# Searches for Mass-Asymmetric Compact Binary Coalescence Events using Neural
Networks in the LIGO/Virgo Third Observation Period

M. Andrés-Carcasona  Institut de Física d’Altes Energies (IFAE), Barcelona
Institute of Science and Technology, E-08193 Barcelona, Spain  A. Menéndez-
Vázquez  Institut de Física d’Altes Energies (IFAE), Barcelona Institute of
Science and Technology, E-08193 Barcelona, Spain  M. Martínez  Institut de
Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology,
E-08193 Barcelona, Spain  Catalan Institution for Research and Advanced
Studies (ICREA), E-08010 Barcelona, Spain  Ll. M. Mir  Institut de Física
d’Altes Energies (IFAE), Barcelona Institute of Science and Technology,
E-08193 Barcelona, Spain

###### Abstract

We present the results on the search for the coalescence of compact binary
mergers with very asymmetric mass configurations using convolutional neural
networks and the LIGO/Virgo data for the O3 observation period. Two-
dimensional images in time and frequency are used as input. Masses in the
range between 0.01 $\rm{M\textsubscript{$\odot$}}$ and 20
$\rm{M\textsubscript{$\odot$}}$ are considered. We explore neural networks
trained with input information from a single interferometer, pairs of
interferometers, or all three interferometers together, indicating that the
use of the maximum information available leads to an improved performance. A
scan over the O3 data set using the convolutional neural networks for
detection results into no significant excess from an only-noise hypothesis.
The results are translated into 90$\%$ confidence level upper limits on the
merger rate as a function of the mass parameters of the binary system.

###### pacs:

95.85.Sz, 04.80.Nn, 95.55.Ym, 04.30-w, 04.30.Tv

##  I Introduction

Since the discovery of Gravitational Waves (GW) in 2015 Abbott et al. (2016a),
generated by a compact binary coalescence (CBC) of black holes (BH), the LIGO
and Virgo experiments have improved their sensitivity and observed an
increasing number of GW signals, including also events attributed to the
coalescence of neutron stars (NS), as well as the coalescence of BH-NS binary
systems. The latest catalogue of events, from O1, O2 and O3 observation runs,
collects a total of 90 events, dominated by BH-BH candidates Abbott et al.
(2019a, 2020a); Abbott et al. (2021). The data indicate that the masses in the
binary systems range between $1.17$ M$\odot$(GW191219_163120) and $105$
M$\odot$(GW190426_190642), with a mass ratio $q\equiv m_{1}/m_{2}$, where
$m_{1}$ denotes the heaviest of the two objects, in the range between $1.1$
(GW170817) and $26.5$ (GW191219_163120). The LIGO and Virgo Collaborations use
matched-filtering techniques to extract the events from the much larger
background (for a comprehensive review of the experimental techniques see Ref.
Abbott et al. (2020b)). The use of machine learning tools has been extensively
explored in LIGO and Virgo (for a comprehensive review see Ref. Cuoco et al.
(2020)). In particular, the presence of a distinct chirp-like shape in the CBC
events, when represented in spectrograms showing the signal in frequency-time
domain, makes the use of a convolutional neural network (CNN) a valid
alternative suitable for GW detection Gabbard et al. (2018); George and Huerta
(2017); Gebhard et al. (2019); George and Huerta (2018); Menéndez-Vázquez et
al. (2021). In addition, the use of CNNs has been explored to distinguish
between families of glitches Razzano and Cuoco (2018); Biswas et al. (2013);
Cavaglia et al. (2019).

