<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Single-Branch Architectures for Recommendation</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Marta Moscati</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Johannes Kepler University Linz</institution>
          ,
          <addr-line>Linz</addr-line>
          ,
          <country country="AT">Austria</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>Single-branch architectures have been proven efective for several multimodal learning tasks. In this talk, after reviewing the use of single-branch architectures in multimodal learning, I describe their use in multimodal recommendation, showing how they allow to address missing-modality and cold-start scenarios. I then describe the use of single-branch architectures in collaborative filtering, showing how they allow to reduce the number of model parameters without substantially afecting the quality of recommendations.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Multimodal Learning</kwd>
        <kwd>Multimodal Recommender Systems</kwd>
        <kwd>Collaborative Filtering</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>
        batch
userinterac ons
batch
batch
contras ve
loss
recommloesnsda on
(a) SiBraR [
        <xref ref-type="bibr" rid="ref21">21</xref>
        ]: Single-branch multimodal RS.
(b) CoBraR [26]: Single-branch for CF.
provides more accurate recommendations compared to well-established CF and multimodal RS [
        <xref ref-type="bibr" rid="ref21">21</xref>
        ],
and that the performance improvement is to be attributed to the simultaneous use of the single-branch
architecture and the contrastive loss [25].
      </p>
      <p>Single-Branch Architectures in Collaborative Filtering. Modern CF algorithms [27] rely on
representing users and items in a joint embedding space where these are close if corresponding to a
positive interaction. Motivated by the analogy between this approach and the objective of reducing
the modality gap in multimodal learning, as well as by the observation that weight sharing allows to
simultaneously reduce the modality gap and to reduce the number of model parameters, we proposed
the use of a single-branch architecture for CF. The resulting model, named Collaborative Branch
Recommender (CoBraR [26]), is depicted in Figure 1b. The architecture and training paradigm of
CoBraR are similar to the well-established two-branch CF algorithm DMF [28], where the user and item
representations are obtained by converting their sparse interaction vectors, i.e., the corresponding row
or column in the user–item interaction matrix, to dense vectors by mean of two multi-layer perceptrons
(MLP) - one MLP for the user and one MLP for the item. The novelty of CoBraR is that the same MLP is
used to encode both users and items. We showed that CoBraR reduces the number of model parameters
compared to its two-tower counterpart DMF, improving beyond-accuracy aspects of recommendation
quality without compromising accuracy.</p>
      <p>Future Applications of Single-Branch Architectures to Recommendation. Both SiBraR and
CoBraR translate single-branch architectures to RS and open the way for future applications. First,
although SiBraR has been proven efective for tackling scenarios where one modality is missing at
inference time, its architecture has not yet been evaluated on scenarios where one modality is also
missing during training. As for CoBraR, its architecture and training paradigm are based on DMF.
Therefore, there is no evidence yet of whether using weight sharing between users and items would also
be efective with other loss functions for recommendation, or for other two-branch CF models as well,
such as NeuMF [29]. Finally, SiBraR and CoBraR could be combined in a model where a same multimodal
single-branch is applied to all multimodal data of both users and items, including interactions and
side-information.</p>
    </sec>
    <sec id="sec-2">
      <title>1. Acknowledgments</title>
      <p>I am grateful to Markus Schedl, Shah Nawaz, Christian Ganhör, and Anna Hausberger for the fruitful
collaboration and invaluable discussions that led to the development SiBraR and CoBraR. This research
was funded in whole or in part by the Austrian Science Fund (FWF) https://doi.org/10.55776/P33526,
https://doi.org/10.55776/DFH23, https://doi.org/10.55776/COE12, https://doi.org/10.55776/P36413. No
generative AI tool was used during the preparation of this work.</p>
    </sec>
    <sec id="sec-3">
      <title>Declaration on Generative AI</title>
      <p>The author have not employed any Generative AI tools.
[24] A. van den Oord, Y. Li, O. Vinyals, Representation learning with contrastive predictive coding,
2019. arXiv:1807.03748.
