{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T18:13:24Z","timestamp":1764267204730,"version":"3.46.0"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"11-12","license":[{"start":{"date-parts":[[2024,10,26]],"date-time":"2024-10-26T00:00:00Z","timestamp":1729900800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,10,26]],"date-time":"2024-10-26T00:00:00Z","timestamp":1729900800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"AI Interdisciplinary Institute ANITI","award":["ANR-19-PIA3-0004"],"award-info":[{"award-number":["ANR-19-PIA3-0004"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2024,12]]},"DOI":"10.1007\/s10994-024-06624-w","type":"journal-article","created":{"date-parts":[[2024,10,26]],"date-time":"2024-10-26T17:02:06Z","timestamp":1729962126000},"page":"8655-8686","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Adversarial attacks on neural networks through canonical Riemannian foliations"],"prefix":"10.1007","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6988-7450","authenticated-orcid":false,"given":"Eliot","family":"Tron","sequence":"first","affiliation":[]},{"given":"Nicolas","family":"Cou\u00ebllan","sequence":"additional","affiliation":[]},{"given":"St\u00e9phane","family":"Puechmorel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,10,26]]},"reference":[{"key":"6624_CR1","doi-asserted-by":"crossref","unstructured":"Amari, S. -I. (2016). Information geometry and its applications. (Vol. 194). Tokyo: Springer.","DOI":"10.1007\/978-4-431-55978-8"},{"issue":"153","key":"6624_CR2","first-page":"1","volume":"18","author":"AG Baydin","year":"2018","unstructured":"Baydin, A. G., Pearlmutter, B. A., Radul, A. A., & Siskind, J. M. (2018). Automatic differentiation in machine learning: A survey. Journal of Machine Learning Research, 18(153), 1\u201343.","journal-title":"Journal of Machine Learning Research"},{"key":"6624_CR3","unstructured":"Croce, F., & Hein, M. (2020). Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks. In: III, H.D., Singh, A. (Eds.), Proceedings of the 37th international conference on machine learning. Proceedings of machine learning research, (Vol. 119, pp. 2206\u20132216). PMLR: Cambridge. https:\/\/proceedings.mlr.press\/v119\/croce20b.html."},{"key":"6624_CR4","doi-asserted-by":"crossref","unstructured":"Dennis, J. E., & Schnabel, R. B. (1996). Numerical methods for unconstrained optimization and nonlinear equations. Philadelphia: Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9781611971200"},{"key":"6624_CR5","unstructured":"Fawzi, A., Fawzi, H., & Fawzi, O. (2018). Adversarial vulnerability for any classifier. Advances in Neural Information Processing Systems, 31."},{"issue":"3","key":"6624_CR6","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1007\/s10994-017-5663-3","volume":"107","author":"A Fawzi","year":"2018","unstructured":"Fawzi, A., Fawzi, O., & Frossard, P. (2018). Analysis of classifiers\u2019 robustness to adversarial perturbations. Machine Learning, 107(3), 481\u2013508.","journal-title":"Machine Learning"},{"issue":"6","key":"6624_CR7","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1109\/MSP.2017.2740965","volume":"34","author":"A Fawzi","year":"2017","unstructured":"Fawzi, A., Moosavi-Dezfooli, S.-M., & Frossard, P. (2017). The robustness of deep networks: A geometrical perspective. IEEE Signal Processing Magazine, 34(6), 50\u201362.","journal-title":"IEEE Signal Processing Magazine"},{"key":"6624_CR8","doi-asserted-by":"publisher","first-page":"983","DOI":"10.1090\/jams\/852","volume":"29","author":"C Fefferman","year":"2016","unstructured":"Fefferman, C., Mitter, S., & Narayanan, H. (2016). Testing the manifold hypothesis. Journal of the American Mathematical Society, 29, 983\u20131049.","journal-title":"Journal of the American Mathematical Society"},{"key":"6624_CR9","unstructured":"Gilmer, J., Metz, L., Faghri, F., Schoenholz, S. S., Raghu, M., Wattenberg, M., & Goodfellow, I. (2018). Adversarial spheres."},{"key":"6624_CR10","doi-asserted-by":"crossref","unstructured":"Golub, G. H., & Van\u00a0Loan, C. F. (2013). Matrix computations. JHU press.","DOI":"10.56021\/9781421407944"},{"key":"6624_CR11","unstructured":"Goodfellow, I. J., Shlens, J., & Szegedy, C. (2015). Explaining and harnessing adversarial examples. In: Bengio, Y., LeCun, Y. (Eds.), 3rd International conference on learning representations, ICLR 2015, Conference track proceedings, San Diego, May 7\u20139, 2015."},{"key":"6624_CR12","doi-asserted-by":"crossref","unstructured":"Grementieri, L., & Fioresi, R. (2021). Model-centric data manifold: The data through the eyes of the model","DOI":"10.1137\/21M1437056"},{"key":"6624_CR13","unstructured":"Karakida, R., Akaho, S., & Amari, S.-I. (2019). Universal statistics of fisher information in deep neural networks: Mean field approach. In: Chaudhuri, K., Sugiyama, M. (Eds.), Proceedings of the twenty-second international conference on artificial intelligence and statistics. Proceedings of machine learning research, (Vol. 89, pp. 1032\u20131041). Cambridge: PMLR."},{"key":"6624_CR14","unstructured":"Kolter, J. Z., & Wong, E. (2018). Provable defenses against adversarial examples via the convex outer adversarial polytope. International conference on machine learning."},{"key":"6624_CR15","unstructured":"Krizhevsky, A., Nair, V., & Hinton, G. (2009). CIFAR-10 (Canadian Institute for Advanced Research). Canada: University of Toronto."