In this paper, we explore the implementation of a CNN for the identification
of CBC events with very asymmetric mass configurations with $q<2000$, and
$m_{1}$ and $m_{2}$ in range between $1$ – $20$ M$\odot$ and $0.01$ – $1$
M$\odot$, respectively. This is motivated by the search for CBC candidates
with the presence of subsolar-mass (SSM) BHs. Since there is no well-
established astrophysical explanation for the origin of SSM BHs, their
discovery would point to the presence of new physics. The presence of SSM BHs
are predicted by different models, including primordial black holes (PBHs)
from the the collapse of overdensities in the early universe Hawking (1971);
Carr and Hawking (1974); Hütsi et al. (2019, 2021); gravitational collapse of
dark matter halos D’Amico et al. (2018); Khlopov (2010); Belotsky et al.
(2014); Shandera et al. (2018); the accumulation of dark matter by neutron
stars leading to SSM BHs Kouvaris and Tinyakov (2011); or SSM boson stars Kaup
(1968); Guo et al. (2019); Colpi et al. (1986). As illustrated in Figure 1,
this study complements the phase space in mass considered by previous searches
for SSM events using O3 data and matched-filtering based selections Abbott et
al. (2021); Abbott et al. (2022a); Nitz and Wang (2022); Abbott et al.
(2022b). Previous results using other observational periods are included in
Refs. Nitz and Wang (2021a); Nitz et al. (2021); Phukon et al. (2021); Abbott
et al. (2019b).

Figure 1: Region of interest compared to other recent searches. The blue
region is the one searched by the LVK collaboration as part of the GWTC-3
catalog Abbott et al. (2021), the magenta hatched region corresponds to the
LVK subsolar mass targeted search performed over O3 data Abbott et al.
(2022a); Abbott et al. (2022b) while the green hatched region corresponds to
the broad search performed by Nitz and Wang over the O3 data Nitz and Wang
(2022).

##  II Data Preparation

The study uses the O3 data from LIGO-Hanford (H1), LIGO-Livingston (L1) and
Virgo (V1) interferometers with 4096 Hz sampling rate. After imposing quality
requirements, dealing with the understanding of the interferometer stationary
noise budget as well as the identification and suppression of glitches and
spectral noise contributions (for a comprehensive discussion see Refs. The
LIGO Scientific Collaboration (2021); Virgo Collaboration (2022)), the
H1-L1-V1 combined samples have a total duration of 155 days. The H1-L1-V1 O3
data is used for constructing an image containing a spectrogram with only
background and background plus injected signal for the purposes of the CNN
training. Special precaution was taken in the preparation of the background
images to exclude any of the identified GWs events in O3, as collected in the
GWTC-3 catalog Abbott et al. (2021). A total of $142,944$ images were used.
The results obtained (see below) show that this number of images is enough for
an adequate training and validation of the network. The images are divided as
follows: $115,200$ $(80.6\%)$ for training, $12,800$ $(9.0\%)$ for validating
and $14,944$ ($10.4\%$) for testing, evenly distributed into background-only
and background with a signal injected.

Waveforms for GW signals are generated using PyCBC Usman et al. (2016); Nitz
et al. (2017, 2020) with the IMRPhenomD Husa et al. (2016); Khan et al. (2016)
model and combined with data segments from the different interferometers,
after taking into account the proper relative orientations, times of arrival
and antenna factors. The parameters considered are uniformly sampled, as
described in Table 1, and zero spin components are assumed. Masses in the
range between 1 - 20 $\rm{M\textsubscript{$\odot$}}$ (0.01 - 1
$\rm{M\textsubscript{$\odot$}}$) are considered for $m_{1}$ ($m_{2}$), and the
corresponding luminosity distance $D_{\rm{L}}$ is limited to nearby events in
the range 1 - 100 Mpcs. Other parameters related to the position in the sky
and orientation of the source are taken as homogeneously distributed.

$m_{1}~{}[\rm{M\textsubscript{$\odot$}}]$ | $m_{2}~{}[\rm{M\textsubscript{$\odot$}}]$ |  $D_{\rm{L}}~{}[$Mpc$]$ | $\psi$ | $\theta_{JN}$ | $\alpha$ | $\cos(\delta)$
---|---|---|---|---|---|---
$[1,20]$ | $[0.01,1]$ | $[1,100]$ | $\left[0,\pi/2\right]$ | $[0,\pi]$ | $[0,2\pi]$ | $[-1,1]$
Table 1: Range of the uniformly sampled variables for the training set, being
$(m_{1},m_{2})$ the component masses, $D_{\rm{L}}$ the luminosity distance,
$\psi$ the inclination of the orbit with respect to the line of sight,
$\theta_{JN}$ the polarization of the gravitational wave and $(\alpha,\delta)$
the right ascension and declination, respectively.

