17  References

References

References are pulled automatically from references/references.bib.

[1]

V. Bosca and R. Ghrist, “Neural networks as local-to-global computations,” arXiv preprint arXiv:2603.14831, 2026, Available: https://arxiv.org/abs/2603.14831

[2]

V. Bosca and R. Ghrist, “Selective adaptation of beliefs and communication on cellular sheaves,” arXiv preprint arXiv:2601.22431, 2026, Available: https://arxiv.org/abs/2601.22431

[3]

J. M. Curry, “Sheaves, cosheaves and applications,” PhD thesis, University of Pennsylvania, 2014. Available: https://arxiv.org/abs/1303.3255

[4]

J. Hansen and R. Ghrist, “Toward a spectral theory of cellular sheaves,” Journal of Applied and Computational Topology, vol. 3, no. 4, pp. 315–358, 2019.

[5]

J. Hansen and R. Ghrist, “Opinion dynamics on discourse sheaves,” SIAM Journal on Applied Mathematics, vol. 81, no. 5, pp. 2033–2060, 2021, doi: 10.1137/20M1341088.

[6]

J. Hansen and T. Gebhart, “Sheaf neural networks,” in NeurIPS 2020 workshop on topological data analysis and beyond, 2020. Available: https://arxiv.org/abs/2012.06333

[7]

C. Bodnar, F. Di Giovanni, B. P. Chamberlain, P. Liò, and M. M. Bronstein, “Neural sheaf diffusion: A topological perspective on heterophily and oversmoothing in GNNs,” in Advances in neural information processing systems, 2022. Available: https://arxiv.org/abs/2202.04579

[8]

R. Ghrist, Elementary applied topology. Createspace, 2014.

[9]

J. Cortés, “Discontinuous dynamical systems: A tutorial on solutions, nonsmooth analysis, and stability,” IEEE Control Systems Magazine, vol. 28, no. 3, pp. 36–73, 2008.

[10]

R. Arora, A. Basu, P. Mianjy, and A. Mukherjee, “Understanding deep neural networks with rectified linear units,” 2018.

[11]

G. F. Montúfar, R. Pascanu, K. Cho, and Y. Bengio, “On the number of linear regions of deep neural networks,” 2014.

[12]

L.-H. Lim, “Hodge Laplacians on graphs,” SIAM Review, vol. 62, no. 3, 2020.

[13]

J. J. Gould, “Cellular sheaves of Hilbert spaces,” PhD thesis, University of Pennsylvania, Philadelphia, PA, 2025. Available: https://repository.upenn.edu/entities/publication/a40a44d9-f4e2-4c56-abcb-53936caeffad

[14]

J. Seely, “Sheaf cohomology of linear predictive coding networks.” arXiv:2511.11092, 2025. Available: https://arxiv.org/abs/2511.11092

[15]

V. Bosca, T. Rask, S. Tanweer, A. R. Tawfeek, and B. Stone, “Topological signatures of ReLU neural network activation patterns,” in Topology, algebra, and geometry in data science, 2025. Available: https://openreview.net/forum?id=Q88w76j2Dd

[16]

Y. Liu, C. M. Cole, C. Peterson, and M. Kirby, “ReLU neural networks, polyhedral decompositions, and persistent homology.” arXiv:2306.17418, 2023. Available: https://arxiv.org/abs/2306.17418

[17]

A. F. Filippov, Differential equations with discontinuous righthand sides. Dordrecht: Kluwer Academic Publishers, 1988.

[18]

D. Shevitz and B. Paden, “Lyapunov stability theory of nonsmooth systems,” IEEE Transactions on Automatic Control, vol. 39, no. 9, pp. 1910–1914, 1994.