[14] Song Han, Jeff Pool, John Tran, and William Dally. Learning both weights and connections for efficient neural network. In C. Cortes, N. Lawrence, D. Lee, M. Sugiyama, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 28. Curran Associates, Inc., 2015.
[15] P. Kainen, V. Kürková, and A. Vogt. Best approximation by heaviside perceptron networks. Neural Networks, 13(7):695-697, 2000.
[16] Věra Kürková. Approximation of functions by perceptron networks with bounded number of hidden units. Neural Networks, 8(5):745-750, 1995.
[17] Quoc-Tung Le, Rémi Gribonval, and Elisa Riccietti. Code for reproducible research: Does a sparse ReLU network training problemals admit an optimum? Code repository available at https://hal.science/hal-04233925, October 2023.
[18] Quoc-Tung Le, Elisa Riccietti, and Rémi Gribonval. Spurious Valleys, NP-hardness, and Tractability of Sparse Matrix Factorization With Fixed Support. SIAM Journal on Matrix Analysis and Applications, 2022.
[19] Namhoon Lee, Thalaiyasingam Ajanthan, and Philip HS Torr. SNIP: single-shot network pruning based on connection sensitivity. *ICLR*, 2019.
[20] Lek-Heng Lim, Mateusz Michalek, and Yang Qi. Best  $k$ -layer neural network approximations. Constructive Approximation, June 2021.
[21] Rui Lin, Jie Ran, King Hung Chiu, Graziano Chesi, and Ngai Wong. Deformable butterfly: A highly structured and sparse linear transform. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P.S. Liang, and J. Wortman Vaughan, editors, Advances in Neural Information Processing Systems, volume 34, pages 16145-16157. Curran Associates, Inc., 2021.
[22] Shiwei Liu, Tianlong Chen, Xiaohan Chen, Li Shen, Decebal Constantin Mocanu, Zhangyang Wang, and Mykola Pechenizkiy. The unreasonable effectiveness of random pruning: Return of the most naive baseline for sparse training. arXiv preprint arXiv:2202.02643, 2022.
[23] Scott Mahan, Emily J. King, and Alex Cloninger. Nonclosedness of sets of neural networks in sobolev spaces. Neural Networks, 137:85-96, may 2021.
[24] Guido Montúfar, Razvan Pascanu, Kyunghyun Cho, and Yoshua Bengio. On the number of linear regions of deep neural networks. In Proceedings of the 27th International Conference on Neural Information Processing Systems - Volume 2, NIPS'14, page 2924-2932, Cambridge, MA, USA, 2014. MIT Press.
[25] Pavel Okunev and Charles R. Johnson. Necessary and sufficient conditions for existence of the lu factorization of an arbitrary matrix, 2005.
[26] Philipp Petersen, Mones Raslan, and Felix Voigtlaender. Topological properties of the set of functions generated by neural networks of fixed size. Found. Comput. Math., 21(2):375-444, apr 2021.
[27] E. Quemener and M. Corvellec. SIDUS—the Solution for Extreme Dedduplication of an Operating System. Linux Journal, 2013.
[28] Pierre Stock and Rémi Gribonval. An Embedding of ReLU Networks and an Analysis of their Identifiability. Constructive Approximation, 2022.
[29] Hidenori Tanaka, Daniel Kunin, Daniel L. K. Yamins, and Surya Ganguli. Pruning neural networks without any data by iteratively conserving synaptic flow. In Proceedings of the 34th International Conference on Neural Information Processing Systems, NIPS'20, Red Hook, NY, USA, 2020. Curran Associates Inc.
[30] Jared Tanner, Andrew Thompson, and Simon Vary. Matrix rigidity and the ill-posedness of robust pca and matrix completion. SIAM Journal on Mathematics of Data Science, 1(3):537-554, 2019.