{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T09:29:06Z","timestamp":1769938146449,"version":"3.49.0"},"publisher-location":"Singapore","reference-count":21,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819549689","type":"print"},{"value":"9789819549696","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T00:00:00Z","timestamp":1764028800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T00:00:00Z","timestamp":1764028800000},"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\/978-981-95-4969-6_11","type":"book-chapter","created":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T08:48:33Z","timestamp":1763974113000},"page":"137-149","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Probabilistic Lipschitzness and\u00a0the\u00a0Stable Rank for\u00a0Measuring XAI Model Robustness"],"prefix":"10.1007","author":[{"given":"Lachlan","family":"Simpson","sequence":"first","affiliation":[]},{"given":"Kyle","family":"Millar","sequence":"additional","affiliation":[]},{"given":"Adriel","family":"Cheng","sequence":"additional","affiliation":[]},{"given":"Cheng-Chew","family":"Lim","sequence":"additional","affiliation":[]},{"given":"Hong Gunn","family":"Chew","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,25]]},"reference":[{"key":"11_CR1","unstructured":"Agarwal, S., Jabbari, S., Agarwal, C., Upadhyay, S., Wu, S., Lakkaraju, H.: Towards the unification and robustness of perturbation and gradient based explanations. In: Proceedings of the 38th International Conference on Machine Learning, vol. 139, pp. 110\u2013119 (2021)"},{"key":"11_CR2","unstructured":"Alvarez-Melis, D., Jaakkola, T.S.: On the robustness of interpretability methods. arXiv preprint arXiv:1806.08049 (2018)"},{"key":"11_CR3","unstructured":"Avant, T., Morgansen, K.A.: Analytical bounds on the local lipschitz constants of relu networks. IEEE Trans. Neural Networks Learn. Syst. 1\u201312 (2023)"},{"key":"11_CR4","unstructured":"Bartlett, P.L., Foster, D.J., Telgarsky, M.J.: Spectrally-normalized margin bounds for neural networks. In: Advances in Neural Information Processing Systems (NeurIPS), vol. 30 (2017)"},{"key":"11_CR5","doi-asserted-by":"crossref","unstructured":"Bommer, P., Kretschmer, M., Hedstr\u00f6m, A., Bareeva, D., H\u00f6hne, M.M.C.: Finding the right XAI method \u2013 a guide for the evaluation and ranking of explainable AI methods in climate science. arXiv preprint arXiv:2303.00652 (2023)","DOI":"10.1175\/AIES-D-23-0074.1"},{"key":"11_CR6","unstructured":"Federer, H.: Geometric Measure Theory. Springer, Berlin and Heidelberg (2005)"},{"key":"11_CR7","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/s10994-020-05929-w","volume":"110","author":"H Gouk","year":"2020","unstructured":"Gouk, H., Frank, E., Pfahringer, B., Cree, M.J.: Regularisation of neural networks by enforcing lipschitz continuity. Mach. Learn. 110, 393\u2013416 (2020)","journal-title":"Mach. Learn."},{"key":"11_CR8","unstructured":"Jordan, M., Dimakis, A.G.: Exactly computing the local lipschitz constant of relu networks. In: Advances in Neural Information Processing Systems (NeurIPS), vol. 33, pp. 7344\u20137353 (2020)"},{"key":"11_CR9","unstructured":"Khan, Z., Hill, D., Masoomi, A., Bone, J., Dy, J.: Analyzing explainer robustness via lipschitzness of prediction functions. arXiv preprint arXiv:2206.12481 (2023)"},{"key":"11_CR10","doi-asserted-by":"crossref","unstructured":"Mangal, R., Sarangmath, K., Nori, A.V., Orso, A.: Probabilistic lipschitz analysis of neural networks. Inte. Static Anal. Symp. (SAS) 274\u2013309 (2020)","DOI":"10.1007\/978-3-030-65474-0_13"},{"key":"11_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.dsp.2017.10.011","volume":"73","author":"G Montavon","year":"2018","unstructured":"Montavon, G., Samek, W., M\u00fcller, K.R.: Methods for interpreting and understanding deep neural networks. Digital Sig. Process. 73, 1\u201315 (2018)","journal-title":"Digital Sig. Process."