29 INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy

30 Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater
Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127
Bologna, Italy

31 Centre National d'Etudes Spatiales – Centre spatial de Toulouse,
18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France

32 Institut national de physique nucléaire et de physique des particules,
3 rue Michel-Ange, 75794 Paris Cedex 16, France

33 Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK

34 Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK

35 European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy

36 ESAC/ESA, Camino Bajo del Castillo s/n, Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain

37 University of Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, 69622 Villeurbanne, France

38 Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK

39 Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016 Lisboa, Portugal

40 Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal

41 Department of Astronomy, University of Geneva, ch. d'Ecogia 16, 1290 Versoux, Switzerland

42 INFN-Padova, Via Marzolo 8, 35131 Padova, Italy

43 Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France

44 INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy

45 INAF-Osservatorio Astronomico di Padova, Via dell'Osservatorio 5, 35122 Padova, Italy

46 University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679 Munich, Germany

47 INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy

48 INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy

49 Institute of Theoretical Astrophysics, University of Oslo,
PO Box 1029 Blindern, 0315 Oslo, Norway

50 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, 91109, USA

51 von Hoerner & Sulger GmbH, SchloßPlatz 8, 68723 Schwetzingen, Germany

52 Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark

53 Cosmic Dawn Center (DAWN), Denmark

54 Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany

55 Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany

56 Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France

57 Université de Genève, Département de Physique Théorique and
Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, 1211
Genève 4, Switzerland

58 Department of Physics, PO Box 64, 00014 University of Helsinki, Finland

59 Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland

60 NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, 7991PD Dwingeloo, The Netherlands

61 Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

62 Department of Physics, Institute for Computational Cosmology,
Durham University, South Road, Durham DH1 3LE, UK

63 Université Paris-Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France

64 University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland

65 Institut d'Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France

66 CEA Saclay, DFR/IRFU, Service d'Astrophysique, Bât. 709, 91191 Gif-sur-Yvette, France

67 European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands

68 Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands

69 Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands

70 Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, 8000 Aarhus C, Denmark

71 Université Paris-Saclay, Université Paris Cité, CEA, CNRS, Astro-
physique, Instrumentation et Modélisation Paris-Saclay, 91191
Gif-sur-Yvette, France

72 Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy

73 Dipartimento di Fisica e Astronomia "G. Galilei", Università di Padova, Via Marzolo 8, 35131 Padova, Italy

74 Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile

75 Institut d'Estudis Espacials de Catalunya (IEEC), Carrer Gran Capitá 2-4, 08034 Barcelona, Spain

76 Institut de Ciencies de l'Espai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n Cerdanyola del Vallés, 08193 Barcelona, Spain

77 Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain

78 Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal

79 Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain

80 Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France

81 INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy

82 Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA

83 Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, 38204, San Cristóbal de La Laguna, Tenerife, Spain

84 INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere 100, 00100 Roma, Italy

85 Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland

86 Junia, EPA department, 41 Bd Vauban, 59800 Lille, France

87 Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain

88 CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA

89 Laboratoire de Physique de l'École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, 75005 Paris, France

90 Observatoire de Paris, Université PSL, Sorbonne Université, LERMA, 750 Paris, France

91 Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK

92 Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

93 SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, TS, Italy

94 IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy

95 INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, TS, Italy

96 Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy

97 Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
98 Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy

99 NASA Ames Research Center, Moffett Field, CA 94035, USA

100 Kavli Institute for Particle Astrophysics & Cosmology (KIPAC),
Stanford University, Stanford, CA 94305, USA

101 Department of Astronomy and Astrophysics, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA

102 INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy

103 Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Bd de l'Observatoire, CS 34229, 06304 Nice Cedex 4, France

104 Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany

105 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA

106 Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA

107 UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France

108 Department of Astronomy & Physics and Institute for Computational Astrophysics, Saint Mary's University, 923 Robie Street, Halifax, NS B3H 3C3, Canada

109 Dipartimento di Fisica, Università degli studi di Genova, and INFN-Sezione di Genova, via Dodecaneso 33, 16146 Genova, Italy

110 Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain

111 Department of Computer Science, Aalto University, PO Box 15400, Espoo 00 076, Finland

112 Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany

113 Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK

114 Instituto de Astrofísica de Canarias (IAC), Departamento de Astrofísica, Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain

115 Université Paris-Cité, 5 rue Thomas Mann, 75013 Paris, France

116 Université PSL, Observatoire de Paris, Sorbonne Université, CNRS, LERMA, 75014 Paris, France

117 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

118 Department of Physics and Astronomy, Vesiilinnantie 5, 20014 University of Turku, Turku, Finland

119 AIM, CEA, CNRS, Université Paris-Saclay, Université de Paris, 91191 Gif-sur-Yvette, France

120 Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm 106 91, Sweden

121 Centre de Calcul de l'IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France

122 Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy

123 INFN-Sezione di Roma, Piazzale Aldo Moro 2, c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy

124 Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal

125 Department of Mathematics and Physics E. De Giorgi, University of Salento, Via per Arnesano, CP-193, 73100 Lecce, Italy

126 INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica, Via per Arnesano, 73100 Lecce, Italy

127 INFN, Sezione di Lecce, Via per Arnesano, CP-193, 73100 Lecce, Italy

128 Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania

129 Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland

130 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany

131 Université St Joseph; Faculty of Sciences, Beirut, Lebanon

132 Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA

133 Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, 44001 Teruel, Spain
98 Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy

99 NASA Ames Research Center, Moffett Field, CA 94035, USA

100 Kavli Institute for Particle Astrophysics & Cosmology (KIPAC),
Stanford University, Stanford, CA 94305, USA

101 Department of Astronomy and Astrophysics, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA

102 INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy

103 Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Bd de l'Observatoire, CS 34229, 06304 Nice Cedex 4, France

104 Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany

105 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA

106 Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA

107 UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France

108 Department of Astronomy & Physics and Institute for Computational Astrophysics, Saint Mary's University, 923 Robie Street, Halifax, NS B3H 3C3, Canada

109 Dipartimento di Fisica, Università degli studi di Genova, and INFN-Sezione di Genova, via Dodecaneso 33, 16146 Genova, Italy

110 Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain

111 Department of Computer Science, Aalto University, PO Box 15400, Espoo 00 076, Finland

112 Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany

113 Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK

114 Instituto de Astrofísica de Canarias (IAC), Departamento de Astrofísica, Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain

115 Université Paris-Cité, 5 rue Thomas Mann, 75013 Paris, France

116 Université PSL, Observatoire de Paris, Sorbonne Université, CNRS, LERMA, 75014 Paris, France

117 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

118 Department of Physics and Astronomy, Vesiilinnantie 5, 20014 University of Turku, Turku, Finland

119 AIM, CEA, CNRS, Université Paris-Saclay, Université de Paris, 91191 Gif-sur-Yvette, France

120 Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm 106 91, Sweden

121 Centre de Calcul de l'IN2P3/CNRS, 21 avenue Pierre de Coubertin, 69627 Villeurbanne Cedex, France

122 Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy

123 INFN-Sezione di Roma, Piazzale Aldo Moro 2, c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy

124 Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal

125 Department of Mathematics and Physics E. De Giorgi, University of Salento, Via per Arnesano, CP-193, 73100 Lecce, Italy

126 INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica, Via per Arnesano, 73100 Lecce, Italy

127 INFN, Sezione di Lecce, Via per Arnesano, CP-193, 73100 Lecce, Italy

128 Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania

129 Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland

130 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany

131 Université St Joseph; Faculty of Sciences, Beirut, Lebanon

132 Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA

133 Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, 44001 Teruel, Spain
# Appendix A: Network architectures

The three figures in this appendix show the architectures of the networks we implemented. In particular, Fig.A.1 shows the VGG-like network, Fig. A.2 shows the IncNet, and Fig. A.3 shows the ResNet.

<figure><img src="image_9.png" /><figcaption>**Fig. A.1.** VGG-like network configurations tested on (a) VIS images and (b) multiband images. We report the dimension (*D*) and number (*F*) of the filters used in the convolutional layers in the format *D×D*, *F*. We also indicate the pooling region (*R*) and the strides (*S*) in the pooling layers in the format *R×R*, *S*. The numbers in square brackets indicate the dimension and number of the feature maps obtained as the output of the layers in the format [*D×D×F*] in the case of the convolutional layers, and the number of nodes in the format [*N*] in the case of the fully connected layers.</figcaption></figure>
Appendix A: Network architectures

The three figures in this appendix show the architectures of the networks we implemented. In particular, Fig.A.1 shows the VGG-like network, Fig. A.2 shows the IncNet, and Fig. A.3 shows the ResNet.