The injected signals are limited to a fixed maximum duration of five seconds.
The five-seconds window is computed backward from the merger time to remove
low-amplitude monochromatic-like parts of the waveform and avoid confusing the
network during training. A low frequency threshold of 45 Hz is applied in
order to control the duration of the injected signal. Finally, the signals are
randomly placed within the five-seconds window. Once the GW signals are
injected in the different H1, L1 and V1 background segments, the data is
processed. First, the time series are whitened following the same prescription
as in Refs. Abbott et al. (2020b); Abbott et al. (2020c). Two-dimensional
arrays holding spectrogram data are then produced using $Q$-transforms Brown
(1991); Brown and Puckette (1992); Schörkhuber and Klapuri (2010) in order to
arrive to the desired images in terms of amplitude vs time vs frequency, with
400 bins in time and 100 bins in frequency. Figure 2 presents an example of
spectograms corresponding to a binary BH event with $m_{1}=2.6\
\rm{M\textsubscript{$\odot$}}$ and $m_{2}=0.35\ \rm{M\textsubscript{$\odot$}}$
at a distance of $3.4$ Mpcs. In the case of H1 and L1, the characteristic
chirp is clearly observed.

In order to account for the presence of glitches in the data, not completely
suppressed by the whitening process and leading to instabilities in the CNN
training Ioffe and Szegedy (2015), the contents in each image are renormalized
in such a way that they have an average equal to zero and a variance equal to
one, following the same prescription as in Ref. Menéndez-Vázquez et al.
(2021).

Figure 2: Spectrograms for a binary system with
$m_{1}=2.6~{}\rm{M\textsubscript{$\odot$}}$ and
$m_{2}=0.35~{}\rm{M\textsubscript{$\odot$}}$ and a distance $D_{\rm{L}}=3.4$
Mpcs, as seen in H1, L1 and V1.

##  III Neural network definition and training

This study closely follows that of Ref. Menéndez-Vázquez et al. (2021), using
a ResNet50 architecture He et al. (2016a, b) (see Table 2) with modifications
in the last layer, for which average pooling and a fully connected dense layer
(1-d fc) with a sigmoid activation function are implemented. For the loss
function, a binary cross-entropy is employed. Finally, a learning rate of
$0.01$ alongside an Adam optimizer Kingma and Ba (2014); Ruder (2016);
Goodfellow et al. (2016) and a batch size of $32$ are used for a total of $10$
epochs. With all these parameters, different CNNs have been trained using the
GPU enhanced capabilities of Keras and TensorFlow Abadi et al. (2016).

We train seven different CNNs. Three CNNs are trained separately for H1, L1
and V1 data. In addition, three CNNs are trained for H1-L1, H1-V1, and L1-V1
pairs of input data, and one CNN is trained for H1-L1-V1 combined input data,
where information from two or three interferometers are input simultaneously
to the corresponding CNNs. As expected, the performances of the CNNs improve
by including the information of multiple interferometers during the training
process, since the CNN learns about correlations across images in different
channels when the signal is present. Therefore, CNNs using single
interferometer information are discarded for the final scan over the O3 data.

