# Can semi-supervised learning reduce the amount of manual labelling required
for effective radio galaxy morphology classification?

Inigo V. Slijepcevic
Department of Physics and Astronomy
University of Manchester, UK
<EMAIL_ADDRESS>&Anna M. M. Scaife
Department of Physics and Astronomy
University of Manchester, UK
<EMAIL_ADDRESS>The Alan Turing Institute, 96 Euston Rd, London,
UK<EMAIL_ADDRESS>
###### Abstract

In this work, we examine the robustness of state-of-the-art semi-supervised
learning (SSL) algorithms when applied to morphological classification in
modern radio astronomy. We test whether SSL can achieve performance comparable
to the current supervised state of the art when using many fewer labelled data
points and if these results generalise to using truly unlabelled data. We find
that an artifical SSL scenario provides additional regularisation and improves
baseline test set accuracy for a range of labelled data volumes. However,
using truly unlabelled data degrades accuracy, which we show may be due to
class imbalance in the unlabelled data.

##  1 Introduction

The Fanaroff-Riley (FR) binary classification of radio galaxies has been
widely adopted and utilised since its inception over four decades ago [10].
However, in spite of progress in relating the two classes to the dynamics and
energetics of the sources [12, 21], our understanding of the causal
relationship between the source physical properties/environment and FR
classification is far from complete. To improve our inferences about the
physics of these objects, we need to accurately identify and classify more
radio galaxies while also detecting anomalous/rare examples [16].

In particular for new sky surveys, such as those anticipated for the Square
Kilometre Array (SKA) radio telescope, automated classification algorithms are
increasingly being developed to replace the manual by eye approaches used
historically. CNNs have been used with success for image-based classification
of radio galaxies ([25, 1]), including attempts to use more novel techniques
such as capsule networks [15] and attention gating [5] to help improve
performance and interpretability. [2] provides a more comprehensive survey of
current techniques.

Currently, archival data-sets for training radio galaxy classifiers are of
comparable size to many of those used in computer vision (e.g. CIFAR [13]),
with around $10^{5}$ samples available. However, a fundamental difference is
the sparsity of labels in radio galaxy data-sets: only a small fraction of
data-points are labelled. This is largely due to the domain knowledge required
for labelling, which incurs a high cost per label compared to typical machine
learning data-sets. Currently, the largest labelled machine learning data-set
of radio galaxies is MiraBest [17, 20] which has 1256 samples, orders of
magnitude lower than the number of unlabelled images in its originating sky
survey.

(a) FR Class I

(b) FR Class II

Figure 1: Example radio galaxies from the MiraBest dataset (cherry-picked for
prototypicity) [17].

This work: In this work, we focus on morphological classification of radio-
galaxies within the FR classification scheme, see Figure 1. We aim to test
whether we can achieve performance comparable to the current supervised state
of the art on the MiraBest dataset with many fewer labels by using semi-
supervised learning (SSL). This work will guide decision making on how to
construct pipelines for upcoming radio surveys such as those for the SKA.

Many SSL algorithms are successful on benchmarking datasets such as CIFAR-10
[13], MNIST [14] and SVHN [18] in the regime of low data ($\sim[10,10^{3}]$
data points). However, less work has been done in assessing the robustness to
various real world problems, such as unclean or covariate shifted data, new
classes appearing in the unlabelled data or even simply varying sizes of
labelled/unlabelled data: the shortcomings of the SSL literature have
previously been documented in this context [19].

Of particular interest in astronomy is the problem of biased sampling for our
training data. We observe phenomena driven by complex natural processes which
are selected for labelling in a biased manner due to instrumental,
observational and intrinsic effects which favour, for example, particular flux
density (brightness) and redshift (distance) ranges. This makes it difficult
to know how representative our data catalogues are of all observed data, and
the consequent effects on model performance are therefore not always clear a
priori. Specific examples of how this is being addressed for machine learning
applications in astronomy include the use of Gaussian process modelling to
augment training data and make it more representative of test data in
photometric classification [4] and in galaxy merger classification where
domain adaptation techniques have also been explored [8]. In both of these
cases the solutions are tackling covariate shift between the labelled and test
data.