<figure><img src="image_11.png" /><figcaption>**Fig. A.1.** VGG-like network configurations tested on (a) VIS images and (b) multiband images. We report the dimension (D) and number (F) of the filters used in the convolutional layers in the format *D×D*, *F*. We also indicate the pooling region (R) and the strides (S) in the pooling layers in the format *R×R*, *S*. The numbers in square brackets indicate the dimension and number of the feature maps obtained as the output of the layers in the format [*D×D×F*] in the case of the convolutional layers, and the number of nodes in the format [*N*] in the case of the fully connected layers.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. A.2.** Inception network configurations tested on (a) VIS images and (b) multiband images. These diagrams use the same notation as in Fig. A.1. Every inception module (IncMod) is built as described in subsection 2.1.2.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. A.2.** Inception network configurations tested on (a) VIS images and (b) multiband images. These diagrams use the same notation as in Fig. A.1. Every inception module (IncMod) is built as described in subsection 2.1.2.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. A.3.** Residual network configurations tested on (a) VIS images and (b) multiband images. These diagrams use the same notation as in Fig. A.1. Every residual block (ResBlock) is built as described in subsection 2.1.3: c8 refers to the cardinality of the block, which we set to be equal to eight.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Fig. A.3.** Residual network configurations tested on (a) VIS images and (b) multiband images. These diagrams use the same notation as in Fig. A.1. Every residual block (ResBlock) is built as described in subsection 2.1.3: c8 refers to the cardinality of the block, which we set to be equal to eight.</figcaption></figure>
## Appendix B: Tables

In this appendix, we summarize the main results of our tests. In Table B.1 we show the results of training our models on VIS images, in Table B.2 we compare the results of applying our models trained on S2 and on S4 to the test set S4, in Table B.3 we show the results of two additional tests, S2/S3, and S2/S4, in Table B.4 we show the results of training our models on multiband images, and in Table B.5 we present the results of a test with realistic proportions between lenses and nonlenses.

<table><caption>**Table B.1.** Summary of the performance of the VGG-like network, the IncNet, and the ResNet in classifying the objects of the four selections of images in the $I_E$ band.</caption><thead><tr><th colspan="9">VGG-like network</th></tr><tr><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><th scope="row">Precision</th><td>0.95</td><td>0.98</td><td>0.94</td><td>0.97</td><td>0.92</td><td>0.94</td><td>0.79</td><td>0.89</td></tr><tr><th scope="row">Recall</th><td>0.98</td><td>0.94</td><td>0.98</td><td>0.94</td><td>0.94</td><td>0.92</td><td>0.90</td><td>0.77</td></tr><tr><th scope="row">F1-score</th><td>0.96</td><td>0.96</td><td>0.96</td><td>0.96</td><td>0.93</td><td>0.93</td><td>0.84</td><td>0.83</td></tr><tr><th scope="row">Accuracy</th><td>0.96</td><td></td><td>0.96</td><td></td><td>0.93</td><td></td><td>0.84</td><td></td></tr><tr><th scope="row">AUC</th><td>0.77</td><td></td><td>0.58</td><td></td><td>0.88</td><td></td><td>0.57</td><td></td></tr></tbody><tbody><tr><th colspan="9">Inception Network</th></tr><tr><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th></th><th></th><th></th><th></th></tr><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><th scope="row">Precision</th><td>0.97</td><td>1.0</td><td>0.97</td><td>0.96</td><td>0.94</td><td>0.93</td><td>0.84</td><td>0.90</td></tr><tr><th scope="row">Recall</th><td>1.0</td><td>0.96</td><td>0.96</td><td>0.97</td><td>0.93</td><td>0.94</td><td>0.91</td><td>0.83</td></tr><tr><th scope="row">F1-score</th><td>0.98</td><td>0.98</td><td>0.96</td><td>0.96</td><td>0.93</td><td>0.94</td><td>0.87</td><td>0.86</td></tr><tr><th scope="row">Accuracy</th><td>0.98</td><td></td><td>0.96</td><td></td><td>0.94</td><td></td><td>0.87</td><td></td></tr><tr><th scope="row">AUC</th><td>0.92</td><td></td><td>0.88</td><td></td><td>0.90</td><td></td><td>0.81</td><td></td></tr></tbody><tbody><tr><th colspan="9">Residual Network</th></tr><tr><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th></th><th></th><th></th><th></th></tr><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><th scope="row">Precision</th><td>0.93</td><td>0.97</td><td>0.90</td><td>0.92</td><td>0.86</td><td>0.89</td><td>0.71</td><td>0.84</td></tr><tr><th scope="row">Recall</th><td>0.97</td><td>0.92</td><td>0.92</td><td>0.89</td><td>0.89</td><td>0.85</td><td>0.87</td><td>0.66</td></tr><tr><th scope="row">F1-score</th><td>0.95</td><td>0.94</td><td>0.91</td><td>0.91</td><td>0.88</td><td>0.87</td><td>0.78</td><td>0.74</td></tr><tr><th scope="row">Accuracy</th><td>0.95</td><td></td><td>0.91</td><td></td><td>0.87</td><td></td><td>0.76</td><td></td></tr><tr><th scope="row">AUC</th><td>0.81</td><td></td><td>0.85</td><td></td><td>0.79</td><td></td><td>0.70</td><td></td></tr></tbody></table>

