An Introduction to Hyperplane Arrangements

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On the Number of Linear Regions of Deep Neural Networks (2014, background): “For details on these arrangements see (Stanley 2004; Corollary 5.1 and Proposition 5.15).”
Provable Certificates for Adversarial Examples: Fitting a Ball in the Union of Polytopes (2019, unknown): “[23] Richard P Stanley.”
Poset Topology: Tools and Applications (2006, background): “See the chapters in this volume by Fomin and Reading [71] and Stanley [174] for further discussion of Coxeter arrangements.”
Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks (2021, background): “By virtue of a theorem of Whitney (see Stanley 2004, Theorem 2.4 and Orlik & Terao 1992, Lemma 2.55), it can be written as χA(t) = ∑ (−1)|B|tN−rank(B), where the sum runs over subarrangements B ⊆ A that are central (hyperplanes in B have a nonempty intersection), and rank(B) denotes the dimension…”
On the number of response regions of deep feed forward networks with piece-wise linear activations (2013, background): “For arrangements in general position, Zaslavsky’s theorem can be stated in the following way (see Stanley, 2004, Proposition 2.4).”