},{"key":"11_CR12","unstructured":"Neyshabur, B., Tomioka, R., Srebro, N.: Norm-based capacity control in neural networks. In: Proceedings of the 28th Conference on Learning Theory, vol. 40, pp. 1376\u20131401 (2015)"},{"key":"11_CR13","doi-asserted-by":"crossref","unstructured":"Ramasinghe, S., Lucey, S.: Beyond periodicity: towards a unifying framework for activations in coordinate-mlps. In: European Conference on Computer Vision (ECCV), pp. 142\u2013158 (2022)","DOI":"10.1007\/978-3-031-19827-4_9"},{"key":"11_CR14","unstructured":"Sanyal, A., Torr, P., Dokania, P.: Stable rank normalization for improved generalization in neural networks and GANS. In: Eighth International Conference on Learning Representations (ICLR) (2020)"},{"key":"11_CR15","unstructured":"Scaman, K., Virmaux, A.: Lipschitz regularity of deep neural networks: analysis and efficient estimation. In: Advances in Neural Information Processing Systems (NeurIPS), vol. 31 (2018)"},{"key":"11_CR16","unstructured":"Simpson, L., Costanza, F., Millar, K., Cheng, A., Lim, C.C., Chew, H.G.: Tangentially aligned integrated gradients for user-friendly explanations. In: Irish Conference on Artificial Intelligence and Cognitive Science (AICS), pp. 1\u201312 (2024)"},{"key":"11_CR17","unstructured":"Smilkov, D., Thorat, N., Kim, B., Vi\u00e9gas, F., Wattenberg, M.: Smoothgrad: removing noise by adding noise. arXiv preprint arXiv:1706.03825 (2017)"},{"key":"11_CR18","unstructured":"Sundararajan, M., Taly, A., Yan, Q.: Axiomatic attribution for deep networks. In: Proceedings of the 34th International Conference on Machine Learning (ICML), vol. 70, pp. 3319\u20133328 (2017)"},{"issue":"11","key":"11_CR19","doi-asserted-by":"publisher","first-page":"4793","DOI":"10.1109\/TNNLS.2020.3027314","volume":"32","author":"E Tjoa","year":"2021","unstructured":"Tjoa, E., Guan, C.: A survey on explainable artificial intelligence (XAI): Toward medical XAI. IEEE Trans. Neural Networks Learn. Syst. 32(11), 4793\u20134813 (2021)","journal-title":"IEEE Trans. Neural Networks Learn. Syst."},{"key":"11_CR20","unstructured":"Yeh, C.K., Hsieh, C.Y., Suggala, A.S., Inouye, D.I., Ravikumar, P.: On the (in)fidelity and sensitivity of explanations. In: Proceedings of the 33rd International Conference on Neural Information Processing Systems (2019)"},{"key":"11_CR21","doi-asserted-by":"publisher","first-page":"93104","DOI":"10.1109\/ACCESS.2022.3204051","volume":"10","author":"Z Zhang","year":"2022","unstructured":"Zhang, Z., Hamadi, H.A., Damiani, E., Yeun, C.Y., Taher, F.: Explainable artificial intelligence applications in cyber security: state-of-the-art in research. IEEE Access 10, 93104\u201393139 (2022)","journal-title":"IEEE Access"}],"container-title":["Lecture Notes in Computer Science","AI 2025: Advances in Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-95-4969-6_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T20:57:30Z","timestamp":1769893050000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-95-4969-6_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,25]]},"ISBN":["9789819549689","9789819549696"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-981-95-4969-6_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,25]]},"assertion":[{"value":"25 November 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"AI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Australasian Joint Conference on Artificial Intelligence","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Canberra, ACT","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Australia","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":"1 December 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5 December 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"38","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ausai2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ajcai2025.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}