[53] Joey Huchette, Gonzalo Muñoz, Tiago Serra, and Calvin Tsay. When Deep Learning Meets Polyhedral Theory: A Survey. arXiv preprint, 2023. arXiv:2305.00241.
[54] Paul Jungeblut, Linda Kleist, and Tillmann Miltzow. The Complexity of the Hausdorff Distance. In Xavier Goaoc and Michael Kerber, editors, 38th International Symposium on Computational Geometry (SoCG 2022), volume 224 of Leibniz International Proceedings in Informatics (LIPics), pages 48:1-48:17, 2022. doi:10.4230/LIPics.SoCG.2022.48.
[55] Ross Kang and Tobias Müller. Sphere and Dot Product Representations of Graphs. Discrete & Computational Geometry, 47(3):548-569, 2012. doi:10.1007/s00454-012-9394-8.
[56] Sammy Khalife and Amitabh Basu. Neural networks with linear threshold activations: structure and algorithms. In Karen Aardal and Laura Sanità, editors, International Conference on Integer Programming and Combinatorial Optimization (IPCO 2022), volume 13265 of Lecture Notes in Computer Science, pages 347-360, 2022. doi:10.1007/978-3-031-06901-7_26.
[57] Jan Kratochvil and Jiří Matoušek. Intersection Graphs of Segments. Journal of Combinatorial Theory, Series B, 62(2):289-315, 1994. doi:10.1006/jctb.1994.1071.
[58] Shiyu Liang and Rayadurgam Srikant. Why Deep Neural Networks for Function Approximation? In International Conference on Learning Representations (ICLR 2017), 2017.
[59] Anna Lubiw, Tillmann Miltzow, and Debajyoti Mondal. The Complexity of Drawing a Graph in a Polygonal Region. Journal of Graph Algorithms and Applications, 26(4):421-446, 2022. doi:10.7155/jgaa.00602.
[60] Jiří Matoušek. Intersection graphs of segments and  $\exists \mathbb{R}$ . arXiv preprint, 2014. arXiv:1406.2636.
[61] Colin McDiarmid and Tobias Müller. Integer realizations of disk and segment graphs. Journal of Combinatorial Theory, Series B, 103(1):114-143, 2013. doi:10.1016/j.jctb.2012.09.004.
[62] Tillmann Miltzow and Reinier F. Schmiermann. On Classifying Continuous Constraint Satisfaction Problems. In Nisheeth K. Vishnoi, editor, 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS), pages 781-791, 2022. doi:10.1109/F0CS52979.2021.00081.
[63] Nikolai E. Mnev. The Universality Theorems on the Classification Problem of Configuration Varieties and Convex Polytopes Varieties. In Oleg Y. Viro and Anatoly M Vershik, editors, Topology and Geometry — Rohlin Seminar, volume 1346 of Lecture Notes in Mathematics, pages 527–543. Springer, 1988. doi:10.1007/BFb0082792.
[64] Guido Montúfar, Yue Ren, and Leon Zhang. Sharp Bounds for the Number of Regions of Maxout Networks and Vertices of Minkowski Sums. SIAM Journal on Applied Algebra and Geometry, 6(4):618-649, 2022. doi:10.1137/21M1413699.
[65] Guido F. Montúfar, Razvan Pascanu, Kyunghyun Cho, and Yoshua Bengio. On the Number of Linear Regions of Deep Neural Networks. In Zoubin Ghahramani, Max Welling, Corinna Cortes, Neil Lawrence, and Weinberger Kilian Q., editors, Proceedings of the 27th International Conference on Neural Information Processing Systems (NeurIPS 2014), volume 2, pages 2924-2932, 2014.
[66] Anirbit Mukherjee and Amitabh Basu. Lower bounds over Boolean inputs for deep neural networks with ReLU gates. arXiv preprint, 2017. arXiv:1711.03073.
[67] Quynh Nguyen, Mahesh Chandra Mukkamala, and Matthias Hein. Neural Networks Should Be Wide Enough to Learn Disconnected Decision Regions. In Jennifer Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning (ICML 2018), volume 80 of Proceedings of Machine Learning Research, pages 3740-3749, 2018.
[68] Razvan Pascanu, Guido Montúfar, and Yoshua Bengio. On the number of response regions of deep feed forward networks with piece-wise linear activations. In International Conference on Learning Representations (ICLR 2014), 2014.
[69] Maithra Raghu, Ben Poole, Jon Kleinberg, Surya Ganguli, and Jascha Sohl Dickstein. On the Expressive Power of Deep Neural Networks. In Doina Precup and Yee Whye Teh, editors, Proceedings of the 34th International Conference on Machine Learning (ICML 2017), volume 70 of Proceedings of Machine Learning Research, pages 2847–2854, 2017.