##  2 FixMatch

Semi-supervised learning leverages unlabelled data when only a small labelled
data-set is available. The model is fed a set of image-label pairs
$({\bm{x}}_{l},y_{l})\in{\bm{X}}_{l}$ along with a (usually larger) set of
unlabelled images ${\bm{x}}_{u}\in{\bm{X}}_{u}$. The goal is to predict labels
for held out samples ${\bm{x}}_{test}\in{\bm{X}}_{test}$. An overview of semi-
supervised learning can be found in [7]

We choose the FixMatch algorithm [23] from the pool of SSL techniques as it
achieves state of the art performance on benchmarking datasets, has few
hyperparameters, and is computationally cheap [23]. FixMatch makes use of the
unlabelled data through consistency regularisation and pseudo-labelling by
adding a loss term computed on two different augmentations of the same image:

$\mathcal{L}=\lambda\sum_{u=0}^{\mu
B}\underbrace{\mathds{1}(\textup{max}(p_{m}(\alpha({\bm{x}}_{u})))\geq\tau)}_{\text{threshold
mask}}\times\underbrace{H(\hat{q}_{u},p_{m}(y|\mathcal{A}({\bm{x}}_{u})))}_{\text{pseudo-
label cross
entropy}}+\sum_{l=0}^{B}\underbrace{H(y_{l},p_{m}(y|\alpha({\bm{x}}_{l})))}_{\text{supervised
loss}}.$ (1)

Here the "weak" augmentation, denoted $\alpha(\cdot)$, retains the semantic
meaning of the image and simply uses the standard rotation/flipping
augmentations. The "strong" augmentation, denoted by $\mathcal{A}(\cdot)$,
uses RandAugment [9] to apply a sequence of augmentations that can
significantly alter the image.

If $\mathrm{max}(p_{m}(y|\alpha({\bm{x}}_{u})))>\tau$, the prediction
$\hat{q}_{u}=\mathrm{argmax}(p_{m}(y|\alpha({\bm{x}}_{u}))$ is used as a
pseudo-label for $\mathcal{A}({\bm{x}}_{u})$. Figure 2 shows how an unlabelled
data point flows through the model. $B$ is the labelled batch size, $\mu$,
$\tau$ are hyperparameters controlling unlabelled batch size and confidence
threshold respectively. $\lambda$ controls the weighting of the unlabelled
loss term and is set to 1, following [23].

Figure 2: An unlabelled data point flowing through the FixMatch algorithm [23]

##  3 Experiments

###  3.1 Ensuring fair evaluation

Fair evaluation is a problem in the SSL literature [19], yet is crucial if we
wish to apply it to real data. Hyperparameters and validation set: we keep the
validation set a realistic size by scaling it to $20\%$ of ${\bm{X}}_{l}$, but
set a hard lower limit to produce meaningful results when ${\bm{X}}_{l}$ is
small. We set the learning rate to 0.005 but scale the batch size, $B$, with
${\bm{X}}_{l}$. Astronomical data-sets vary in size and content and large
validation sets may not be available: our models need to perform well across a
range of scenarios without too much hyperparameter sensitivity. For these
reasons, we keep hyperparameter tuning to a minimum, opting instead to choose
reasonable values close to the optimal values in the computer vision
literature [23]. We choose $\mu=7$, which allows the model to use a large
proportion of the unlabelled data in a single epoch, and $\tau=0.95$, which
allows the model’s confidence on unlabelled data to pass the threshold before
it begins to overfit. Model architecture: we use the convolutional
architecture from [24], which has good performance for radio galaxy
classification and relatively few parameters, giving a realistic baseline that
isn’t prone to overfitting. Reproducibility and variance in results and data
splits: each experiment’s results are averaged over 10 runs initialised using
seeds 0-9. This ensures that the same splits are used during each experiment,
while keeping weight initialisations consistent. We use randomly selected,
stratified labelled/unlabelled data splits. The same test set is used after
choosing the model weights with the best validation set accuracy.

The experiments were performed on a single Nvidia A100 GPU with a total of
2.34 days of runtime. We used Weights & Biases [3] to track experiment
results. Code can be found at https://github.com/inigoval/fixmatch.

###  3.2 Does FixMatch outperform the baseline?

Fully supervised baseline. The baseline model is trained in a fully supervised
fashion with a cross-entropy loss, shown as the second term in Equation 1. We
use the same subset of (weakly augmented) labelled samples as in the FixMatch
case, but ignore the unlabelled samples.

