An Unsupervised Hunt for Gravitational Lenses Stephen Sheng Keerthi Vasan G.C. Chi Po Choi James Sharpnack Tucker Jones UC Davis UC Davis UC Davis Amazon1UC Davis

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An Unsupervised Hunt for Gravitational Lenses

Stephen Sheng Keerthi Vasan G.C. Chi Po Choi James Sharpnack Tucker Jones

UC Davis UC Davis UC Davis Amazon1UC Davis

Abstract

Strong gravitational lenses allow us to peer

into the farthest reaches of space by bending

the light from a background object around a

massive object in the foreground. Unfortu-

nately, these lenses are extremely rare, and

manually ﬁnding them in astronomy surveys

is diﬃcult and time-consuming. We are thus

tasked with ﬁnding them in an automated

fashion with few if any, known lenses to form

positive samples. To assist us with train-

ing, we can simulate realistic lenses within

our survey images to form positive samples.

Naively training a ResNet model with these

simulated lenses results in a poor precision

for the desired high recall, because the sim-

ulations contain artifacts that are learned

by the model. In this work, we develop a

lens detection method that combines simu-

lation, data augmentation, semi-supervised

learning, and GANs to improve this perfor-

mance by an order of magnitude. We perform

ablation studies and examine how perfor-

mance scales with the number of non-lenses

and simulated lenses. These ﬁndings allow

researchers to go into a survey mostly “blind”

and still classify strong gravitational lenses

with high precision and recall.

1 Introduction

Massive galaxies can deﬂect the light from background

sources through the eﬀect of gravitational lensing, cre-

ating magniﬁed “arcs” and multiple images of back-

ground galaxies when they are located directly along

the line of sight. Such alignments are rare, and these

lensing systems are important to astronomers for a

Proceedings of the 25th International Conference on Artiﬁ-

cial Intelligence and Statistics (AISTATS) 2022, Valencia,

thor(s).

Figure 1: Non-lens (left), simulated lens (middle), real

lens (right)

range of studies, such as glimpsing into the farthest

regions of space where the light of distant objects is

ordinarily too faint to detect. With strong gravita-

tional lenses, this light becomes focused and ampli-

ﬁed. Additionally, the lensing information can be used

to study the mass distribution in foreground galaxies,

notably including the non-baryonic dark matter which

comprises most mass in the universe (Metcalf et al.,

2019).

A principal challenge is that strong gravitational lenses

are incredibly rare. Across the entire sky only of order

a thousand such systems are currently known (Met-

calf et al., 2019). Previous eﬀorts to ﬁnd strong grav-

itational lenses have largely been done manually by

individuals visually inspecting images. This is both

impractical and expensive. In recent years, various

groups have turned to deep learning methods to search

for lens systems (e.g., Jacobs et al., 2017; Sonnenfeld

et al., 2018; Pourrahmani et al., 2018; Jacobs et al.,

2019; Huang et al., 2020; Li et al., 2020; Ca˜nameras

et al., 2020). These early attempts were rather sim-

plistic as they typically only train and evaluate their

models in a supervised fashion either on small num-

bers of known lenses or by making simulated lenses

from their own surveys. Nonetheless, deep learning is

proving to be a fruitful and eﬃcient approach.

Several surveys are planned for the next decade to ob-

serve wide areas of the sky at unprecedented depth and

angular resolution (e.g., Rubin Observatory [LSST Sci-

ence Collaboration et al., 2009], Euclid [Laureijs et al.,

2011] and Roman Space Telescope [Spergel et al.,

1Work done prior to joining Amazon

arXiv:2210.11681v1 [astro-ph.IM] 21 Oct 2022

An Unsupervised Hunt for Gravitational Lenses

2015]). These will enable the detection of orders-of-

magnitude more strong lenses than with current data

(Oguri and Marshall, 2010). The early challenge of an-

alyzing these surveys is that astronomers will not have

access to lenses to build their classiﬁers. In this case,

there are two primary options: (1) use lenses found

from other surveys and hope the features are eﬀective

and transferable, or (2) create simulated lenses based

on each survey and train a classiﬁer on those. For (1),

the biggest issue is that the transferred performance

may vary signiﬁcantly. This is due to the fact that

images from these other surveys are produced with

diﬀerent instruments as well as diﬀerent preprocessing

techniques. Therefore, the samples used for training

may be too distributionally dissimilar (i.e. covariate

shift) from their target to be useful. One possibility to

ameliorate the eﬀects of covariate shifts is to use Cycle-

GANs (Zhu et al., 2017) to transform these images to

look like the target data distribution. However, it still

doesn’t solve the issue of the extremely small number

of known lenses with heterogeneous imaging. So (2)

is the realistic option for producing consistent perfor-

mance across surveys by simulating lenses directly on

the target set.

