31 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]
M.
M. Bronstein, J. Bruna, T. Cohen, and P. Veličković, “Geometric
deep learning: Grids, groups, graphs, geodesics, and gauges,”
arXiv preprint arXiv:2104.13478, 2021.
[14]
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
[15]
J.
Seely, “Sheaf cohomology of linear predictive coding
networks.” arXiv:2511.11092, 2025. Available: https://arxiv.org/abs/2511.11092
[16]
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
[17]
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
[18]
A.
F. Filippov, Differential equations with discontinuous righthand
sides. Dordrecht: Kluwer Academic Publishers, 1988.
[19]
D.
Shevitz and B. Paden, “Lyapunov stability theory of nonsmooth
systems,” IEEE Transactions on Automatic Control, vol.
39, no. 9, pp. 1910–1914, 1994.
[20]
B.
Millidge, A. Tschantz, and C. L. Buckley, “Predictive coding
approximates backprop along arbitrary computation graphs,”
Neural Computation, vol. 34, no. 6, pp. 1329–1368, 2022.
[21]
B.
Scellier and Y. Bengio, “Equilibrium propagation: Bridging the gap
between energy-based models and backpropagation,” Frontiers
in Computational Neuroscience, vol. 11, p. 24, 2017.
[22]
J.
C. R. Whittington and R. Bogacz, “An approximation of the error
backpropagation algorithm in a predictive coding network with local
hebbian synaptic plasticity,” Neural Computation, vol.
29, no. 5, pp. 1229–1262, 2017.
[23]
K.
He, X. Zhang, S. Ren, and J. Sun, “Delving deep into rectifiers:
Surpassing human-level performance on ImageNet
classification,” pp. 1026–1034, 2015.