Throwing away labels to create an artificial SSL scenario (Case A). We perform
multiple experiments by using a small labelled subset of the MiraBest dataset
[17] and using the remainder as unlabelled data. In all cases we keep the
labelled data stratified (class balance is preserved). In Figure 3 we see that
FixMatch achieves a consistently lower loss on the test data and outperforms
the baseline in test set accuracy when there is little labelled data
available. We are able to recover comparable accuracy ($85.1\%\pm 1.1\%$) to
the supervised baseline with all labels ($86.93\%\pm 0.54\%$) using just
$20\%$ (203) of the labels. However, FixMatch’s performance degrades quickly
with very few labels, which is in stark contrast to similar experiments in
[23], where good performance is achieved even with only one sample per class.
Furthermore, the "sweet spot" where FixMatch has a significant advantage does
not cover the full range of labelled data volumes.

We hypothesise that there is a strong regularisation effect from the strongly
augmented samples, as well as new information being learned from the
unlabelled data. This is illustrated in Figure 4(a), where FixMatch avoids
overfitting at low data volumes, as demonstrated by the well behaved
validation loss. We also observe that this effect is not present with 393
labelled samples, which is reflected in the equal test loss at high label
volumes in Figure 4(b).

(a) Accuracy on the test set.

(b) Loss on the test set

Figure 3: Performance as a function of ${\bm{X}}_{l}$ size.

(a) Validation loss with 50 labelled samples.

(b) Validation loss with 393 labelled samples.

Figure 4: FixMatch (Case A) regularisation effect on validation loss. The
shaded area shows the standard error over 10 runs. We use exponential moving
average smoothing with a weight of 0.3.

Testing FixMatch on real unlabelled data (Case B). We test FixMatch by using a
pool of 20,000 unlabelled data from the Radio Galaxy Zoo Data Release 1 (RGZ
DR1) catalogue (Wong et al. in prep) with labelled samples from MiraBest.
While these data originate from the same radio survey and are pre-processed in
the same manner as MiraBest, the class balance of the RGZ DR1 catalogue is
unknown and the choice of filters for choosing data-points is wider, resulting
in a dataset of $\sim 10^{5}$ datapoints. We find that the RGZ DR1 data-set
contains many unresolved sources, which are uninformative to our model. To
remove these sources, we enforce a lower limit on source extension by
calculating the Frechet Distance (FD; [11]) between the labelled data-set and
the RGZ DR1 dataset (in feature space) for a range of lower limits. We take
the limit with the lowest score (28 arcsec), after which a total of 8848
unlabelled data samples remain.

We find that in Case B FixMatch still provides regularisation as shown by the
comparable test set loss to Case A, see Figure 3(b). However, this does not
result in an improvement in accuracy. Indeed we see a decrease in test set
accuracy compared to the baseline in Case B, for all labelled data volumes. We
hypothesise that this may be due to the unknown class imbalance in the RGZ DR1
data-set.

(a) Removing FRI samples

(b) Removing FRII samples.

Figure 5: Test set accuracy as a function of label balance in the unlabelled
(MiraBest) data-set. We use only samples qualified as confidently classified
in the MiraBest dataset for the labelled subset (69 labels) to reduce the
noise in our results, see [22] for more details on this qualification. Label
balance is quantified by computing $4(1-\beta)\beta$. Error bars show the
standard error after aggregating 20 runs (seeded 0-19).

To test this hypothesis we rerun Case A with an artificially class imbalanced
unlabelled data-set, produced by removing either FRI or FRII samples from the
unlabelled data. We measure test set accuracy for unlabelled data with varying
proportion $\beta$ of FRIs. Figure 5 shows that class imbalance has a
significant negative effect on test set accuracy. This suggests that the
performance gap between Cases A and B could be accounted for by class
imbalance in RGZ DR1, although it is not conclusive that this is the only
factor.

##  4 Conclusion

We find that FixMatch provides some regularisation benefits when learning with
few labelled samples, mitigating the effect of overfitting, as well as
learning from unlabelled data. Furthermore, we are able to achieve better
accuracy on the test set than the baseline with fewer labels. While this is
relatively promising, the improvement in accuracy is much smaller than for the
computer vision data-sets the algorithm was initially tested on.

Poor results using the “real” RGZ DR1 data highlight an important obstacle to
applying SSL “in the wild” on scientific observational data: ${\bm{X}}_{l}$
and ${\bm{X}}_{u}$ are unlikely to be drawn from identical distributions. We
see that even class imbalance in ${\bm{X}}_{\rm u}$ can have a major effect on
SSL performance, noting that in a real scenario we have no way of knowing the
class balance of ${\bm{X}}_{\rm u}$.