**Notes.** The precision, recall, and F1-score are evaluated on the class of the nonlenses (0) and of the lenses (1) separately, while accuracy and AUC are global quantities.
## Appendix B: Tables

In this appendix, we summarize the main results of our tests. In Table B.1 we show the results of training our models on VIS images, in Table B.2 we compare the results of applying our models trained on S2 and on S4 to the test set S4, in Table B.3 we show the results of two additional tests, S2/S3, and S2/S4, in Table B.4 we show the results of training our models on multiband images, and in Table B.5 we present the results of a test with realistic proportions between lenses and nonlenses.

<table><caption>**Table B.1.** Summary of the performance of the VGG-like network, the IncNet, and the ResNet in classifying the objects of the four selections of images in the $I_E$ band.</caption><thead><tr><th colspan="9">VGG-like network</th></tr><tr><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><th scope="row">Precision</th><td>0.95</td><td>0.98</td><td>0.94</td><td>0.97</td><td>0.92</td><td>0.94</td><td>0.79</td><td>0.89</td></tr><tr><th scope="row">Recall</th><td>0.98</td><td>0.94</td><td>0.98</td><td>0.94</td><td>0.94</td><td>0.92</td><td>0.90</td><td>0.77</td></tr><tr><th scope="row">F1-score</th><td>0.96</td><td>0.96</td><td>0.96</td><td>0.96</td><td>0.93</td><td>0.93</td><td>0.84</td><td>0.83</td></tr><tr><th scope="row">Accuracy</th><td>0.96</td><td></td><td>0.96</td><td></td><td>0.93</td><td></td><td>0.84</td><td></td></tr><tr><th scope="row">AUC</th><td>0.77</td><td></td><td>0.58</td><td></td><td>0.88</td><td></td><td>0.57</td><td></td></tr></tbody><tbody><tr><th colspan="9">Inception Network</th></tr><tr><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th></th><th></th><th></th><th></th></tr><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><th scope="row">Precision</th><td>0.97</td><td>1.0</td><td>0.97</td><td>0.96</td><td>0.94</td><td>0.93</td><td>0.84</td><td>0.90</td></tr><tr><th scope="row">Recall</th><td>1.0</td><td>0.96</td><td>0.96</td><td>0.97</td><td>0.93</td><td>0.94</td><td>0.91</td><td>0.83</td></tr><tr><th scope="row">F1-score</th><td>0.98</td><td>0.98</td><td>0.96</td><td>0.96</td><td>0.93</td><td>0.94</td><td>0.87</td><td>0.86</td></tr><tr><th scope="row">Accuracy</th><td>0.98</td><td></td><td>0.96</td><td></td><td>0.94</td><td></td><td>0.87</td><td></td></tr><tr><th scope="row">AUC</th><td>0.92</td><td></td><td>0.88</td><td></td><td>0.90</td><td></td><td>0.81</td><td></td></tr></tbody><tbody><tr><th colspan="9">Residual Network</th></tr><tr><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th></th><th></th><th></th><th></th></tr><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><th scope="row">Precision</th><td>0.93</td><td>0.97</td><td>0.90</td><td>0.92</td><td>0.86</td><td>0.89</td><td>0.71</td><td>0.84</td></tr><tr><th scope="row">Recall</th><td>0.97</td><td>0.92</td><td>0.92</td><td>0.89</td><td>0.89</td><td>0.85</td><td>0.87</td><td>0.66</td></tr><tr><th scope="row">F1-score</th><td>0.95</td><td>0.94</td><td>0.91</td><td>0.91</td><td>0.88</td><td>0.87</td><td>0.78</td><td>0.74</td></tr><tr><th scope="row">Accuracy</th><td>0.95</td><td></td><td>0.91</td><td></td><td>0.87</td><td></td><td>0.76</td><td></td></tr><tr><th scope="row">AUC</th><td>0.81</td><td></td><td>0.85</td><td></td><td>0.79</td><td></td><td>0.70</td><td></td></tr></tbody></table>

