{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T14:48:38Z","timestamp":1742914118715,"version":"3.40.3"},"publisher-location":"Cham","reference-count":31,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031781858"},{"type":"electronic","value":"9783031781865"}],"license":[{"start":{"date-parts":[[2024,11,30]],"date-time":"2024-11-30T00:00:00Z","timestamp":1732924800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,11,30]],"date-time":"2024-11-30T00:00:00Z","timestamp":1732924800000},"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":[[2025]]},"DOI":"10.1007\/978-3-031-78186-5_17","type":"book-chapter","created":{"date-parts":[[2024,11,29]],"date-time":"2024-11-29T14:18:01Z","timestamp":1732889881000},"page":"254-265","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Divergence-Free Neural ODE for\u00a0Classification"],"prefix":"10.1007","author":[{"given":"Zakaria","family":"Jarraya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lucas","family":"Drumetz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simon","family":"Bena\u00efchouche","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Douraied Ben","family":"Salem","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fran\u00e7ois","family":"Rousseau","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,11,30]]},"reference":[{"unstructured":"Azencot, O., Erichson, N.B., Ben-Chen, M., Mahoney, M.W.: A differential geometry perspective on orthogonal recurrent models. ArXiv (2021)","key":"17_CR1"},{"key":"17_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-45468-4","volume-title":"Deep Learning: Foundations and Concepts","author":"C Bishop","year":"2023","unstructured":"Bishop, C., Bishop, H.: Deep Learning: Foundations and Concepts. Springer, New York (2023). https:\/\/doi.org\/10.1007\/978-3-031-45468-4"},{"unstructured":"Chen, R. T., Rubanova, Y., Bettencourt, J., Duvenaud, D.K.: Neural ordinary differential equations. In: Advances in Neural Information Processing Systems (2018)","key":"17_CR3"},{"unstructured":"Chennuru Vankadara, L., von Luxburg, U.: Measures of distortion for machine learning. In: Advances in Neural Information Processing Systems (2018)","key":"17_CR4"},{"unstructured":"Cisse, M., Bojanowski, P., Grave, E., Dauphin, Y., Usunier, N.: Parseval networks: improving robustness to adversarial examples. In: International Conference on Machine Learning (2017)","key":"17_CR5"},{"unstructured":"Croce, F., et al.: RobustBench: a standardized adversarial robustness benchmark. In: Proceedings of the Neural Information Processing Systems Track on Datasets and Benchmarks (2021)","key":"17_CR6"},{"doi-asserted-by":"publisher","unstructured":"Wanner, G., Hairer, E., N\u00f8rsett, S.P.: Solving ordinary differential equations I. Springer, Heidelberg (1993). DOI: https:\/\/doi.org\/10.1007\/978-3-540-78862-1","key":"17_CR7","DOI":"10.1007\/978-3-540-78862-1"},{"unstructured":"Finlay, C., Jacobsen, J.H., Nurbekyan, L., Oberman, A.: How to train your neural ODE: the world of Jacobian and kinetic regularization. In: International Conference on Machine Learning (2020)","key":"17_CR8"},{"unstructured":"Goodfellow, I., Shlens, J., Szegedy, C.: Explaining and harnessing adversarial examples. In: International Conference on Learning Representations (2015)","key":"17_CR9"},{"unstructured":"Goodfellow, I.J., Shlens, J., Szegedy, C.: Explaining and harnessing adversarial examples. STAT 1050, 20 (2015)","key":"17_CR10"},{"issue":"1","key":"17_CR11","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aa9a90","volume":"34","author":"E Haber","year":"2017","unstructured":"Haber, E., Ruthotto, L.: Stable architectures for deep neural networks. Inverse Prob. 34(1), 014004 (2017)","journal-title":"Inverse Prob."},{"unstructured":"Hanshu, Y., Jiawei, D., Vincent, T., Jiashi, F.: On robustness of neural ordinary differential equations. In: International Conference on Learning Representations (2020)","key":"17_CR12"},{"key":"17_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1007\/978-3-319-46493-0_38","volume-title":"Computer Vision \u2013 ECCV 2016","author":"K He","year":"2016","unstructured":"He, K., Zhang, X., Ren, S., Sun, J.: Identity mappings in deep residual networks. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9908, pp. 630\u2013645. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-46493-0_38"},{"unstructured":"Hoffman, J., Roberts, D.A., Yaida, S.: Robust learning with jacobian regularization. STAT 1050, 7 (2019)","key":"17_CR14"},{"key":"17_CR15","first-page":"1","volume":"145","author":"Y Huang","year":"2021","unstructured":"Huang, Y., Yu, Y., Zhang, H., Ma, Y., Yao, Y.: Adversarial robustness of stabilized neural ode might be from obfuscated gradients. Proc. Mach. Learn. Res. 145, 1\u201319 (2021)","journal-title":"Proc. Mach. Learn. Res."},{"unstructured":"Kang, Q., Song, Y., Ding, Q., Tay, W.P.: Stable neural ode with lyapunov-stable equilibrium points for defending against adversarial attacks. In: Advances in Neural Information Processing Systems (2021)","key":"17_CR16"},{"key":"17_CR17","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/978-3-030-67661-2_7","volume-title":"Machine Learning and Knowledge Discovery in Databases","author":"S Karkar","year":"2021","unstructured":"Karkar, S., Ayed, I., B\u00e9zenac, E., Gallinari, P.: A principle of least action for the training of neural networks. In: Hutter, F., Kersting, K., Lijffijt, J., Valera, I. (eds.) ECML PKDD 2020. LNCS (LNAI), vol. 12458, pp. 101\u2013117. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-67661-2_7"},{"unstructured":"Kidger, P.: On neural differential equations. PhD thesis. University of Oxford (2021)","key":"17_CR18"},{"issue":"11","key":"17_CR19","doi-asserted-by":"publisher","first-page":"3964","DOI":"10.1109\/TPAMI.2020.2992934","volume":"43","author":"I Kobyzev","year":"2020","unstructured":"Kobyzev, I., Prince, S.J., Brubaker, M.A.: Normalizing flows: an introduction and review of current methods. IEEE Trans. Pattern Anal. Mach. Intell. 43(11), 3964\u20133979 (2020)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"unstructured":"Liu, K.: Github pytorch-cifar repository. https:\/\/github.com\/kuangliu\/pytorch-cifar","key":"17_CR20"},{"unstructured":"Morel, G., Drumetz, L., Bena\u0131chouche, S., Courty, N., Rousseau, F.: Turning normalizing flows into monge maps with geodesic gaussian preserving flows. Trans. Mach. Learn. Res. (2023)","key":"17_CR21"},{"key":"17_CR22","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","volume":"378","author":"M Raissi","year":"2019","unstructured":"Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686\u2013707 (2019)","journal-title":"J. Comput. Phys."},{"unstructured":"Richter-Powell, J., Lipman, Y., Chen, R.T.Q.: Neural conservation laws: a divergence-free perspective. In: Advances in Neural Information Processing Systems (2022)","key":"17_CR23"},{"unstructured":"Jimenez Rodriguez, I.D., Ames, A., Yue, Y.: LyaNet: a lyapunov framework for training neural ODEs. In: International Conference on Machine Learning (2022)","key":"17_CR24"},{"key":"17_CR25","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/s10851-019-00890-3","volume":"62","author":"F Rousseau","year":"2020","unstructured":"Rousseau, F., Drumetz, L., Fablet, R.: Residual networks as flows of diffeomorphisms. J. Math. Imaging Vision 62, 365\u2013375 (2020)","journal-title":"J. Math. Imaging Vision"},{"key":"17_CR26","first-page":"686","volume":"378","author":"L Ruthotto","year":"2020","unstructured":"Ruthotto, L., Haber, E.: Deep neural networks motivated by partial differential equations. J. Math. Imaging Vision 378, 686\u2013707 (2020)","journal-title":"J. Math. Imaging Vision"},{"issue":"58\u201363","key":"17_CR27","first-page":"94","volume":"55","author":"F Santambrogio","year":"2015","unstructured":"Santambrogio, F.: Optimal transport for applied mathematicians. Birk\u00e4user, NY. 55(58\u201363), 94 (2015)","journal-title":"Birk\u00e4user, NY."},{"issue":"5","key":"17_CR28","first-page":"1","volume":"1","author":"E Weinan","year":"2017","unstructured":"Weinan, E.: A proposal on machine learning via dynamical systems. Commun. Math. Stat. 1(5), 1\u201311 (2017)","journal-title":"Commun. Math. Stat."},{"key":"17_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/978-3-319-46478-7_31","volume-title":"Computer Vision \u2013 ECCV 2016","author":"Y Wen","year":"2016","unstructured":"Wen, Y., Zhang, K., Li, Z., Qiao, Yu.: A discriminative feature learning approach for deep face recognition. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9911, pp. 499\u2013515. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-46478-7_31"},{"unstructured":"Yang, Y.Y., Rashtchian, C., Zhang, H., Salakhutdinov, R.R., Chaudhuri, K.: A closer look at accuracy vs. robustness. In: Advances in Neural Information Processing Systems (2020)","key":"17_CR30"},{"key":"17_CR31","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1109\/LCSYS.2022.3186959","volume":"7","author":"M Zakwan","year":"2022","unstructured":"Zakwan, M., Xu, L., Ferrari-Trecate, G.: Robust classification using contractive Hamiltonian neural ODEs. IEEE Control Syst. Lett. 7, 145\u2013150 (2022)","journal-title":"IEEE Control Syst. Lett."}],"container-title":["Lecture Notes in Computer Science","Pattern Recognition"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-78186-5_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,29]],"date-time":"2024-11-29T15:13:27Z","timestamp":1732893207000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-78186-5_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,30]]},"ISBN":["9783031781858","9783031781865"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-78186-5_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2024,11,30]]},"assertion":[{"value":"30 November 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICPR","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Pattern Recognition","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Kolkata","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"India","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 December 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5 December 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"icpr2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/icpr2024.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}