Using simulations for training data is quite common

in deep learning (Nikolenko, 2019). The problem with

option (2) though is that researchers will be creating

simulated lenses without a reference point for how they

look in their survey. This results in classiﬁers having

good performance when evaluating on held out sim-

ulations, but poor performance when classifying real

lenses. This is especially problematic for multi-channel

images (see Fig. 1) since getting the channel informa-

tion incorrect can lead to an ineﬀective classiﬁer. In-

stead of trying to get all the channel information of the

arcs correct, one possibility is to simulate lenses on a

single channel and build classiﬁers to detect lenses in

this setting (Ca˜nameras et al., 2020). This sidesteps

the issue of getting the channel information correct,

but this workaround causes us to lose some contex-

tual information about the “coloring” of the lenses and

the surrounding objects, which may actually help the

model learn to detect lenses. As a result, we do not

explore this option in this paper. We also do not ex-

plore using pretrained networks here. Instead, we will

focus on a completely self-contained regimen for build-

ing classiﬁers from simulated data. Data augmenta-

tion is one way to address this issue of realism without

sacriﬁcing this multi-channel information from the im-

age. Secondly, while we can obtain a small sample of

non-lensed images to train our classiﬁer, the majority

of the survey remains unlabeled, so the use of semi-

supervised learning (SSL) algorithms is also a prudent

direction to boost the performance of the classiﬁer.

By understanding the correct ways to leverage these

methods in concert, we can show that you can create

highly eﬀective classiﬁers for detecting lenses even if

you only train on potentially “bad” simulated lenses.

2 SSL And Unsupervised Learning

The simplest approach to building a classiﬁer is to use

the simulated lenses as our target and train a fully

supervised classiﬁer. The limitations of course is that

the unlabelled data isn’t leveraged and the simulated

lens distribution may diﬀer from that of the real lenses.

2.1 Semi-supervised Learning

We ﬁnd that SSL algorithms are another indispens-

able tool for classifying lenses. In recent years, the

ﬁeld of deep learning has seen signiﬁcant progress in

the area of semi-supervised learning algorithms (Yang

et al., 2021; van Engelen and Hoos, 2019). Instead of

covering all of them, we will focus on a narrow collec-

tion of state-of-the-art algorithms: Pseudo-label (Lee,

2013), Π-model (Laine and Aila, 2017), Mean Teacher

(Tarvainen and Valpola, 2017), VAT (Tarvainen and

Valpola, 2017), MixMatch (Berthelot et al., 2019).

For semi-supervised learning algorithms, there are usu-

ally two primary goals: consistency regularization and

entropy minimization. Some SSL methods (e.g. consis-

tency regularization) considered here require data aug-

mentation (DA), and we summarize the DA methods

used in Table 2. These methods are chosen speciﬁcally

with this application in mind.

Consistency regularization is based on the idea that

a classiﬁer should output the same predictions even if

the image has been augmented. This is usually carried

out by appending a regularizing term to the loss that

computes the “distance” between the outputs of the

classiﬁer evaluated on two stochastically augmented

versions of the same image. Almost all the algorithms

we listed above utilize this in some form or another,

with the exception of pseudo-label. The set of aug-

mentations is also usually something predeﬁned, which

means that the application isn’t domain agnostic, and

performance will largely depend on the domain-speciﬁc

augmentations. The exception of course is VAT (Miy-

ato et al., 2019), which generates the augmentations

during training instead of being predeﬁned.

Entropy minimization is based on the idea that the

decision boundary of the classiﬁer should lie in low-

density regions. Worded another way, if two images

x1and x2are close in a high-density region then the

predictions y1and y2should be close as well. Pseudo-

label and MixMatch both try to enforce these proper-

ties. Pseudo-label does it by assigning pseudo-labels

to unlabeled images which are determined by the class

Stephen Sheng, Keerthi Vasan G.C., Chi Po Choi, James Sharpnack, Tucker Jones

with the highest predicted value. MixMatch does this

too but less dramatically by sharpening the predicted

values to be used as the label instead of hard thresh-

olding the predictions to produce a pseudo-label.