**Notes.** The precision, recall, and F1-score are evaluated on the class of the nonlenses (0) and of the lenses (1) separately, while accuracy and AUC are global quantities.
<table><caption>**Table B.2.** Comparison between the metrics of tests on the selection S2 with the models trained on S2 (top) and on S4 (bottom).</caption><thead><tr><th></th><th colspan="6">S2/S2</th></tr><tr><th></th><th colspan="2">VGG-like network</th><th colspan="2">Inception Network</th><th colspan="2">Residual Network</th></tr><tr><th>Class</th><th>0</th><th>1</th><th>0</th><th>1</th><th>0</th><th>1</th></tr></thead><tbody><tr><th>Precision</th><td>0.94</td><td>0.97</td><td>0.97</td><td>0.96</td><td>0.90</td><td>0.92</td></tr><tr><th>Recall</th><td>0.98</td><td>0.94</td><td>0.96</td><td>0.97</td><td>0.92</td><td>0.89</td></tr><tr><th>F1-score</th><td>0.96</td><td>0.96</td><td>0.96</td><td>0.96</td><td>0.91</td><td>0.91</td></tr><tr><th>Accuracy</th><td colspan="2">0.96</td><td colspan="2">0.96</td><td colspan="2">0.91</td></tr><tr><th>AUC</th><td colspan="2">0.58</td><td colspan="2">0.88</td><td colspan="2">0.85</td></tr></tbody><thead><tr><th></th><th colspan="6">S4/S2</th></tr><tr><th></th><th colspan="2">VGG-like network</th><th colspan="2">Inception Network</th><th colspan="2">Residual Network</th></tr><tr><th>Class</th><th>0</th><th>1</th><th>0</th><th>1</th><th>0</th><th>1</th></tr></thead><tbody><tr><th>Precision</th><td>0.96</td><td>0.74</td><td>0.99</td><td>0.77</td><td>0.95</td><td>0.67</td></tr><tr><th>Recall</th><td>0.89</td><td>0.91</td><td>0.90</td><td>0.98</td><td>0.85</td><td>0.89</td></tr><tr><th>F1-score</th><td>0.93</td><td>0.82</td><td>0.94</td><td>0.86</td><td>0.90</td><td>0.76</td></tr><tr><th>Accuracy</th><td colspan="2">0.89</td><td colspan="2">0.92</td><td colspan="2">0.86</td></tr><tr><th>AUC</th><td colspan="2">0.51</td><td colspan="2">0.88</td><td colspan="2">0.75</td></tr></tbody></table>

**Notes.** Class 0 refers to the nonlenses, while class 1 refers to the lenses.

<table><caption>**Table B.3.** Summary of the performance of the VGG-like network, the inception network, and the residual network, trained on the selection S2, in classifying the objects that are part of the selections S3 and S4.</caption><thead><tr><th></th><th colspan="2">VGG-like network</th><th colspan="2">Inception Network</th><th colspan="2">Residual Network</th></tr><tr><th></th><th colspan="2">S2/S3</th><th colspan="2">S2/S4</th><th colspan="2">S2/S3</th><th colspan="2">S2/S4</th></tr><tr><th>Class</th><th>0</th><th>1</th><th>0</th><th>1</th><th>0</th><th>1</th><th>0</th><th>1</th></tr></thead><tbody><tr><th>Precision</th><td>0.77</td><td>0.97</td><td>0.62</td><td>0.95</td><td>0.82</td><td>0.96</td><td>0.65</td><td>0.93</td><td>0.75</td><td>0.88</td><td>0.64</td><td>0.85</td></tr><tr><th>Recall</th><td>0.98</td><td>0.68</td><td>0.98</td><td>0.33</td><td>0.97</td><td>0.76</td><td>0.97</td><td>0.42</td><td>0.92</td><td>0.67</td><td>0.94</td><td>0.40</td></tr><tr><th>F1-score</th><td>0.86</td><td>0.80</td><td>0.76</td><td>0.48</td><td>0.89</td><td>0.85</td><td>0.78</td><td>0.58</td><td>0.83</td><td>0.76</td><td>0.76</td><td>0.55</td></tr><tr><th>Accuracy</th><td colspan="2">0.83</td><td colspan="2">0.68</td><td colspan="2">0.87</td><td colspan="2">0.71</td><td colspan="2">0.80</td><td colspan="2">0.69</td></tr><tr><th>AUC</th><td colspan="2">0.57</td><td colspan="2">0.52</td><td colspan="2">0.81</td><td colspan="2">0.7</td><td colspan="2">0.78</td><td colspan="2">0.65</td></tr></tbody></table>

