | 0.8
271 | 329.2513 | 16.9616 | 5061 | 55806 | 704 | 0.999 | 0.28 | 0.278 | 0.419 | 0.417 | 0.8
272 | 32.7654 | 0.838 | 3611 | 55128 | 717 | 0.999 | 0.291 | 0.29 | 0.716 | 0.715 | 0.8
273 | 237.8022 | 44.8269 | 6033 | 56069 | 487 | 0.999 | 0.475 | 0.475 | 0.75 | 0.751 | 0.8
274 | 221.0844 | 13.5378 | 5473 | 56033 | 642 | 0.999 | 0.262 | 0.262 | 0.737 | 0.734 | 0.8
275 | 183.495 | 62.8751 | 6972 | 56426 | 825 | 0.999 | 0.374 | 0.37 | 0.651 | 0.65 | 0.8
276 | 142.0039 | 24.1646 | 5774 | 56002 | 919 | 0.999 | 0.547 | 0.542 | 0.72 | 0.717 | 0.8
277 | 209.3069 | 3.0451 | 4784 | 55677 | 284 | 0.999 | 0.346 | 0.347 | 0.633 | 0.632 | 0.8
278 | 217.9071 | 40.9282 | 5171 | 56038 | 678 | 0.999 | 0.353 | 0.353 | 0.772 | 0.773 | 0.8
279 | 219.354 | 17.344 | 5469 | 56037 | 660 | 0.998 | 0.264 | 0.263 | 0.662 | 0.66 | 0.8
280 | 140.4015 | 32.5592 | 5808 | 56325 | 787 | 0.998 | 0.344 | 0.346 | 0.458 | 0.454 | 0.8
281 | 21.0178 | 2.6268 | 4314 | 55855 | 763 | 0.998 | 0.511 | 0.511 | 0.698 | 0.695 | 0.8
282 | 329.8912 | 24.1816 | 5952 | 56453 | 939 | 0.998 | 0.256 | 0.256 | 0.476 | 0.472 | 0.8
283 | 131.9713 | 7.0192 | 5289 | 55893 | 216 | 0.997 | 0.406 | 0.406 | 0.761 | 0.763 | 0.8
284 | 212.1806 | -1.6042 | 4035 | 55383 | 557 | 0.997 | 0.469 | 0.468 | 0.788 | 0.794 | 0.8
285 | 200.5318 | 26.3394 | 5997 | 56309 | 122 | 0.997 | 0.304 | 0.303 | 0.619 | 0.629 | 0.8
286 | 205.7799 | 15.1811 | 5441 | 56017 | 574 | 0.996 | 0.276 | 0.274 | 0.718 | 0.635 | 0.8
287 | 39.255 | -5.8455 | 4386 | 55540 | 203 | 0.996 | 0.453 | 0.452 | 0.849 | 0.851 | 0.8
288 | 192.5906 | 19.0848 | 5856 | 56090 | 868 | 0.996 | 0.5 | 0.5 | 0.82 | 0.821 | 0.8
289 | 206.9027 | -3.1424 | 4044 | 55359 | 255 | 0.996 | 0.448 | 0.448 | 0.585 | 0.585 | 0.8
290 | 244.0409 | 32.2355 | 4956 | 55737 | 703 | 0.995 | 0.452 | 0.451 | 0.796 | 0.799 | 0.8
291 | 235.7646 | 3.9591 | 4804 | 55679 | 397 | 0.995 | 0.485 | 0.487 | 0.763 | 0.764 | 0.8
292 | 128.065 | 41.9915 | 3808 | 55513 | 884 | 0.995 | 0.336 | 0.337 | 0.468 | 0.468 | 0.8
293 | 17.3649 | 22.7717 | 5126 | 55923 | 495 | 0.994 | 0.498 | 0.498 | 0.797 | 0.8 | 0.8
294 | 237.7069 | 4.8213 | 4877 | 55707 | 322 | 0.994 | 0.362 | 0.363 | 0.664 | 0.671 | 0.8