We believe that a naive application of SSL, although it may outperform the
baseline in some cases and provide useful regularisation, requires further
domain specific development to give a worthwhile advantage in the case of
radio galaxy morphology classification. Future work will consider handcrafting
radio galaxy specific augmentations and implementing more sophisticated SSL
approaches to help tackle the problem of covariate shift between
${\bm{X}}_{\rm u}$ and ${\bm{X}}_{\rm l}$, such as pretraining and/or
incorporating domain adaptation (e.g. [6]).

## Acknowledgments and Disclosure of Funding

The authors gratefully acknowledge support from the UK Alan Turing Institute
under grant reference EP/V030302/1. IVS gratefully acknowledges support from
the Frankopan Foundation.

This work has been made possible by the participation of more than 12,000
volunteers in the Radio Galaxy Zoo Project. The data in this paper are the
result of the efforts of the Radio Galaxy Zoo volunteers, without whom none of
this work would be possible. Their efforts are individually acknowledged at
%****␣neurips_2021.tex␣Line␣275␣****http://rgzauthors.galaxyzoo.org.

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# Z production in pPb collisions and charmonium production in PbPb ultra-
peripheral collisions at LHCb

Hengne Li  on behalf of the LHCb collaboration  Guangdong Provincial Key
Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal
University, Guangzhou 510006, China.

###### Abstract

This article presents recent results of the Z boson production in the proton-
lead collisions and the charmonium production in the ultra-peripheral lead-
lead collisions at the LHC collected during 2013 to 2018 by the LHCb detector.
The potential heavy ion programs in these topics are also discussed.

###### keywords:

Heavy-ion collisions, nuclear modification, Z boson production, ultra-
peripheral collisions, charmonium production, LHCb experiment, LHC

##  1 Introduction

The LHCb detector [1, 2] is a fully instrumented single-arm spectrometer in
the forward region covering a pseudorapidity acceptance of $2<\eta<5$,
providing a high tracking momentum resolution down to very low transverse
momentum ($p_{\rm T}$) and precise vertex reconstruction capability. The
detector is originally designed for heavy-flavour measurements, precision
tests of the standard model (SM), and searches for physics beyond the SM. As a
young member of the LHC heavy ion program, the LHCb experiment also provides
the unique datasets for the heavy ion physics studies at LHC. The heavy ion
program at LHCb includes proton-lead (pPb), lead-lead (PbPb), and xenon-xenon
(XeXe) collisions, together with fixed-target collisions of p or Pb with noble
gases nuclei injected around the interaction point. The summary of the LHCb
heavy ion data in collision mode and recorded integrated luminosities are
given in Table 1.

In this article, we present recent results of the Z boson production in the
proton-lead collisions [3, 4] and the charmonium production in the ultra-
peripheral lead-lead collisions [5] at the LHC using datasets collected during
2013 to 2018 by the LHCb detector.

| 2013 | 2016 | 2015 | 2017 | 2018
---|---|---|---|---|---
$\sqrt{s_{\rm NN}}$ | 5.02 TeV | 8.16 TeV | 5.02 TeV | 5.02 TeV | 5.02 TeV
| pPb | Pbp | pPb | Pbp | PbPb | XeXe | PbPb
$\mathcal{L}$ |  1.1 nb-1 |  0.5 nb-1 |  13.6 nb-1 |  20.8 nb-1 |  10 $\mu$b-1 |  0.4 $\mu$b-1 |  $\sim$210 $\mu$b-1
Table 1: Summary of the LHCb heavy ion collisions and the recorded integrated
luminosities.

##  2 Z boson production in proton-lead collisions

Electroweak bosons are unmodified by the hot and dense medium created in heavy
ion collisions. Their leptonic decays pass through the medium without being
affected by strong interactions. Therefore, electroweak boson productions well
retained the initial conditions of the collisions, can be used to probe
nuclear matter effects and constraint nuclear parton distribution functions
(nPDFs) for Bjorken-x from $\sim 10^{-4}$ to 1 at Q${}^{2}\sim 10^{4}$ GeV2
[6, 7], and can be used as a calibration of the nuclear modification factor of
other processes.