[25] C. Ganhör, M. Moscati, A. Hausberger, S. Nawaz, M. Schedl, Single-branch network architectures
to close the modality gap in multimodal recommendation, ACM Transactions on Recommender
Systems (2025).
[26] M. Moscati, S. Nawaz, M. Schedl, Parameter-eficient single collaborative branch for
recommendation, in: Proc. of ACM RecSys, 2025.
[27] S. Zhang, Y. Tay, L. Yao, A. Sun, C. Zhang, Deep learning for recommender systems, in: F. Ricci,</p>
      <p>L. Rokach, B. Shapira (Eds.), Recommender Systems Handbook, Springer US, New York, NY, 2022.
[28] H.-J. Xue, X.-Y. Dai, J. Zhang, S. Huang, J. Chen, Deep matrix factorization models for recommender
systems, in: Proc. of IJCAI, 2017.
[29] X. He, L. Liao, H. Zhang, L. Nie, X. Hu, T.-S. Chua, Neural collaborative filtering, in: Proc. of
WWW, 2017.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>T.</given-names>
            <surname>Baltrušaitis</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Ahuja</surname>
          </string-name>
          ,
          <string-name>
            <surname>L.-P. Morency,</surname>
          </string-name>
          <article-title>Multimodal machine learning: A survey and taxonomy</article-title>
          ,
          <source>IEEE Transactions on Pattern Analysis and Machine Intelligence</source>
          <volume>41</volume>
          (
          <year>2019</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>P.</given-names>
            <surname>Xu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>X.</given-names>
            <surname>Zhu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D. A.</given-names>
            <surname>Clifton</surname>
          </string-name>
          ,
          <article-title>Multimodal learning with transformers: A survey</article-title>
          ,
          <source>IEEE Transactions on Pattern Analysis and Machine Intelligence</source>
          (
          <year>2023</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>Q.</given-names>
            <surname>Liu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Hu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Y.</given-names>
            <surname>Xiao</surname>
          </string-name>
          ,
          <string-name>
            <given-names>X.</given-names>
            <surname>Zhao</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Gao</surname>
          </string-name>
          ,
          <string-name>
            <given-names>W.</given-names>
            <surname>Wang</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Q.</given-names>
            <surname>Li</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Tang</surname>
          </string-name>
          ,
          <article-title>Multimodal recommender systems: A survey</article-title>
          ,
          <source>ACM Computing Surveys</source>
          <volume>57</volume>
          (
          <year>2024</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>A.</given-names>
            <surname>Radford</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J. W.</given-names>
            <surname>Kim</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Hallacy</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Ramesh</surname>
          </string-name>
          , G. Goh,
          <string-name>
            <given-names>S.</given-names>
            <surname>Agarwal</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G.</given-names>
            <surname>Sastry</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Askell</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Mishkin</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Clark</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G.</given-names>
            <surname>Krueger</surname>
          </string-name>
          ,
          <string-name>
            <surname>I. Sutskever</surname>
          </string-name>
          ,
          <article-title>Learning transferable visual models from natural language supervision</article-title>
          ,
          <source>in: Proc. of ICML</source>
          ,
          <year>2021</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>S.</given-names>
            <surname>Reed</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Z.</given-names>
            <surname>Akata</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Lee</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Schiele</surname>
          </string-name>
          ,
          <article-title>Learning deep representations of fine-grained visual descriptions</article-title>
          ,
          <source>in: Proc. of IEEE CVPR</source>
          ,
          <year>2016</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>A.</given-names>
            <surname>Nagrani</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Albanie</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Zisserman</surname>
          </string-name>
          ,
          <article-title>Seeing voices and hearing faces: Cross-modal biometric matching</article-title>
          ,
          <source>in: Proc. of IEEE CVPR</source>
          ,
          <year>2018</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>A.</given-names>
            <surname>Nagrani</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Albanie</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Zisserman</surname>
          </string-name>
          ,
          <article-title>Learnable pins: Cross-modal embeddings for person identity</article-title>
          ,
          <source>in: Proc. of ECCV</source>
          ,
          <year>2018</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>M. S.</given-names>
            <surname>Saeed</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. H.</given-names>
