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    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Interpretable Neural-Symbolic Concept Reasoning⋆</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Pietro Barbiero</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Gabriele Ciravegna</string-name>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Francesco Giannini</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Mateo Espinosa Zarlenga</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Lucie Charlotte Magister</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Alberto Tonda</string-name>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Pietro Lió</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Frederic Precioso</string-name>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Mateja Jamnik</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Giuseppe Marra</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Experimental Results.</string-name>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Computer Science and Technology, University of Cambridge</institution>
          ,
          <country country="UK">UK</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Department of Computer Science</institution>
          ,
          <addr-line>KU Leuven,</addr-line>
          ,
          <country country="BE">Belgium</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Faculty of Informatics, Università della Svizzera Italiana</institution>
          ,
          <country country="CH">Switzerland</country>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>Maasai</institution>
          ,
          <addr-line>Inria, I3S</addr-line>
          ,
          <institution>CNRS, Université Côte d'Azur</institution>
          ,,
          <country country="FR">France</country>
        </aff>
        <aff id="aff4">
          <label>4</label>
          <institution>UMR 518 MIA-PS, INRAE, Université Paris-Saclay</institution>
          ,
          <addr-line>91120, Palaiseau</addr-line>
          ,
          <country country="FR">France</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2023</year>
      </pub-date>
      <abstract>
        <p>4Consorzio Interuniversitario Nazionale per l'Informatica, CINI, (Italy) 6Institut des Systèmes Complexes de Paris Île-de-France (ISC-PIF) - UAR 3611 CNRS, Paris (France) Deep learning methods are highly accurate, yet their opaque decision process prevents them from earning full human trust [1]. Concept-based models [2, 3] aim to address this issue by learning tasks based on a set of human-understandable concepts. However, state-of-the-art concept-based models rely on high-dimensional concept embedding representations which lack a clear semantic meaning, thus questioning the interpretability of their decision process [4, 5]. To overcome this limitation, we propose the Deep Concept Reasoner (DCR) [6], the first interpretable concept-based model that builds upon concept embeddings. In DCR framework, the utilization of neural networks does not involve direct task predictions. Instead, neural networks are employed to construct syntactic rule structures through the utilization of concept embeddings. These concept embeddings serve as a foundation for the subsequent rule evaluation, enabling the DCR to derive its final prediction. Notably, the evaluation of rules occurs based on the truth values associated with the concepts themselves rather than their embeddings. Consequently, the DCR framework upholds clear semantic principles, facilitating the provision of fully interpretable decision outcomes. The overarching process is illustrated in the accompanying Figure 1-left. One of the key advantages of DCR lies in its diferentiability, which enables its efective training as an independent module on concept databases.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>Italy
∗Corresponding author.
https://www.pietrobarbiero.eu/ (P. Barbiero)
during training, and (iii), facilitates the generation of counterfactual examples providing the
learnt rules as guidance.</p>
    </sec>
    <sec id="sec-2">
      <title>INPUT</title>
    </sec>
    <sec id="sec-3">
      <title>INTERPRETABLE</title>
    </sec>
    <sec id="sec-4">
      <title>PREDICTION</title>
      <sec id="sec-4-1">
        <title>Phenol</title>
        <p>AND</p>
      </sec>
      <sec id="sec-4-2">
        <title>Dimethylamine</title>
        <p>Concept Encoder</p>
        <p>Concept-based Model</p>
        <p>Generalization vs.</p>
        <p>Interpretability
yes</p>
        <p>Interpretable
CE+DCR (ours)
CT+Decision Tree
CT+Logistic Regression
CE+XGBoost</p>
        <p>Acknowledgments
This work was supported by TAILOR and by HumanE-AI-Net, projects funded by EU Horizon
2020 research and innovation programme under GA No 952215 and No 952026, respectively.</p>
      </sec>
    </sec>
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