Quantified neural Markov logic networks
Markov Logic Networks (MLNs) are discrete generative models in the exponential family. However, specifying these rules requires considerable expertise and can pose a significant challenge. To overcome this limitation, Neural MLNs (NMLNs) have been introduced, enabling the specification of potential...
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| Veröffentlicht in: | International journal of approximate reasoning Jg. 171; S. 109172 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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01.08.2024
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| ISSN: | 0888-613X, 1873-4731 |
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| Abstract | Markov Logic Networks (MLNs) are discrete generative models in the exponential family. However, specifying these rules requires considerable expertise and can pose a significant challenge. To overcome this limitation, Neural MLNs (NMLNs) have been introduced, enabling the specification of potential functions as neural networks. Thanks to the compact representation of their neural potential functions, NMLNs have shown impressive performance in modeling complex domains like molecular data. Despite the superior performance of NMLNs, their theoretical expressiveness is still equivalent to that of MLNs without quantifiers. In this paper, we propose a new class of NMLN, called Quantified NMLN, that extends the expressivity of NMLNs to the quantified setting. Furthermore, we demonstrate how to leverage the neural nature of NMLNs to employ learnable aggregation functions as quantifiers, increasing expressivity even further. We demonstrate the competitiveness of Quantified NMLNs over original NMLNs and state-of-the-art diffusion models in molecule generation experiments. |
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| AbstractList | Markov Logic Networks (MLNs) are discrete generative models in the exponential family. However, specifying these rules requires considerable expertise and can pose a significant challenge. To overcome this limitation, Neural MLNs (NMLNs) have been introduced, enabling the specification of potential functions as neural networks. Thanks to the compact representation of their neural potential functions, NMLNs have shown impressive performance in modeling complex domains like molecular data. Despite the superior performance of NMLNs, their theoretical expressiveness is still equivalent to that of MLNs without quantifiers. In this paper, we propose a new class of NMLN, called Quantified NMLN, that extends the expressivity of NMLNs to the quantified setting. Furthermore, we demonstrate how to leverage the neural nature of NMLNs to employ learnable aggregation functions as quantifiers, increasing expressivity even further. We demonstrate the competitiveness of Quantified NMLNs over original NMLNs and state-of-the-art diffusion models in molecule generation experiments. |
| ArticleNumber | 109172 |
| Author | Jung, Peter Kuželka, Ondřej Marra, Giuseppe |
| Author_xml | – sequence: 1 givenname: Peter surname: Jung fullname: Jung, Peter email: jungpete@fel.cvut.cz organization: Faculty of Electrical Engineering, Czech Technical University in Prague, Czechia – sequence: 2 givenname: Giuseppe surname: Marra fullname: Marra, Giuseppe email: giuseppe.marra@kuleuven.be organization: Department of Computer Science, KU Leuven, Belgium – sequence: 3 givenname: Ondřej orcidid: 0000-0002-6523-9114 surname: Kuželka fullname: Kuželka, Ondřej email: ondrej.kuzelka@fel.cvut.cz organization: Faculty of Electrical Engineering, Czech Technical University in Prague, Czechia |
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| Cites_doi | 10.1093/nar/gky1075 10.1007/s10994-006-5833-1 10.1016/j.artint.2021.103504 10.1093/bioinformatics/btp421 10.1613/jair.1.12320 10.1613/jair.1.11203 10.1016/0004-3702(90)90019-V 10.1016/j.artint.2015.08.011 10.3389/fphar.2020.565644 10.1007/BF02551274 10.1016/j.artint.2023.104062 10.1016/0893-6080(89)90020-8 |
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