{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T20:54:10Z","timestamp":1782161650121,"version":"3.54.5"},"publisher-location":"Cham","reference-count":22,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032299208","type":"print"},{"value":"9783032299215","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"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\/978-3-032-29921-5_6","type":"book-chapter","created":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T20:19:14Z","timestamp":1782159554000},"page":"80-94","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modeling Nonlinear Feature Interactions with\u00a0Product-Unit Residual Networks"],"prefix":"10.1007","author":[{"given":"Ziyuan","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Uwe","family":"Jaekel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Babette","family":"Dellen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,23]]},"reference":[{"key":"6_CR1","unstructured":"Allen-Zhu, Z., Li, Y., Song, Z.: On the convergence rate of training recurrent neural networks. Adv. Neural. Inf. Process. Syst. 32 (2019)"},{"key":"6_CR2","unstructured":"Bishop, C.M., Nasrabadi, N.M.: Pattern recognition and machine learning, Springer (2006)"},{"issue":"4","key":"6_CR3","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/BF02551274","volume":"2","author":"G Cybenko","year":"1989","unstructured":"Cybenko, G.: Approximation by superpositions of a sigmoidal function. Math. Control Signals Syst. 2(4), 303\u2013314 (1989)","journal-title":"Math. Control Signals Syst."},{"key":"6_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.physletb.2024.138608","volume":"852","author":"B Dellen","year":"2024","unstructured":"Dellen, B., Jaekel, U., Freitas, P.S., Clark, J.W.: Predicting nuclear masses with product-unit networks. Phys. Lett. B 852, 138608 (2024)","journal-title":"Phys. Lett. B"},{"key":"6_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1007\/978-3-030-22741-8_13","volume-title":"Computational Science \u2013 ICCS 2019","author":"B Dellen","year":"2019","unstructured":"Dellen, B., Jaekel, U., Wolnitza, M.: Function and pattern extrapolation with product-unit networks. In: Rodrigues, J.M.F., Cardoso, P.J.S., Monteiro, J., Lam, R., Krzhizhanovskaya, V.V., Lees, M.H., Dongarra, J.J., Sloot, P.M.A. (eds.) ICCS 2019. LNCS, vol. 11537, pp. 174\u2013188. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-22741-8_13"},{"issue":"1","key":"6_CR6","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1162\/neco.1989.1.1.133","volume":"1","author":"R Durbin","year":"1989","unstructured":"Durbin, R., Rumelhart, D.E.: Product units: a computationally powerful and biologically plausible extension to backpropagation networks. Neural Comput. 1(1), 133\u2013142 (1989)","journal-title":"Neural Comput."},{"issue":"1","key":"6_CR7","first-page":"1","volume":"19","author":"JH Friedman","year":"1991","unstructured":"Friedman, J.H.: Multivariate adaptive regression splines. Ann. Stat. 19(1), 1\u201367 (1991)","journal-title":"Ann. Stat."},{"key":"6_CR8","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., Sun, J.: Delving deep into rectifiers: surpassing human-level performance on imagenet classification. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1026\u20131034 (2015)","DOI":"10.1109\/ICCV.2015.123"},{"key":"6_CR9","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 770\u2013778 (2016)","DOI":"10.1109\/CVPR.2016.90"},{"key":"6_CR10","first-page":"537","volume":"7","author":"LR Leerink","year":"1995","unstructured":"Leerink, L.R., Giles, C.L., Horne, B.G., Jabri, M.A.: Learning with product units. Adv. Neural. Inf. Process. Syst. 7, 537 (1995)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"6_CR11","doi-asserted-by":"crossref","unstructured":"Li, Z., Jaekel, U., Dellen, B.: Data-driven 3d shape completion with product units. In: International Conference on Computational Science, pp. 302\u2013315. Springer (2024)","DOI":"10.1007\/978-3-031-63749-0_21"},{"key":"6_CR12","doi-asserted-by":"crossref","unstructured":"Li, Z., Jaekel, U., Dellen, B.: Advancing complex-valued neural networks with product units for MRI reconstruction. In: International Conference on Neural Information Processing, pp. 540\u2013554. Springer (2025)","DOI":"10.1007\/978-981-95-4378-6_38"},{"key":"6_CR13","unstructured":"Li, Z., Jaekel, U., Dellen, B.: Deep residual learning with product units (2025). arXiv:2505.04397 arXiv preprint"},{"key":"6_CR14","unstructured":"Lundberg, S.M., Lee, S.I.: A unified approach to interpreting model predictions. Adv. Neural Inf. Process. Syst. 30 (2017)"},{"key":"6_CR15","doi-asserted-by":"crossref","unstructured":"Molnar, C., Casalicchio, G., Bischl, B.: Interpretable machine learning-a brief history, state-of-the-art and challenges. In: Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pp. 417\u2013431. Springer (2020)","DOI":"10.1007\/978-3-030-65965-3_28"},{"issue":"3","key":"6_CR16","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/S0167-7152(96)00140-X","volume":"33","author":"RK Pace","year":"1997","unstructured":"Pace, R.K., Barry, R.: Sparse spatial autoregressions. Stat. Probab. Lett. 33(3), 291\u2013297 (1997)","journal-title":"Stat. Probab. Lett."},{"key":"6_CR17","unstructured":"Poggio, T., et al.: Theory of deep learning iii: explaining the non-overfitting puzzle (2017). arXiv:1801.00173 arXiv preprint"},{"issue":"6088","key":"6_CR18","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1038\/323533a0","volume":"323","author":"DE Rumelhart","year":"1986","unstructured":"Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning representations by back-propagating errors. Nature 323(6088), 533\u2013536 (1986)","journal-title":"Nature"},{"key":"6_CR19","unstructured":"Tsang, M., Cheng, D., Liu, Y.: Detecting statistical interactions from neural network weights (2017). arXiv:1705.04977 arXiv preprint"},{"key":"6_CR20","unstructured":"Veit, A., Wilber, M.J., Belongie, S.: Residual networks behave like ensembles of relatively shallow networks. Adv. Neural. Inf. Process. Syst 29 (2016)"},{"issue":"12","key":"6_CR21","doi-asserted-by":"publisher","first-page":"1797","DOI":"10.1016\/S0008-8846(98)00165-3","volume":"28","author":"IC Yeh","year":"1998","unstructured":"Yeh, I.C.: Modeling of strength of high-performance concrete using artificial neural networks. Cem. Concr. Res. 28(12), 1797\u20131808 (1998)","journal-title":"Cem. Concr. Res."},{"key":"6_CR22","unstructured":"Zhang, C., Bengio, S., Hardt, M., Recht, B., Vinyals, O.: Understanding deep learning requires rethinking generalization (2016). arXiv preprint arXiv:1611.03530"}],"container-title":["Lecture Notes in Computer Science","Computational Science \u2013 ICCS 2026"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-29921-5_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T20:19:23Z","timestamp":1782159563000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-29921-5_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032299208","9783032299215"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-29921-5_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"23 June 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICCS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Computational Science","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Hamburg","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Germany","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 June 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 July 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iccs-computsci2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.iccs-meeting.org\/iccs2026\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}