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\u91cc\u514b\u662f\u5fb7\u570b\u5f17\u91cc\u5821\u5927\u5b78\uff08University of Fribourg\uff09\u7684\u6a5f\u5668\u5b78\u7fd2\u6559\u6388\uff0c\u4e26\u64d4\u4efbAI\u8cc7\u6599\u79d1\u5b78\u5be6\u9a57\u5ba4\uff08AI for Data-Oriented Science\uff09\u9996\u5e2d\u7814\u7a76\u54e1\u3002\u4ed6\u7814\u7a76\u5982\u4f55\u900f\u904e\u5e7e\u4f55\u5b78\u548c\u62d3\u6a38\u5b78\u7684\u8996\u89d2\uff0c\u6539\u5584\u6a5f\u5668\u5b78\u7fd2\u548c AI\u6240\u9700\u8981\u7684\u5805\u5be6\u57fa\u790e\u3002<\/p>\n\n\n\n\u8b6f\u8005<\/strong>\u3000\u738b\u590f\u8072<\/p>\n\n\n\n\u8b6f\u8005\u7c21\u4ecb<\/strong>
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\u672c\u6587\u8b6f\u81eaBastian Rieck,\u201cTopology Meets Machine Learning: An Introduction Using the Euler Characteristic Transforms\u201d, Notices of the AMS 72\uff082025\uff09No. 7, AMS\u3002\u00a9 American Mathematical Society 2008. All rights reserved\u3002\u611f\u8b1dAMS\u8207\u4f5c\u8005\u540c\u610f\u8f49\u8f09\u7ffb\u8b6f\u3002<\/p>\n\n\n\n\u5ef6\u4f38\u95b1\u8b80<\/strong>
\u672c\u520a\u66fe\u520a\u767b\u7684\u7b2c10\u671f\u300c\u4eba\u5de5\u667a\u6167\u8207AlphaGo\u300d\u8207\u7b2c17\u671f\u300c\u6a5f\u5668\u5b78\u7fd2\u300d\u7684\u5c08\u984c\u3001\u7b2c18\u671f\u6797\u8ed2\u7530\u7684\u3008\u4ec0\u9ebc\u662f\u6a5f\u5668\u5b78\u7fd2\u2014\u2014\u6a5f\u5668\u5b78\u7fd2\u6f2b\u8ac7\u3009\u4ee5\u53ca\u7b2c19\u671f\u9102\u7dad\u5357\u7684\u3008\u6a5f\u5668\u5b78\u7fd2\u2014\u2014\u6578\u5b78\u7406\u8ad6\u8207\u79d1\u5b78\u61c9\u7528\u3009\u8af8\u7bc7\u6587\u7ae0\uff0c\u8b80\u8005\u53ef\u4ee5\u53c3\u7167\u672c\u6587\u95b1\u8b80\u3002<\/p>\n\n\n\n\u53c3\u8003\u6587\u737b<\/strong>
[CAD+21] Anirban Chakraborty, Manaar Alam, Vishal Dey, Anupam Chattopadhyay, and Debdeep Mukhopadhyay, A survey on adversarial attacks and defences, CAAI Transactions on Intelligence Technology 6 (2021), no. 1, 25\u201345.
[CMT22] Justin Curry, Sayan Mukherjee, and Katharine Turner, How many directions determine a shape and other sufficiency results for two topological transforms, Trans. Amer. Math. Soc. Ser. B 9 (2022), 1006\u20131043.
[Ghr25] Robert Ghrist, AI & mathematics as a career (January 2025).
[GLM18] Robert Ghrist, Rachel Levanger, and Huy Mai, Persistent homology and Euler integral transforms, J. Appl. Comput. Topol. 2 (2018), no. 1-2, 55\u201360.
[HH19] Catherine F. Higham and Desmond J. Higham, Deep learning: an introduction for applied mathematicians, SIAM Rev. 61 (2019), no. 4, 860\u2013891.
[HIZ20] Mustafa Hajij, Kyle Istvan, and Ghada Zamzmi, Cell complex neural networks, \u201cTopological Data Analysis and Beyond\u201d Workshop at NeurIPS, 2020.
[HSW89] Kurt Hornik, Maxwell Stinchcombe, and Halbert White, Multilayer feedforward networks are universal approximators, Neural Networks 2 (1989), no. 5, 359\u2013366.
[MHR24] Kelly Maggs, Celia Hacker, and Bastian Rieck, Simplicial representation learning with neural \ud835\udc58-forms, International Conference on Learning Representations, 2024.
[Mun25] Elizabeth Munch, An invitation to the Euler characteristic transform, Amer. Math. Monthly 132 (2025), no. 1, 15\u201325.
[PBB+24] Theodore Papamarkou, Tolga Birdal, Michael Bronstein, Gunnar Carlsson, Justin Curry, Yue Gao, Mustafa Hajij, Roland Kwitt, Pietro Li\u00f2, Paolo Di Lorenzo, Vasileios Maroulas, Nina Miolane, Farzana Nasrin, Karthikeyan Natesan Ramamurthy, Bastian Rieck, Simone Scardapane, Michael T. Schaub, Petar Veli\u010dkovi\u0107, Bei Wang, Yusu Wang, Guo-Wei Wei, and Ghada Zamzmi, Position: Topological deep learning is the new frontier for relational learning, Proceedings of the 41st International Conference on Machine Learning, 2024, pp. 39529\u201339555.
[RR24] Ernst R\u00f6ell and Bastian Rieck, Differentiable Euler characteristic transforms for shape classification, International Conference on Learning Representations, 2024.
[Sch22] J\u00fcrgen Schmidhuber, Annotated history of modern AI and deep learning, 2022.
[TMB14] Katharine Turner, Sayan Mukherjee, and Doug M. Boyer, Persistent homology transform for modeling shapes and surfaces, Inf. Inference 3 (2014), no. 4, 310\u2013344.
[Vel23] Petar Veli\u010dkovi\u0107, Everything is connected: Graph neural networks, Current Opinion in Structural Biology 79 (2023), 102538.
[WAM+22] Dominik J. E. Waibel, Scott Atwell, Matthias Meier, Carsten Marr, and Bastian Rieck, Capturing shape information with multi-scale topological loss terms for 3D reconstruction, Medical Image Computing and Computer Assisted Intervention, 2022, pp. 150\u2013159.
[Won24] Matteo Wong, We\u2019re entering uncharted territory for math, The Atlantic (October 2024).<\/p>\n\n\n\n<\/p>\n\n\n\n
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