Layer name | Output size | Layer structure
---|---|---
conv1 |  112$\times$112 |  7$\times$7, 64, stride 2
conv2_x | 56$\times$56 |  3$\times$3 max pool, stride 2
$\left[\begin{array}[]{c}\text{1$\times$1, 64}\\\\[-0.80005pt]
\text{3$\times$3, 64}\\\\[-0.80005pt] \text{1$\times$1,
256}\end{array}\right]$$\times$3
conv3_x | 28$\times$28 | $\left[\begin{array}[]{c}\text{1$\times$1, 128}\\\\[-0.80005pt] \text{3$\times$3, 128}\\\\[-0.80005pt] \text{1$\times$1, 512}\end{array}\right]$$\times$4
conv4_x | 14$\times$14 | $\left[\begin{array}[]{c}\text{1$\times$1, 256}\\\\[-0.80005pt] \text{3$\times$3, 256}\\\\[-0.80005pt] \text{1$\times$1, 1024}\end{array}\right]$$\times$6
conv5_x | 7$\times$7 | $\left[\begin{array}[]{c}\text{1$\times$1, 512}\\\\[-0.80005pt] \text{3$\times$3, 512}\\\\[-0.80005pt] \text{1$\times$1, 2048}\end{array}\right]$$\times$3
|  1$\times$1 | Global average pool, 1-d fc, sigmoid
Hyper parameters
Learning rate | 0.01
Batch size | 32
Number of epochs | 10
Optimizer | Adam
Loss function | Binary-cross entropy
Table 2:  CNN architecture and the associated hyper parameters. Building
blocks are shown in brackets, with the numbers of blocks stacked. Downsampling
is performed by conv3_1, conv4_1, and conv5_1 with a stride of 2 (partially
taken from He et al. (2016a)).

Figure 3 shows, for the H1-L1-V1 case, the evolution of the accuracy and loss
as a function of epochs, demonstrating stability after about eight to ten
epochs, with an accuracy above 0.8 and a loss below 0.4. In addition, the
validation accuracy is presented, demonstrating a healthy evolution of the
training process. The final CNN output for the H1-L1-V1 case is shown in
Figure 4, where a clear discrimination is obtained between signal and
background samples. Similar features in the training process and the
distribution of the final CNN discriminant are observed in the rest of CNNs.

Figure 3: Accuracy, loss and validation accuracy during the training epochs
for the H1-L1-V1 CNN.

The receiver operating characteristic (ROC) curves for the separate CNNs,
representing the true positive (TP) versus the false positive (FP) rates are
presented in Figure 5 for the H1-L1, H1-V1, L1-V1, and H1-L1-V1 CNNs. For very
low FP rates, the TP rates only reach values around $70\%$, indicating a
limited efficiency for event detection. The efficiency steadily increases at
the cost of much larger FP rates. The ROC curve, along with a tolerable
maximum false alarms rate (FAR) for detection, determines the final operating
point of a given CNN. The computation of the FAR for each CNN follows the
prescription in Ref. Abbott et al. (2016b). The FAR is defined as
${\rm{FAR(\eta)}}=N(\eta)/T$, where $\eta\in[0,1]$ is the CNN discriminant
output, $N(\eta)$ is the number of events with a CNN discriminant above or
equal to $\eta$ and $T$ the period of time analysed. In order to effectively
increase the time considered in the calculation, reaching very low FAR values,
the time slide technique Abbott et al. (2005); Abbott et al. (2016b) is used.
This allows accumulating $\mathcal{O}(10^{9})$ images of $5$ s duration each
and accessing FAR values down to $1/152.6$ years-1.

Figure 4: CNN discriminating output corresponding to the H1-L1-V1 case for
background and signal images. Figure 5: ROC curves for the different CNNs.

We initially establish a CNN discriminant $\eta_{0}$ corresponding to a
$\rm{FAR(\eta_{0})}$ value of $1$ years-1. However, the number of FP detected
remains sizable when $\eta_{0}\to 1$ and the CNNs never reach a discriminant
capable of producing only one false positive event per year. A further
improvement of the global sensitivity is achieved by combining the outputs of
the separate CNNs into a global discriminant. Such combination provides an
additional tool for suppressing glitches in the data affecting independently
the interferometers and in different time stamps. A simple average of the
H1-L1-V1, H1-L1, L1-V1, and H1-V1 CNN outputs has been considered.
Alternatively, a number of algorithms, potentially giving different weights to
different CNNs, were explored leading to very similar or even worse results.
The resulting discriminant is presented in Figure 6 demonstrating an improved
separation between background and signal, leading to a higher significance for
the events finally selected as signal. Table 3 collects the corresponding
detection rates and the computed FAR upper limit in the case of $\eta_{0}=1$
for the separate CNNs and their combination, where only the latter shows FAR
values less than 1 event per year.

