{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:08:21Z","timestamp":1777900101762,"version":"3.51.4"},"publisher-location":"Cham","reference-count":31,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032060952","type":"print"},{"value":"9783032060969","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T00:00:00Z","timestamp":1758931200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T00:00:00Z","timestamp":1758931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-06096-9_3","type":"book-chapter","created":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T09:54:12Z","timestamp":1758880452000},"page":"38-55","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Role of\u00a0Transformer Architecture in\u00a0the\u00a0Logic-as-Loss Framework"],"prefix":"10.1007","author":[{"given":"Mattia","family":"Medina Grespan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vivek","family":"Srikumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,9,27]]},"reference":[{"key":"3_CR1","doi-asserted-by":"crossref","unstructured":"Ahmed, K., Chang, K.W., Van\u00a0den Broeck, G.: A pseudo-semantic loss for autoregressive models with logical constraints. In: NeurIPS (2023)","DOI":"10.52202\/075280-0806"},{"key":"3_CR2","unstructured":"Ahmed, K., Chang, K.W., Van\u00a0den Broeck, G.: Semantic strengthening of neuro-symbolic learning. In: AISTATS (2023)"},{"key":"3_CR3","doi-asserted-by":"crossref","unstructured":"Ahmed, K., Teso, S., Chang, K.W., Van\u00a0den Broeck, G., Vergari, A.: Semantic probabilistic layers for neuro-symbolic learning. In: Proceedings of the 36th International Conference on Neural Information Processing Systems (2022)","DOI":"10.52202\/068431-2171"},{"key":"3_CR4","unstructured":"C\u0103t\u0103lina Stoian, M., Giunchiglia, E., Lukasiewicz, T.: Exploiting T-norms for deep learning in autonomous driving. arXiv (2024)"},{"key":"3_CR5","doi-asserted-by":"crossref","unstructured":"Defresne, M., Barbe, S., Schiex, T.: Scalable coupling of deep learning with logical reasoning. In: IJCAI (2023)","DOI":"10.24963\/ijcai.2023\/402"},{"key":"3_CR6","unstructured":"Dosovitskiy, A., et al.: An image is worth 16x16 words: transformers for image recognition at scale. In: ICLR (2021)"},{"key":"3_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.scico.2025.103280","volume":"244","author":"T Flinkow","year":"2025","unstructured":"Flinkow, T., Pearlmutter, B.A., Monahan, R.: Comparing differentiable logics for learning with logical constraints. Sci. Comput. Program. 244, 103280 (2025)","journal-title":"Sci. Comput. Program."},{"key":"3_CR8","doi-asserted-by":"publisher","unstructured":"Fl\u00fcgel, S., Glauer, M., Mossakowski, T., Neuhaus, F.: A fuzzy loss for ontology classification. In: Besold, T.R., d\u2019Avila Garcez, A., Jimenez-Ruiz, E., Confalonieri, R., Madhyastha, P., Wagner, B. (eds.) Neural-Symbolic Learning and Reasoning: 18th International Conference, NeSy 2024, Barcelona, Spain, September 9\u201312, 2024, Proceedings, Part I. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-71167-1_6","DOI":"10.1007\/978-3-031-71167-1_6"},{"key":"3_CR9","doi-asserted-by":"crossref","unstructured":"Giunchiglia, E., Stoian, M.C., Lukasiewicz, T.: Deep learning with logical constraints. In: IJCAI (2022)","DOI":"10.24963\/ijcai.2022\/767"},{"key":"3_CR10","unstructured":"Grespan, M.M., Gupta, A., Srikumar, V.: Evaluating relaxations of logic for neural networks: a comprehensive study. In: IJCAI (2021)"},{"key":"3_CR11","doi-asserted-by":"crossref","unstructured":"He, H.Y., Dai, W.Z., Li, M.: Reduced implication-bias logic loss for neuro-symbolic learning. Machine Learning (2024)","DOI":"10.1007\/s10994-023-06436-4"},{"key":"3_CR12","doi-asserted-by":"publisher","unstructured":"Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms, vol.