            <surname>Khan</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Nawaz</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. H.</given-names>
            <surname>Yousaf</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Del Bue</surname>
          </string-name>
          ,
          <article-title>Fusion and orthogonal projection for improved face-voice association</article-title>
          ,
          <source>in: Proc. of ICASSP</source>
          ,
          <year>2022</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>O.</given-names>
            <surname>Arshad</surname>
          </string-name>
          , I. Gallo,
          <string-name>
            <given-names>S.</given-names>
            <surname>Nawaz</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Calefati</surname>
          </string-name>
          ,
          <article-title>Aiding intra-text representations with visual context for multimodal named entity recognition</article-title>
          ,
          <source>in: Proc. of IEEE ICDAR</source>
          ,
          <year>2019</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <given-names>A.</given-names>
            <surname>Vaswani</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Shazeer</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Parmar</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Uszkoreit</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Jones</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A. N.</given-names>
            <surname>Gomez</surname>
          </string-name>
          , L. u. Kaiser,
          <string-name>
            <surname>I. Polosukhin</surname>
          </string-name>
          ,
          <article-title>Attention is all you need</article-title>
          ,
          <source>in: Proc. of NeurIPS</source>
          ,
          <year>2017</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <given-names>J.</given-names>
            <surname>Lu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Batra</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Parikh</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Lee</surname>
          </string-name>
          ,
          <article-title>Vilbert: Pretraining task-agnostic visiolinguistic representations for vision-and-language tasks</article-title>
          ,
          <source>in: Proc. of NeurIPS</source>
          ,
          <year>2019</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>H.</given-names>
            <surname>Tan</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Bansal</surname>
          </string-name>
          ,
          <article-title>Lxmert: Learning cross-modality encoder representations from transformers</article-title>
          ,
          <source>in: Proc. of EMNLP</source>
          ,
          <year>2019</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <given-names>A.</given-names>
            <surname>Hannan</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. A.</given-names>
            <surname>Manzoor</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Nawaz</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. I.</given-names>
            <surname>Liaqat</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Schedl</surname>
          </string-name>
          ,
          <string-name>
            <surname>M.</surname>
          </string-name>
          <article-title>Noman, PAEFF: Precise Alignment and Enhanced Gated Feature Fusion for Face-Voice Association</article-title>
          , in
          <source>: Proc. of Interspeech</source>
          ,
          <year>2025</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14]
          <string-name>
            <given-names>M. S.</given-names>
            <surname>Saeed</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Nawaz</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. H.</given-names>
            <surname>Khan</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. Z.</given-names>
            <surname>Zaheer</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Nandakumar</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. H.</given-names>
            <surname>Yousaf</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Mahmood</surname>
          </string-name>
          ,
          <article-title>Single-branch network for multimodal training</article-title>
          ,
          <source>in: Proc. of ICASSP</source>
          ,
          <year>2023</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          [15]
          <string-name>
            <given-names>M.</given-names>
            <surname>Tschannen</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Mustafa</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Houlsby</surname>
          </string-name>
          ,
          <article-title>Clippo: Image-and-language understanding from pixels only</article-title>
          ,
          <source>in: Proc. of IEEE/CVF CVPR</source>
          ,
          <year>2023</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          [16]
          <string-name>
            <given-names>M. I.</given-names>
            <surname>Liaqat</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Nawaz</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. Z.</given-names>
            <surname>Zaheer</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. S.</given-names>
            <surname>Saeed</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Sajjad</surname>
          </string-name>
          ,
          <string-name>
            <given-names>T. D.</given-names>
            <surname>Schepper</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Nandakumar</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. H.</given-names>