Figure 6: CNN global discriminating output corresponding to the average of the H1-L1-V1, H1-L1, L1-V1, and H1-V1 CNN outputs for background and signal images. CNN | Threshold | TP rate | FP rate |  $\rm{FAR(\eta_{0}=1)}$ $[$yrs${}^{-1}]$
---|---|---|---|---
H1 – L1 | $1.0$ | $0.46$ | $\leq 2\cdot 10^{-4}$ | $\sim 10^{2}$
L1 – V1 | $1.0$ | $0.47$ | $\leq 2\cdot 10^{-4}$ | $\sim 10^{3}$
H1 – V1 | $1.0$ | $0.44$ | $\leq 2\cdot 10^{-4}$ | $\sim 10^{2}$
H1 – L1 – V1 | $1.0$ | $0.58$ | $\leq 2\cdot 10^{-4}$ | $\sim 10^{3}$
Combined | $0.998$ | $0.50$ | $\leq 2\cdot 10^{-4}$ | $\sim 10^{-2}$
Table 3: Anticipated TP and FP rates and FAR for the different CNNs and a
discriminant $\eta_{0}=1$. The FP rates represent a 95% confidence level upper
limits according to a null observation of FP in the testing set assuming
Poisson statistics.

Signal injection studies are performed to establish the sensitivity of the
different CNNs to the presence of a GW signal. For each GW signal, the signal-
to-noise ratio (SNR), $\rho$, is computed following the prescription in Ref.
Gabbard et al. (2018) solving the integral

$\rho^{2}=4\ \int_{f_{\rm{min}}}^{f_{\rm{max}}}{\rm d}f\
\frac{|\tilde{h}(f)|^{2}}{S_{n}(f)},$ (1)

in the frequency domain $(f)$, where $\tilde{h}(f)$ denotes the signal in the
frequency domain and $S_{n}(f)$ the power spectral density of the background.
A Tukey window with $\alpha=1/9$ is considered for the Fourier transform. The
SNR defined above refers to each of the interferometers separately. Following
the work in Refs. Littenberg et al. (2016); Lee et al. (2021), when
appropriate we define a network SNR, $\rho_{\rm net}$, as

$\rho_{\rm net}^{2}=\sum_{i}\rho_{i}^{2}\ ,$ (2)

where $i$ denotes the different interferometers. Figure 7 shows the fraction
of GW signals identified by the CNNs as a function of $\rho_{\rm net}$ in the
different cases. As expected, the efficiency for signal detection increases
rapidly with increasing SNR, becoming more efficient for large $\rho_{\rm
net}$ values and improving with the inclusion of information from multiple
interferometers. The best results are obtained by the H1-L1-V1 CNN. The
results from the combination of CNNs is a compromise between the H1-L1-V1 CNN
and the rest. Events with $\rho_{\rm net}\geq 25$ would be detected with an
efficiency above 95$\%$ in the case of the H1-L1-V1 CNN. Table 4 collects the
values of $\rho_{\rm net}$ at given detection efficiencies for the different
CNNs.

Figure 7: Signal detection efficiency as a function of $\rho_{\rm net}$ for the different CNNs and their combination. CNN | $\rho_{\rm net}(80\%)$ | $\rho_{\rm net}(90\%)$ | $\rho_{\rm net}(95\%)$
---|---|---|---
H1 – L1 | $24.4$ | $30.5$ | $42.0$
L1 – V1 | $23.7$ | $29.0$ | $41.2$
H1 – V1 | $26.8$ | $21.1$ | $25.8$
H1 – L1 – V1 | $17.3$ | $21.1$ | $25.8$
Combined | $22.4$ | $28.0$ | $40.1$
Table 4: Values of $\rho_{\rm net}$ at given detection efficiencies for the
different CNNs and the combination of outputs.