},{"key":"6624_CR16","doi-asserted-by":"crossref","unstructured":"Kuhn, H. W., & Tucker, A. W. (1951). Nonlinear programming. Proceedings of 2nd Berkeley symposium, (Vol. 2, pp. 481\u2013492). Berkeley: University of California Press.","DOI":"10.1525\/9780520411586-036"},{"key":"6624_CR17","unstructured":"Kurakin, A., Goodfellow, I., &Bengio, S. (2016). Adversarial machine learning at scale."},{"key":"6624_CR18","unstructured":"LeCun, Y. (1998). The MNIST database of handwritten digits. http:\/\/yann.lecun.com\/exdb\/mnist\/"},{"key":"6624_CR19","unstructured":"Madry, A., Makelov, A., Schmidt, L., Tsipras, D., & Vladu, A. (2019). Towards deep learning models resistant to adversarial attacks."},{"key":"6624_CR20","doi-asserted-by":"crossref","unstructured":"Molino, P. (1988). Riemannian foliations. Progress in Mathematics. MA, USA: Birkh\u00e4user Boston.","DOI":"10.1007\/978-1-4684-8670-4"},{"key":"6624_CR21","doi-asserted-by":"crossref","unstructured":"Moosavi-Dezfooli, S., Fawzi, A., & Frossard, P. (2016). Deepfool: A simple and accurate method to fool deep neural networks. 2016 IEEE conference on computer vision and pattern recognition (CVPR), (pp. 2574\u20132582). Los Alamitos: IEEE Computer Society.","DOI":"10.1109\/CVPR.2016.282"},{"issue":"10","key":"6624_CR22","doi-asserted-by":"publisher","first-page":"1100","DOI":"10.3390\/e22101100","volume":"22","author":"F Nielsen","year":"2020","unstructured":"Nielsen, F. (2020). An elementary introduction to information geometry. Entropy, 22(10), 1100.","journal-title":"Entropy"},{"issue":"3","key":"6624_CR23","doi-asserted-by":"publisher","first-page":"2698","DOI":"10.1109\/TPAMI.2022.3174724","volume":"45","author":"M Picot","year":"2022","unstructured":"Picot, M., Messina, F., Boudiaf, M., Labeau, F., Ayed, I. B., & Piantanida, P. (2022). Adversarial robustness via Fisher\u2013Rao regularization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(3), 2698\u20132710.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"6624_CR24","unstructured":"Raghunathan, A., Steinhardt, J., & Liang, P. (2020). Certified defenses against adversarial examples."},{"key":"6624_CR25","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/j.neucom.2018.04.027","volume":"307","author":"U Shaham","year":"2018","unstructured":"Shaham, U., Yamada, Y., & Negahban, S. (2018). Understanding adversarial training: Increasing local stability of supervised models through robust optimization. Neurocomputing, 307, 195\u2013204.","journal-title":"Neurocomputing"},{"key":"6624_CR26","unstructured":"Shen, C., Peng, Y., Zhang, G., &Fan, J. (2019). Defending against adversarial attacks by suppressing the largest eigenvalue of Fisher information matrix."},{"key":"6624_CR27","doi-asserted-by":"crossref","unstructured":"Strikwerda, J. C. (2004). Finite difference schemes and partial differential equations (2nd ed.). Philadelphia: Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9780898717938"},{"key":"6624_CR28","unstructured":"Szegedy, C., Zaremba, W., Sutskever, I., Bruna, J., Erhan, D., Goodfellow, I., & Fergus, R. (2014). Intriguing properties of neural networks. International conference on learning representations (ICLR)."},{"key":"6624_CR29","unstructured":"Tron, E. CurvNetAttack (2024). https:\/\/github.com\/eliot-tron\/CurvNetAttack."},{"key":"6624_CR30","unstructured":"Willmore, T. J. (2013). An introduction to differential geometry. USA: Courier Corporation."},{"key":"6624_CR31","doi-asserted-by":"publisher","DOI":"10.1109\/TAI.2024.3364121","author":"J Yan","year":"2024","unstructured":"Yan, J., Yin, H., Zhao, Z., Ge, W., & Zhang, J. (2024). Enhance adversarial robustness via geodesic distance. IEEE Transactions on Artificial Intelligence. https:\/\/doi.org\/10.1109\/TAI.2024.3364121","journal-title":"IEEE Transactions on Artificial Intelligence"},{"key":"6624_CR32","doi-asserted-by":"crossref","unstructured":"Zhao, C., Fletcher, P. T., Yu, M., Peng, Y., Zhang, G., & Shen, C. (2019). The adversarial attack and detection under the Fisher information metric. Proceedings of the AAAI conference on artificial intelligence, (Vol. 33, pp. 5869\u20135876).","DOI":"10.1609\/aaai.v33i01.33015869"},{"key":"6624_CR33","unstructured":"Zhu, J., Qiu, J., Guha, A., Yang, Z., Nguyen, X., Li, B., & Zhao, D. (2023). Interpolation for robust learning: Data augmentation on Wasserstein geodesics. International conference on machine learning,PMLR (pp. 43129\u201343157)."}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-024-06624-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10994-024-06624-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-024-06624-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T18:08:43Z","timestamp":1764266923000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10994-024-06624-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,26]]},"references-count":33,"journal-issue":{"issue":"11-12","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["6624"],"URL":"https:\/\/doi.org\/10.1007\/s10994-024-06624-w","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"type":"print","value":"0885-6125"},{"type":"electronic","value":"1573-0565"}],"subject":[],"published":{"date-parts":[[2024,10,26]]},"assertion":[{"value":"4 May 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 August 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 September 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 October 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"All authors agree and are committed to the ethical COPE guidelines.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"All authors have given their consent for publication.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}