Typically, the SSL setting assumes that the training

and test distributions are the same. However, we will

train on simulated images and test on real lenses. A

priori it was unclear if the SSL algorithms would im-

prove the metrics in question. Furthermore, there is

also the question of whether or not SSL algorithms

will even improve over baselines tuned with data aug-

mentations since it has been shown in the past that a

classiﬁer’s performance can often match the state-of-

the-art SSL algorithms by choosing the correct data

augmentations (Oliver et al., 2018). Nevertheless, we

ﬁnd that SSL algorithms are an indispensable tool in

our arsenal.

2.2 Unsupervised Learning

In unsupervised learning, the typical use case is to

learn a data distribution. In deep learning, this is

typically done by training a GAN (Goodfellow et al.,

2014; Arjovsky et al., 2017; Gulrajani et al., 2017).

The outcome of training a GAN is a generator that

can produce similar samples from the data distribu-

tion it learned from. Those samples are then used for

training the classiﬁer. One can think of this as another

form of data augmentation. The diﬀerence in our case

is that the data distribution(i.e. the simulated lenses)

we would use to train our GAN does not come from

our target distribution(i.e. the real lenses). However,

we believe that this can still be helpful because, as we

mentioned earlier, we have no a priori notion of what a

lensed image would look like coming from the DLS sur-

vey. And because GANs do not necessarily faithfully

reproduce the data distribution it was trained on, this

more exotic form of augmentation should nevertheless

be beneﬁcial for improving our classiﬁer’s ability to

generalize to real lenses.

3 Data And Experimental Setup

The data that will be the focus of our study comes from

the Deep Lens Survey (DLS; Wittman et al., 2002).

Due to the paucity of known lenses in this survey, we

do not allow any training or validation (model tuning)

to be done on real lenses. Rather they were reserved

for the ﬁnal comparison of a handful of methods at-

tempted.

3.1 Deep Lens Survey (DLS) and Lens

Simulations

The Deep Lens Survey consists of 5 independent ﬁelds

of 4 deg2each, with images taken over ∼100 nights us-

ing the 4-meter Blanco and Mayall telescopes. The full

20 deg2area contains ∼5 million cataloged galaxies im-

aged in 4 diﬀerent astronomical ﬁlters (B,V,R,z) which

roughly cover the visible spectrum (i.e. 3000-10000˚

A).

The throughput curve for the ﬁlters is published in

Schmidt and Thorman (2013) and the data products

from the survey are available for public use. For this

work, we make use of only the BVR ﬁlters as they have

the highest SNR. A total of 267,961 galaxies which

are likely to act as strong lenses (i.e. which appear

to be massive galaxies at moderate cosmological red-

shifts) were photometrically selected for this analysis

by applying a R band magnitude cut (17.5< R < 22).

Color images are then constructed for these galaxies

using HumVI (Marshall et al., 2015) with the target

galaxies centered in the images.

For any given image from the survey, we create a sim-

ulated lens counterpart which we use for training. We

assume a background galaxy is present behind the cen-

tral galaxy, and use the glafic (Oguri, 2010) lens

modeling code to trace the background galaxy’s light

through the foreground lensing potential. We add the

resulting simulated lensed arcs to the DLS survey im-

ages using HumVI. The values chosen for the back-

ground galaxy and the lensing potential used in the

simulations do not rely on any physical property of

the foreground and background galaxy. Instead, they

randomly probe a range of Einstein radii and redshift

values, appropriate for the selected target galaxies,

yielding a wide variety of lens conﬁgurations. Each

simulated lens image has exactly one non-lensed im-

age pair. In other words, we do not use the same

non-lensed image to create multiple simulated lensed

images in diﬀerent lens conﬁgurations. For this work,

we limit our simulations to background sources with

relatively blue colors, as these are the most common

at high redshifts (z > 1) and the most likely to be

detectable in DLS data. Finally, we visually inspected

the simulated lenses and removed any images where

the central galaxy was signiﬁcantly brighter than the

arc. This resulted in 259,489 simulated lenses.