**Notes.** The precision, recall, and F1-score are evaluated on the class of the nonlenses (0) and of the lenses (1) separately.
<table><caption>**Table B.2.** Comparison between the metrics of tests on the selection S2 with the models trained on S2 (top) and on S4 (bottom).</caption><thead><tr><th></th><th colspan="6">S2/S2</th></tr><tr><th></th><th colspan="2">VGG-like network</th><th colspan="2">Inception Network</th><th colspan="2">Residual Network</th></tr><tr><th>Class</th><th>0</th><th>1</th><th>0</th><th>1</th><th>0</th><th>1</th></tr></thead><tbody><tr><th>Precision</th><td>0.94</td><td>0.97</td><td>0.97</td><td>0.96</td><td>0.90</td><td>0.92</td></tr><tr><th>Recall</th><td>0.98</td><td>0.94</td><td>0.96</td><td>0.97</td><td>0.92</td><td>0.89</td></tr><tr><th>F1-score</th><td>0.96</td><td>0.96</td><td>0.96</td><td>0.96</td><td>0.91</td><td>0.91</td></tr><tr><th>Accuracy</th><td colspan="2">0.96</td><td colspan="2">0.96</td><td colspan="2">0.91</td></tr><tr><th>AUC</th><td colspan="2">0.58</td><td colspan="2">0.88</td><td colspan="2">0.85</td></tr></tbody><thead><tr><th></th><th colspan="6">S4/S2</th></tr><tr><th></th><th colspan="2">VGG-like network</th><th colspan="2">Inception Network</th><th colspan="2">Residual Network</th></tr><tr><th>Class</th><th>0</th><th>1</th><th>0</th><th>1</th><th>0</th><th>1</th></tr></thead><tbody><tr><th>Precision</th><td>0.96</td><td>0.74</td><td>0.99</td><td>0.77</td><td>0.95</td><td>0.67</td></tr><tr><th>Recall</th><td>0.89</td><td>0.91</td><td>0.90</td><td>0.98</td><td>0.85</td><td>0.89</td></tr><tr><th>F1-score</th><td>0.93</td><td>0.82</td><td>0.94</td><td>0.86</td><td>0.90</td><td>0.76</td></tr><tr><th>Accuracy</th><td colspan="2">0.89</td><td colspan="2">0.92</td><td colspan="2">0.86</td></tr><tr><th>AUC</th><td colspan="2">0.51</td><td colspan="2">0.88</td><td colspan="2">0.75</td></tr></tbody></table>

**Notes.** Class 0 refers to the nonlenses, while class 1 refers to the lenses.

<table><caption>**Table B.3.** Summary of the performance of the VGG-like network, the inception network, and the residual network, trained on the selection S2, in classifying the objects that are part of the selections S3 and S4.</caption><thead><tr><th></th><th colspan="2">VGG-like network</th><th colspan="2">Inception Network</th><th colspan="2">Residual Network</th></tr><tr><th></th><th colspan="2">S2/S3</th><th colspan="2">S2/S4</th><th colspan="2">S2/S3</th><th colspan="2">S2/S4</th></tr><tr><th>Class</th><th>0</th><th>1</th><th>0</th><th>1</th><th>0</th><th>1</th><th>0</th><th>1</th></tr></thead><tbody><tr><th>Precision</th><td>0.77</td><td>0.97</td><td>0.62</td><td>0.95</td><td>0.82</td><td>0.96</td><td>0.65</td><td>0.93</td><td>0.75</td><td>0.88</td><td>0.64</td><td>0.85</td></tr><tr><th>Recall</th><td>0.98</td><td>0.68</td><td>0.98</td><td>0.33</td><td>0.97</td><td>0.76</td><td>0.97</td><td>0.42</td><td>0.92</td><td>0.67</td><td>0.94</td><td>0.40</td></tr><tr><th>F1-score</th><td>0.86</td><td>0.80</td><td>0.76</td><td>0.48</td><td>0.89</td><td>0.85</td><td>0.78</td><td>0.58</td><td>0.83</td><td>0.76</td><td>0.76</td><td>0.55</td></tr><tr><th>Accuracy</th><td colspan="2">0.83</td><td colspan="2">0.68</td><td colspan="2">0.87</td><td colspan="2">0.71</td><td colspan="2">0.80</td><td colspan="2">0.69</td></tr><tr><th>AUC</th><td colspan="2">0.57</td><td colspan="2">0.52</td><td colspan="2">0.81</td><td colspan="2">0.7</td><td colspan="2">0.78</td><td colspan="2">0.65</td></tr></tbody></table>