##  IV Results

We performed a scan of the full O3 data set, using the H1-L1-V1 combined
sample, for which a slicing window of five seconds duration was used in steps
of 2.5 seconds (leading to a 50$\%$ overlap between consecutive images) in
each of the interferometers. This translates into more than eighty million
images to be tested for the presence of potential signals. The CNN global
discriminating output, defined as the average of the H1-L1-V1, H1-L1, L1-V1,
and H1-V1 CNN outputs, is used to search for signal of SSM events. A scan over
the data using different global discriminating values in the range between 0
and 1 is performed. In each case, the corresponding FAR is computed. The
computation time for the entire O3 scan has been of the order of $2,000$ CPU-
hours (on an Intel${}^{\text{\textregistered}}$
Xeon${}^{\text{\textregistered}}$ CPU E5-2680 v4 @ 2.40GHz). This represents a
major improvement compared with the typically required CPU-time for known
matched filtering pipelines.

Figure 8: Observed cumulative event count as a function of the inverse false
alarm rate for the O3 scan (dots). The data is compared to foreground
predictions (dashed line) and including 1$\sigma$, 2$\sigma$, and 3$\sigma$
bands (shadowed areas).

The resulting inverse FAR distribution (IFAR), in units of years, is presented
in Figure 8 compared to the expected yield of noise events following a Poisson
probability distribution. No significant deviation from the expected noise is
observed and no claim of SSM event detection can be made. For illustration
purposes, Figure 9 shows the H1, L1 and V1 spectrograms for the most
significant event having a FAR of $1.9$ years-1, a combined CNN value equal to
0.9635, and CNN values equal to 0.9848, 0.9172, 0.9774 and 0.9747 for the
H1-L1-V1, H1-L1, L1-V1, and H1-V1 neural networks, respectively.

Figure 9: Spectrogram of the most significant image. Corresponds to a
$\mathrm{FAR}=1.9~{}\mathrm{yrs}^{-1}$

The results are translated into 90$\%$ confidence level (CL) upper limits of
the merger rate of binary systems in the range of masses and $q$ values
considered. Since the sensitivity for detection mostly depends on the chirp
mass of the binary system, defined as
$\mathcal{M}_{c}\equiv\frac{(m_{1}m_{2})^{3/5}}{(m_{1}+m_{2})^{1/5}}$, the
computed merger rates are binned in $\mathcal{M}_{c}$ instead of in the single
masses of the binary system. The 90$\%$ CL upper limits are calculated using
the loudest event statistics approach Tiwari (2018); Abbott et al. (2022a);
Nitz and Wang (2021b, 2022); Abbott et al. (2022b) in terms of the surveyed
time-volume $\langle VT\rangle$, following the expression

$\mathcal{R}_{\rm{90}}=\frac{2.3}{\langle VT\rangle},\ \langle VT\rangle=T\
\int{\rm d}z\frac{1}{1+z}\frac{{\rm d}V_{c}}{{\rm d}z}\varepsilon(z),$ (3)

where $T$ is the total observation time, $z$ denotes the redshift, $V_{c}$ is
the comoving volume and $\varepsilon$ is the efficiency for detection. In this
study $T$ is limited to $155$ days when H1, L1 and V1 interferometers were all
taking data simultaneously. Figure 10 presents the detection efficiency of the
combined CNN discriminant as a function of $z$ in several $\mathcal{M}_{c}$
bins. The efficiency is computed using injected signals and it vanishes for
$z>0.06$. The integral above is marginalized over the rest of parameters of
the binary system (see Table 1), which are considered homogeneously
distributed in comoving volume.

Figure 10: Detection efficiency for the combined CNN discriminant as a
function of $z$ for different values of the chirp mass.