295 | 244.4578 | 50.5162 | 6316 | 56483 | 157 | 0.993 | 0.057 | 0.053 | 0.625 | 0.63 | 0.8
296 | 204.0125 | -1.3843 | 4046 | 55605 | 207 | 0.992 | 0.451 | 0.453 | 0.792 | 0.795 | 0.79
297 | 177.1556 | 34.5531 | 4646 | 55622 | 69 | 0.992 | 0.481 | 0.482 | 0.816 | 0.814 | 0.79
298 | 207.2167 | 7.1418 | 4865 | 55713 | 994 | 0.991 | 0.377 | 0.376 | 0.567 | 0.568 | 0.79
299 | 145.6952 | 4.8124 | 4798 | 55672 | 609 | 0.991 | 0.369 | 0.37 | 0.676 | 0.676 | 0.79
300 | 28.4645 | 29.1361 | 6269 | 56246 | 26 | 0.991 | 0.358 | 0.359 | 0.822 | 0.825 | 0.79

| RA | DEC | PLATE | MJD | FIBER | $P_{L}$ | z | $z_{PG}$ | $z_{PE}$ | $mean_{eyeZE}$ | $P_{T}$
---|---|---|---|---|---|---|---|---|---|---|---
301 | 140.8969 | 44.7792 | 4696 | 56354 | 602 | 0.991 | 0.453 | 0.454 | 0.647 | 0.647 | 0.79
302 | 207.8508 | 12.348 | 5443 | 56010 | 181 | 0.99 | 0.475 | 0.488 | 0.793 | 0.795 | 0.79
303 | 16.1574 | 24.6193 | 5701 | 55949 | 938 | 0.99 | 0.262 | 0.261 | 0.483 | 0.48 | 0.79
304 | 156.6061 | 49.5063 | 6694 | 56386 | 449 | 0.99 | 0.502 | 0.501 | 0.638 | 0.634 | 0.79
305 | 189.6456 | 53.8166 | 6680 | 56420 | 276 | 0.99 | 0.389 | 0.39 | 0.735 | 0.737 | 0.79
306 | 175.499 | 12.0599 | 5379 | 55986 | 804 | 0.989 | 0.32 | 0.319 | 1.022 | 1.02 | 0.79
307 | 38.7375 | -9.026 | 4389 | 55539 | 171 | 0.989 | 0.485 | 0.487 | 0.616 | 0.609 | 0.79
308 | 163.4217 | 61.7198 | 7096 | 56683 | 949 | 0.989 | 0.521 | 0.522 | 0.804 | 0.805 | 0.79
309 | 163.8089 | 63.6662 | 7104 | 56711 | 683 | 0.989 | 0.507 | 0.506 | 0.643 | 0.645 | 0.79
310 | 332.7269 | 5.7945 | 4427 | 56107 | 478 | 0.988 | 0.177 | 0.177 | 0.776 | 0.776 | 0.79
311 | 173.2826 | 36.7101 | 4615 | 55618 | 751 | 0.988 | 0.478 | 0.477 | 0.847 | 0.846 | 0.79
312 | 169.3396 | 42.4221 | 4686 | 56013 | 402 | 0.987 | 0.324 | 0.324 | 0.781 | 0.78 | 0.79
313 | 169.1691 | 54.9578 | 7093 | 56657 | 415 | 0.987 | 0.462 | 0.463 | 0.754 | 0.754 | 0.79
314 | 120.3392 | 26.2055 | 4458 | 55536 | 341 | 0.987 | 0.388 | 0.442 | 1.039 | 0.513 | 0.79
315 | 129.6789 | 19.4517 | 4484 | 55565 | 133 | 0.986 | 0.459 | 0.458 | 0.699 | 0.696 | 0.79
316 | 337.6379 | 3.389 | 4291 | 55525 | 488 | 0.985 | 0.295 | 0.294 | 0.515 | 0.508 | 0.79
317 | 177.8081 | 59.7521 | 7098 | 56661 | 382 | 0.984 | 0.26 | 0.26 | 0.788 | 0.781 | 0.79