Using pPb datasets collected by the LHCb detector at 5.02 TeV and 8.16 TeV as
summarized in Table 1, the Z boson production cross-sections in the muon decay
channel are measured in the fiducial volume in both the forward (p-Pb) and
backward (Pb-p) collision configurations [3, 4] based on the following
equation: $\sigma_{{\rm Z}\to\mu^{+}\mu^{-}}=\left[{\rm
N_{cand}}\cdot\rho\right]/\left[\mathcal{L}\cdot\epsilon\right]$, where
$\sigma_{{\rm Z}\to\mu^{+}\mu^{-}}$ is the production cross-section to be
measured, ${\rm N_{cand}}$ is the number of ${\rm Z}\to\mu^{+}\mu^{-}$
candidates pass signal selection, $\rho$ is the signal purity of the selected
Z candidates, $\mathcal{L}$ is the integrated luminosity, and $\epsilon$ is
the total efficiency includes trigger, reconstruction and selection
efficiencies. The fiducial volume is defined as $60<m_{\mu^{+}\mu^{-}}<120$
GeV, $2.0<\eta_{\mu^{\pm}}<4.5$, and $p_{\rm T}^{\mu^{\pm}}>20$ GeV. The
purity is measured using data-driven methods, and the efficiencies are
estimated using Monte-Carlo (MC) samples together with tag-and-probe data
driven corrections.

The invariant mass distributions of selected signal candidates are shown in
Fig. 1 for datasets taken in 2016 at $\sqrt{s_{\rm NN}}=8.16$ TeV.

(a)(b)

Fig. 1: (color online) The dimuon invariant mass distributions after the
offline selection for pPb (a) and Pbp (b) configurations, using datasets taken
in 2016 at $\sqrt{s_{\rm NN}}=8.16$ TeV. The red line shows the distributions
from simulation generated using PYTHIA 8 [8] with CTEQ6L1 [9] PDF set,
normalised to the number of observed candidates.

(a)(b)(c)

Fig. 2: (color online) (a, b) Measured fiducial cross-sections of Z production
and theoretical calculations using various PDF sets with or without nuclear
modification. Figure (a) is for dataset taken in 2013 at $\sqrt{s_{\rm
NN}}=5.02$ TeV and figure (b) is for dataset taken in 2016 at $\sqrt{s_{\rm
NN}}=8.16$ TeV. (c) Comparison of LHCb 8.16 TeV results with previous 5.02 TeV
results from ATLAS, CMS, ALICE, and LHCb. The uncertainties on the data over
theory ratios include only the experimental statistical and systematic
uncertainties; the PDF uncertainties are shown separately on the line at one.
The central values of the LHCb and ALICE results at 5.02 TeV are shifted to
left and right by 0.1 units in rapidity, respectively, for better visibility.

The resulting fiducial cross-sections for centre-of-mass energies at 5.02 TeV
and 8.16 TeV [3, 4] are shown in Fig. 2 (a) and (b), respectively. The results
are compared with theoretical calculations using FEWZ [10, 11] with MSTW08
[12] free nucleon PDF together EPS09 (NLO) [13] nPDF for dataset at 5.02 TeV,
and with NNPDF 3.1 [14] free nucleon PDF together EPPS16 (NLO) [7] and nCTEQ15
(NLO) [6, 15] nPDFs for dataset at 8.16 TeV. The results are also compared
with previous 5.02 TeV results from LHCb [3], ATLAS [16], CMS [17], and ALICE
[18], as shown in Fig. 2 (c). The new LHCb 8.16 TeV results are compatible
with previous 5.02 TeV results at LHCb, but with about 20 times higher
statistics, it is the most precise measurement at forward region at LHC.

The ratio of the Z boson production cross-sections for forward and backward
configurations, $R_{\mathrm{FB}}$, is particularly sensitive to nuclear
effects. $R_{\mathrm{FB}}$ is measured in the common rapidity region
($2.5<|y^{*}|<4.0$) in the centre-of-mass frame of the produced Z boson using
2016 dataset [4] as $R_{\mathrm{FB}}^{2.5<|y^{*}|<4.0}=1.28\pm 0.14({\rm
stat})\pm 0.14({\rm syst})\pm 0.05({\rm lumi})$, which is compatible with
theoretical calculations using FEWZ with the following nPDFs:
$R_{\mathrm{FB,NNPDF3.1+EPPS16}}^{2.5<|y^{*}|<4.0}=1.45\pm 0.10{\rm(theo.)}\pm
0.01{\rm(num.)}\pm 0.27{\rm(nPDF)}$, and
$R_{\mathrm{FB,NNPDF3.1+nCTEQ15}}^{2.5<|y^{*}|<4.0}=1.44\pm
0.10{\rm(theo.)}\pm 0.01{\rm(num.)}\pm 0.20{\rm(nPDF)}$, where, the
uncertainty num. from the numerical precision.