**Notes.** The precision, recall, and F1-score are evaluated on the class of the nonlenses (0) and of the lenses (1) separately.
<table><caption>**Table B.4.** Same as in Table B.1, but using images in the VIS and NISP bands.</caption><thead><tr><th colspan="9">VGG-like network</th></tr><tr><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><th scope="row">Precision</th><td>0.99</td><td>0.97</td><td>0.98</td><td>0.97</td><td>0.91</td><td>0.96</td><td>0.81</td><td>0.91</td></tr><tr><th scope="row">Recall</th><td>0.97</td><td>0.99</td><td>0.97</td><td>0.98</td><td>0.96</td><td>0.91</td><td>0.92</td><td>0.79</td></tr><tr><th scope="row">F1-score</th><td>0.98</td><td>0.98</td><td>0.98</td><td>0.98</td><td>0.94</td><td>0.93</td><td>0.86</td><td>0.84</td></tr><tr><th scope="row">Accuracy</th><td>0.98</td><td></td><td>0.98</td><td></td><td>0.93</td><td></td><td>0.85</td><td></td></tr><tr><th scope="row">AUC</th><td>0.65</td><td></td><td>0.87</td><td></td><td>0.67</td><td></td><td>0.62</td><td></td></tr><tr><th colspan="9">Inception Network</th></tr><tr><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th></th><th></th><th></th><th></th></tr><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><th scope="row">Precision</th><td>0.98</td><td>0.96</td><td>0.97</td><td>0.98</td><td>0.96</td><td>0.96</td><td>0.87</td><td>0.91</td></tr><tr><th scope="row">Recall</th><td>0.96</td><td>0.98</td><td>0.98</td><td>0.96</td><td>0.96</td><td>0.96</td><td>0.91</td><td>0.87</td></tr><tr><th scope="row">F1-score</th><td>0.97</td><td>0.97</td><td>0.97</td><td>0.97</td><td>0.96</td><td>0.96</td><td>0.89</td><td>0.89</td></tr><tr><th scope="row">Accuracy</th><td>0.97</td><td></td><td>0.97</td><td></td><td>0.96</td><td></td><td>0.89</td><td></td></tr><tr><th scope="row">AUC</th><td>0.77</td><td></td><td>0.9</td><td></td><td>0.92</td><td></td><td>0.84</td><td></td></tr><tr><th colspan="9">Residual Network</th></tr><tr><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th></th><th></th><th></th><th></th></tr><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><th scope="row">Precision</th><td>0.96</td><td>0.95</td><td>0.92</td><td>0.94</td><td>0.86</td><td>0.92</td><td>0.74</td><td>0.85</td></tr><tr><th scope="row">Recall</th><td>0.94</td><td>0.96</td><td>0.94</td><td>0.92</td><td>0.92</td><td>0.87</td><td>0.87</td><td>0.71</td></tr><tr><th scope="row">F1-score</th><td>0.95</td><td>0.95</td><td>0.93</td><td>0.93</td><td>0.90</td><td>0.89</td><td>0.80</td><td>0.77</td></tr><tr><th scope="row">Accuracy</th><td>0.95</td><td></td><td>0.93</td><td></td><td>0.90</td><td></td><td>0.78</td><td></td></tr><tr><th scope="row">AUC</th><td>0.81</td><td></td><td>0.88</td><td></td><td>0.81</td><td></td><td>0.72</td><td></td></tr></tbody></table>

<table><caption>**Table B.5.** Results of testing our best-performing networks, trained on S1, on a test set with 200 lenses and 80 000 nonlenses.</caption><thead><tr><th></th><th colspan="2">VGG-like network</th><th colspan="2">Inception Network</th><th colspan="2">Residual Network</th><th colspan="2">Ensemble Network</th></tr><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr></thead><tbody><tr><th scope="row">Precision</th><td>1.0</td><td>0.15</td><td>1.0</td><td>0.45</td><td>1.0</td><td>0.13</td><td>1.0</td><td>0.46</td></tr><tr><th scope="row">Recall</th><td>0.98</td><td>0.94</td><td>0.99</td><td>0.96</td><td>0.98</td><td>0.92</td><td>1.0</td><td>0.97</td></tr><tr><th scope="row">F1-score</th><td>0.99</td><td>0.26</td><td>0.99</td><td>0.61</td><td>0.99</td><td>0.23</td><td>1.0</td><td>0.63</td></tr><tr><th scope="row">Accuracy</th><td>0.98</td><td></td><td>0.99</td><td></td><td>0.98</td><td></td><td>1.0</td><td></td></tr><tr><th scope="row">AUC</th><td>0.76</td><td></td><td>0.83</td><td></td><td>0.81</td><td></td><td>0.99</td><td></td></tr></tbody></table>