            <surname>Khan</surname>
          </string-name>
          , I. Gallo,
          <string-name>
            <given-names>M.</given-names>
            <surname>Schedl</surname>
          </string-name>
          ,
          <article-title>Chameleon: A multimodal learning framework robust to missing modalities</article-title>
          ,
          <source>International Journal of Multimedia Information Retrieval</source>
          <volume>14</volume>
          (
          <year>2025</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation>
          [17]
          <string-name>
            <given-names>J.</given-names>
            <surname>Geiger</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Moscati</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Nawaz</surname>
          </string-name>
          ,
          <string-name>
            <surname>M.</surname>
          </string-name>
          <article-title>Schedl, Music4all a+a: A multimodal dataset for music information retrieval tasks</article-title>
          ,
          <source>in: Proc. of CBMI</source>
          ,
          <year>2025</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref18">
        <mixed-citation>
          [18]
          <string-name>
            <given-names>M.</given-names>
            <surname>Ma</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Ren</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Zhao</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Testuggine</surname>
          </string-name>
          ,
          <string-name>
            <given-names>X.</given-names>
            <surname>Peng</surname>
          </string-name>
          ,
          <article-title>Are multimodal transformers robust to missing modality?</article-title>
          ,
          <source>in: Proc. of IEEE/CVF CVPR</source>
          ,
          <year>2022</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref19">
        <mixed-citation>
          [19]
          <string-name>
            <given-names>D.</given-names>
            <surname>Malitesta</surname>
          </string-name>
          , G. Cornacchia,
          <string-name>
            <given-names>C.</given-names>
            <surname>Pomo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F. A.</given-names>
            <surname>Merra</surname>
          </string-name>
          ,
          <string-name>
            <given-names>T. Di</given-names>
            <surname>Noia</surname>
          </string-name>
          ,
          <string-name>
            <surname>E. Di Sciascio</surname>
          </string-name>
          ,
          <article-title>Formalizing multimedia recommendation through multimodal deep learning</article-title>
          ,
          <source>ACM Transactions on Recommender Systems</source>
          <volume>3</volume>
          (
          <year>2025</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref20">
        <mixed-citation>
          [20]
          <string-name>
            <given-names>F.</given-names>
            <surname>Ricci</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Rokach</surname>
          </string-name>
          ,
          <string-name>
            <surname>B.</surname>
          </string-name>
          Shapira (Eds.),
          <source>Recommender Systems Handbook</source>
          , Springer US, New York, NY,
          <year>2022</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref21">
        <mixed-citation>
          [21]
          <string-name>
            <given-names>C.</given-names>
            <surname>Ganhör</surname>
          </string-name>
          * , M. Moscati* ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Hausberger</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Nawaz</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Schedl</surname>
          </string-name>
          ,
          <article-title>A multimodal single-branch embedding network for recommendation in cold-start and missing modality scenarios</article-title>
          ,
          <source>in: Proc. of ACM RecSys, *Equal Contributions</source>
          ,
          <year>2024</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref22">
        <mixed-citation>
          [22]
          <string-name>
            <given-names>S.</given-names>
            <surname>Rendle</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Freudenthaler</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Z.</given-names>
            <surname>Gantner</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Schmidt-Thieme</surname>
          </string-name>
          ,
          <article-title>Bpr: Bayesian personalized ranking from implicit feedback</article-title>
          ,
          <source>in: Proc. of UAI</source>
          ,
          <year>2009</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref23">
        <mixed-citation>
          [23]
          <string-name>
            <given-names>Z.</given-names>
            <surname>Yuhui</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Y.</given-names>
            <surname>Wada</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Waida</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Goto</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Y.</given-names>
            <surname>Hino</surname>
          </string-name>
          , T. Kanamori,
          <article-title>Deep clustering with a constraint for topological invariance based on symmetric infonce</article-title>
          ,
          <source>Neural Computation</source>
          <volume>35</volume>
          (
          <year>2023</year>
          ).
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>