##  3 Charmonium production in ultra-peripheral lead-lead collisions

Ultra-peripheral collisions (UPC) [19, 20] refer to the photon-induced
interactions when two nuclei bypass each other with an impact parameter larger
than the sum of their radii. In case of nuclei with higher atomic numbers such
as lead (Pb), the photon-induced interactions are enhanced by the strong
electromagnetic field, which include photon-photon and photon-pomeron
interactions. Charmonium can be produced in the photon-pomeron interactions,
where a photon emitted from one nucleus converted to a $c\bar{c}$ pair
interacts with a pair of gluon exchanges (pomeron) emitted from the other
nucleus. These productions can be distinguished as (1) coherent if the photon
interact coherently with the whole nucleus, or (2) incoherent if the photon
interacts with a single nucleon inside the nucleus. Because of the gluon
exchange mechanism in the UPC charmonium production, such production is
expected to probe the nuclear gluon distribution functions for Bjorken-$x$
between $\sim 10^{-5}$ and $10^{-2}$ with a hard scales of ${\rm Q^{2}\sim
m^{2}_{J/\psi,\psi(2S)}/4}$. The UPC charmonium productions are therefore
essential to constrain the uncertainty over the initial state, which is
currently limiting the measurements of certain fundamental properties of the
quark gluon plasma, such as the viscosity, to a high precision.

Considering the extremely low transverse momentum exchange, the event
selection of the UPC charmonium production requires a near empty detector with
two long muon tracks reconstructed. The inclusive $J/\psi$ and $\psi({\rm
2S})$ production yields are extracted from the dimuon invariant mass fit, as
shown in Fig. 3 (a) for the LHCb 2015 PbPb dataset corresponding to an
integrated luminosity of about 10 $\mu$b-1 [5], and (b) for the 2018 PbPb
dataset corresponding integrated luminosity about 20 times higher than the
2015 dataset. The coherent and incoherent parts are then distinguished using a
fit to the ${\rm\log(p_{T}^{2})}$ spectrum, as shown in Fig. 4 (a) for the
2015 dataset. The same ${\rm\log(p_{T}^{2})}$ fit is performed for five
separated charmonium rapidity bins to extract the coherent $J/\psi$ production
yields differentially.

(a)(b)

Fig. 3: (color online) Mass distributions fit to determine the fractions of
$J/\psi$ and $\psi({\rm 2S})$ and non-resonant events. Figure (a) is for 2015
dataset, and figure (b) is for 2018 dataset.

The resulting coherent $J/\psi$ production differential cross-section measured
using the 2015 data sample is shown in Fig. 4 (b), which is compatible with
most of the theoretical predictions shown in the figure, including pQCD
calculations [21] and parametrisation based on the framework of colour-dipole
model [22, 23, 24].

(a)(b)

Fig. 4: (color online) (a) Fit to the distribution of ${\rm log(p_{T}^{2})}$
of dimuon candidates after all requirements have been applied to extract the
yields of coherent and incoherent $J/\psi$ productions. (b) Differential
cross-section for coherent $J/\psi$ production measured using 2015 PbPb
dataset compared to different phenomenological predictions.

##  4 Conclusion and outlook

LHCb provides a unique opportunity to probe the cold nuclear matter effects
using Z boson production. Results of pPb collisions at 5.02 TeV and 8.16 TeV
results are presented, which are compatible with theoretical predictions
involving nPDFs, where 8.16 TeV results give the highest precision in the
forward region at LHC. Charmonium production in ultra-peripheral PbPb
collisions are of particular interests to probe gluon PDFs. Results based on
2015 PbPb dataset at 5.02 TeV are presented. Higher precision results using
2018 dataset with 20 times higher statistics for both the $J/\psi$ and
$\psi({\rm 2S})$ cross-sections are coming soon.

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Edward M. Sion https://orcid.org/0000-0003-4440-0551

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