3.2 Training Data

From the non-lenses and the corresponding simulated

lenses, we make two training sets: TrainingV1 and

TrainingV2. For TrainingV1 we use 266,301 images

for non-lenses and 257,874 corresponding simulations

as lenses. For TrainingV2 we use the 7,074 human-

labeled objects as non-lenses and 6,929 corresponding

An Unsupervised Hunt for Gravitational Lenses

Table 1: Summary Of Images In Datasets

Dataset Non-lenses Simulated lenses Real lenses Unlabeled data Percentage of lenses

TrainingDataPure 267961 259489 0 0 -

TrainingV1 266301 257874 0 0 -

TrainingV2 7074 6929 0 259248 -

SimTest 786 773 0 0 -

TestV1 874 0 52 0 5.6156

TestV2 874 0 27 0 2.9967

Table 2: Augmentations Used During Training

Name Description

RGB-shuﬄe Randomly perturb the order of the channels in the images

JPEG quality Randomly apply JPEG compression with quality between 50-100%

Rot90 Randomly rotate the images by a multiple of 90 degrees

Translations Randomly translate the images by at most 20 pixels in the up, down, left and right directions

Horizontal ﬂips Randomly ﬂips the images across the x-axis

Color augmentation Randomly perturb the brightness(-0.1-0.1), saturation(0.9-1.3), hue(0.96-1.00),

and gamma(1.23-1.25) of the images

simulations as lenses. The rest of the 259,248 images

serve as unlabelled data. During training, we do a 90-

10 split whereby 90 percent of this data is used for

training the ResNet model and 10 percent is reserved

for validation. We also created a holdout set, SimTest,

of 786 images for non-lenses and 773 images for lenses

to be explicitly used for testing in the simulated set-

ting. We summarize these details in Table 1.

3.3 Initial Lens Discovery and Testing Data

Prior to this work, there were only a few real lenses,

with which we might form our test set, known in the

entire DLS survey. Since manually searching the en-

tire survey for lenses (which are very rare) is a labo-

rious and time-consuming task, we use a pilot model

to perform an initial search of the survey. The pilot

model was built with the convolution neural network

ResNet (He et al., 2016a,b) of 11 layers depth with

polar-transformed images as the input. The motiva-

tion behind transforming the images to a polar coordi-

nate system is that at lower Einstein radii and galaxy

scales, the arcs are approximately symmetric around

the image center and a polar transform captures this

symmetry as a straight line. The pilot model was an

ensemble of 5 ResNet model instances, and each in-

stance was trained on a randomly selected subset of a

pilot training dataset which contained 200,000 simu-

lated lenses and 200,000 non-lenses. The entire sam-

ple of unlabeled survey images from the DLS survey

(279,149 images in total) was scored by the ResNet

ensemble. Around 3000 galaxy images (1% of survey)

that had the highest median scores were taken for hu-

man inspection by a team of astronomers. 52 were

labeled as good lens candidates and form our test set

TestV1. 27 out of the 52 were deemed very likely to

be strong real lens candidates and form our test set

TestV2.

In order to populate our test sets with real non-lenses,

the same team of astronomers were asked to label a

fraction of images (∼3%) from the survey. Since most

of the images are expected to be non-lenses, this is an

easy task and does not warrant an ML model. A total

of 8734 galaxy images were labelled to be non-lenses

from the entire survey and 874 (i.e., 10%) were ran-

domly chosen out of those to be included as non-lenses

for both the TestV1 and TestV2 test sets. Therefore

with the help of the pilot model and human labeling,

two test sets: TestV1 (52 Lenses, 874 NonLenses) and

TestV2 (27 Lenses, 874 NonLenses) are constructed.

This initial lens discovery was done independently of

the experiments in order to prevent data leakage be-

tween the real lens test sets and the supervised models

trained in the main experiment. In addition, we set

the number of candidate images returned by the pilot

model to be much larger than the expected number

of lenses in the DLS survey. As a result, the num-

ber of discovered lenses is reasonable given what has

been found in other surveys. With this being the case,

we believe that the main source of error in the test

set labels is human error in the hand labeling of real

lenses.

3.4 Experimental Setup And

Implementations

We used a standard ResNet-11 architecture for all

experiments. The models we use are broadly bro-

ken up into 3 groups: supervised, semi-supervised,

and GAN+semi-supervised. There are four supervised

models: SupervisedV1, SupervisedV1+DA, Super-

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An Unsupervised Hunt for Gravitational Lenses Stephen Sheng Keerthi Vasan G.C. Chi Po Choi James Sharpnack Tucker Jones UC Davis UC Davis UC Davis Amazon1UC Davis

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