\u00a08. Springer Science & Business Media (2013). https:\/\/doi.org\/10.1007\/978-94-015-9540-7","DOI":"10.1007\/978-94-015-9540-7"},{"key":"3_CR13","doi-asserted-by":"crossref","unstructured":"Li, T., Gupta, V., Mehta, M., Srikumar, V.: A logic-driven framework for consistency of neural models. In: EMNLP-IJCNLP (2019)","DOI":"10.18653\/v1\/D19-1405"},{"key":"3_CR14","unstructured":"Li, Z., et al.: Learning with logical constraints but without shortcut satisfaction. In: ICLR (2023)"},{"key":"3_CR15","unstructured":"Li, Z., Guo, J., Jiang, Y., Si, X.: Learning reliable logical rules with satnet. In: NeurIPS (2023)"},{"key":"3_CR16","unstructured":"Loshchilov, I., Hutter, F.: Decoupled weight decay regularization. In: ICLR (2019)"},{"key":"3_CR17","doi-asserted-by":"crossref","unstructured":"Medina\u00a0Grespan, M., et al.: Logic-driven indirect supervision: an application to crisis counseling. In: ACL (2023)","DOI":"10.18653\/v1\/2023.acl-long.654"},{"key":"3_CR18","unstructured":"Nam, A.J., Abdool, M., Maxfield, T., McClelland, J.L.: Achieving and understanding out-of-distribution generalization in systematic reasoning in small-scale transformers. arXiv (2022)"},{"key":"3_CR19","unstructured":"Nandwani, Y., Jain, V., Mausam, Singla, P.: Neural models for output-space invariance in combinatorial problems. In: ICLR (2022)"},{"key":"3_CR20","unstructured":"OpenAI: GPT-4 technical report. Tech. rep., OpenAI (2023)"},{"key":"3_CR21","unstructured":"Palm, R.B., Paquet, U., Winther, O.: Recurrent relational networks. In: NeurIPS, pp. 3368\u20133378 (2018)"},{"key":"3_CR22","unstructured":"Richardson, K., Srikumar, V., Sabharwal, A.: Understanding the logic of direct preference alignment through logic. In: ICML (2025)"},{"key":"3_CR23","unstructured":"Tay, Y., et al.: Scale efficiently: insights from pretraining and finetuning transformers. In: ICLR (2022)"},{"key":"3_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2021.103602","volume":"302","author":"E van Krieken","year":"2022","unstructured":"van Krieken, E., Acar, E., van Harmelen, F.: Analyzing differentiable fuzzy logic operators. Artif. Intell. 302, 103602 (2022)","journal-title":"Artif. Intell."},{"key":"3_CR25","unstructured":"Van\u00a0Krieken, E., Minervini, P., Ponti, E.M., Vergari, A.: On the independence assumption in neurosymbolic learning. In: Proceedings of the 41st International Conference on Machine Learning (2024)"},{"key":"3_CR26","unstructured":"Vaswani, A., et al.: Attention is all you need. In: NeurIPS (2017)"},{"key":"3_CR27","doi-asserted-by":"crossref","unstructured":"Wang, H., Chen, M., Zhang, H., Roth, D.: Joint constrained learning for event-event relation extraction. In: EMNLP (2020)","DOI":"10.18653\/v1\/2020.emnlp-main.51"},{"issue":"1","key":"3_CR28","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s10032-020-00360-2","volume":"24","author":"Z Wang","year":"2020","unstructured":"Wang, Z., Liu, J.-C.: Translating math formula images to LaTeX sequences using deep neural networks with sequence-level training. Int. J. Document Anal. Recognit. (IJDAR) 24(1), 63\u201375 (2020). https:\/\/doi.org\/10.1007\/s10032-020-00360-2","journal-title":"Int. J. Document Anal. Recognit. (IJDAR)"},{"key":"3_CR29","doi-asserted-by":"crossref","unstructured":"Warner, B., et al.: Smarter, better, faster, longer: a modern bidirectional encoder for fast, memory efficient, and long context finetuning and inference. arXiv (2024)","DOI":"10.18653\/v1\/2025.acl-long.127"},{"key":"3_CR30","unstructured":"Xu, J., Zhang, Z., Friedman, T., Liang, Y., Van\u00a0den Broeck, G.: A semantic loss function for deep learning with symbolic knowledge. In: ICML (2018)"},{"key":"3_CR31","unstructured":"Yang, Z., Ishay, A., Lee, J.: Learning to solve constraint satisfaction problems with recurrent transformer. In: ICLR (2023)"}],"container-title":["Lecture Notes in Computer Science","Machine Learning and Knowledge Discovery in Databases. Research Track"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-06096-9_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T10:23:29Z","timestamp":1777631009000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-06096-9_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,27]]},"ISBN":["9783032060952","9783032060969"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-06096-9_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,27]]},"assertion":[{"value":"27 September 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"ECML PKDD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Joint European Conference on Machine Learning and Knowledge Discovery in Databases","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Porto","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Portugal","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ecml2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ecmlpkdd.org\/2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}