Figures 11 and 12 presents the 90$\%$ CL upper limits on the merging rate as a
function of the chirp mass and as a function of $m_{2}$ in different $m_{1}$
regions, respectively. The results are compared to similar results from
matched-filtering based analyses. Our result provides 90$\%$ CL upper limits
in the range between $3\times 10^{6}~{}\mathrm{Gpc}^{-3}\mathrm{yrs}^{-1}$ and
$560~{}\mathrm{Gpc}^{-3}\mathrm{yrs}^{-1}$ with increasing chirp mass,
extending previous results to chirp masses up to 3
$\rm{M\textsubscript{$\odot$}}$. At lower chirp mass, our constrains are
weaker than previous results. This is partially attributed to the effective
reduction of the observation time, by a factor of about two, from limiting the
data to simultaneous H1-L1-V1 configurations, as a way to obtain manageable
false alarm rates. As shown in Figure 12, the constrains from our analysis are
more stringent with increasing mass difference $m_{1}-m_{2}$, as expected for
a CNN trained on very asymmetric configurations.

Figure 11: The 90$\%$ confidence level upper limit on $\mathcal{R}_{\rm{90}}$
as a function of the chirp mass. Our result (solid line) is compared with
matched-filtering based results Abbott et al. (2022b); Nitz and Wang (2022)
(dashed lines). Figure 12: The 90$\%$ confidence level upper limit on
$\mathcal{R}_{\rm{90}}$ as function of $m_{2}$ in different $m_{1}$ regions.
Our result (solid lines) is compared with Nitz et al. results Nitz and Wang
(2022) (dashed line).

##  V Conclusions

We present the results on a search for compact binary coalescence events with
asymmetric mass configurations with masses in the range
$0.01~{}\rm{M\textsubscript{$\odot$}}$ and $1~{}\rm{M\textsubscript{$\odot$}}$
for the lighter object and between $1~{}\rm{M\textsubscript{$\odot$}}$ and
$20~{}\rm{M\textsubscript{$\odot$}}$ for the heavier, using LIGO-Virgo O3 data
and dedicated convoluted neural networks based on the analysis of frequency-
time spectrograms. Different neural networks and combination of them are
explored, involving the simultaneous use of several interferometers data. The
scan over the O3 data results into no significant signal events found. The CNN
approach for scanning the data is found to be much faster than traditional
matched-filtering based pipelines. The CNN results are translated into 90$\%$
confidence level upper limits on the merger rates as a function of the mass
parameters of the binary system for events within $z<0.06$ and for the trained
range. Although the results do not improve other bounds using matched-
filtering techniques, partially due to the limited observation time
considered, the CNN approach allows for effectively extending the search
towards larger chirp masses.

## Acknowledgements

This material is based upon work supported by NSF’s LIGO Laboratory which is a
major facility fully funded by the National Science Foundation. The authors
also gratefully acknowledge the support of the Science and Technology
Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS),
and the State of Niedersachsen/Germany for support of the construction of
Advanced LIGO and construction and operation of the GEO 600 detector.
Additional support for Advanced LIGO was provided by the Australian Research
Council. The authors gratefully acknowledge the Italian Istituto Nazionale di
Fisica Nucleare (INFN), the French Centre National de la Recherche
Scientifique (CNRS) and the Netherlands Organization for Scientific Research
(NWO), for the construction and operation of the Virgo detector and the
creation and support of the EGO consortium. The authors thankfully acknowledge
the computer resources at MinoTauro and the technical support provided by
Barcelona Supercomputing Center (RES-FI-2021-3-0020). MAC is supported by the
2022 FI-00335 grant. This paper has been given LIGO DCC number
LIGO-P2200184-v2. This work is partially supported by the Spanish MCIN/AEI/
10.13039/501100011033 under the grants SEV-2016-0588, PGC2018-101858-B-I00,
and PID2020-113701GB-I00 some of which include ERDF funds from the European
Union. IFAE is partially funded by the CERCA program of the Generalitat de
Catalunya. This work was carried out within the framework of the EU COST
action No. CA17137.

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