**Notes.** Class 0 refers to the nonlenses, while class 1 refers to the lenses. Ensemble network refers to the combination of the predictions of the three networks.
<table><caption>**Table B.4.** Same as in Table B.1, but using images in the VIS and NISP bands.</caption><thead><tr><th colspan="9">VGG-like network</th></tr><tr><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><th scope="row">Precision</th><td>0.99</td><td>0.97</td><td>0.98</td><td>0.97</td><td>0.91</td><td>0.96</td><td>0.81</td><td>0.91</td></tr><tr><th scope="row">Recall</th><td>0.97</td><td>0.99</td><td>0.97</td><td>0.98</td><td>0.96</td><td>0.91</td><td>0.92</td><td>0.79</td></tr><tr><th scope="row">F1-score</th><td>0.98</td><td>0.98</td><td>0.98</td><td>0.98</td><td>0.94</td><td>0.93</td><td>0.86</td><td>0.84</td></tr><tr><th scope="row">Accuracy</th><td>0.98</td><td></td><td>0.98</td><td></td><td>0.93</td><td></td><td>0.85</td><td></td></tr><tr><th scope="row">AUC</th><td>0.65</td><td></td><td>0.87</td><td></td><td>0.67</td><td></td><td>0.62</td><td></td></tr><tr><th colspan="9">Inception Network</th></tr><tr><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th></th><th></th><th></th><th></th></tr><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><th scope="row">Precision</th><td>0.98</td><td>0.96</td><td>0.97</td><td>0.98</td><td>0.96</td><td>0.96</td><td>0.87</td><td>0.91</td></tr><tr><th scope="row">Recall</th><td>0.96</td><td>0.98</td><td>0.98</td><td>0.96</td><td>0.96</td><td>0.96</td><td>0.91</td><td>0.87</td></tr><tr><th scope="row">F1-score</th><td>0.97</td><td>0.97</td><td>0.97</td><td>0.97</td><td>0.96</td><td>0.96</td><td>0.89</td><td>0.89</td></tr><tr><th scope="row">Accuracy</th><td>0.97</td><td></td><td>0.97</td><td></td><td>0.96</td><td></td><td>0.89</td><td></td></tr><tr><th scope="row">AUC</th><td>0.77</td><td></td><td>0.9</td><td></td><td>0.92</td><td></td><td>0.84</td><td></td></tr><tr><th colspan="9">Residual Network</th></tr><tr><th></th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th></th><th></th><th></th><th></th></tr><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><th scope="row">Precision</th><td>0.96</td><td>0.95</td><td>0.92</td><td>0.94</td><td>0.86</td><td>0.92</td><td>0.74</td><td>0.85</td></tr><tr><th scope="row">Recall</th><td>0.94</td><td>0.96</td><td>0.94</td><td>0.92</td><td>0.92</td><td>0.87</td><td>0.87</td><td>0.71</td></tr><tr><th scope="row">F1-score</th><td>0.95</td><td>0.95</td><td>0.93</td><td>0.93</td><td>0.90</td><td>0.89</td><td>0.80</td><td>0.77</td></tr><tr><th scope="row">Accuracy</th><td>0.95</td><td></td><td>0.93</td><td></td><td>0.90</td><td></td><td>0.78</td><td></td></tr><tr><th scope="row">AUC</th><td>0.81</td><td></td><td>0.88</td><td></td><td>0.81</td><td></td><td>0.72</td><td></td></tr></tbody></table>

<table><caption>**Table B.5.** Results of testing our best-performing networks, trained on S1, on a test set with 200 lenses and 80 000 nonlenses.</caption><thead><tr><th></th><th colspan="2">VGG-like network</th><th colspan="2">Inception Network</th><th colspan="2">Residual Network</th><th colspan="2">Ensemble Network</th></tr><tr><th scope="row">Class</th><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>1</td></tr></thead><tbody><tr><th scope="row">Precision</th><td>1.0</td><td>0.15</td><td>1.0</td><td>0.45</td><td>1.0</td><td>0.13</td><td>1.0</td><td>0.46</td></tr><tr><th scope="row">Recall</th><td>0.98</td><td>0.94</td><td>0.99</td><td>0.96</td><td>0.98</td><td>0.92</td><td>1.0</td><td>0.97</td></tr><tr><th scope="row">F1-score</th><td>0.99</td><td>0.26</td><td>0.99</td><td>0.61</td><td>0.99</td><td>0.23</td><td>1.0</td><td>0.63</td></tr><tr><th scope="row">Accuracy</th><td>0.98</td><td></td><td>0.99</td><td></td><td>0.98</td><td></td><td>1.0</td><td></td></tr><tr><th scope="row">AUC</th><td>0.76</td><td></td><td>0.83</td><td></td><td>0.81</td><td></td><td>0.99</td><td></td></tr></tbody></table>

**Notes.** Class 0 refers to the nonlenses, while class 1 refers to the lenses. Ensemble network refers to the combination of the predictions of the three networks.