Neural Networks as Sheaves
A Local-to-Global Course
A graduate-level web book developing the cellular-sheaf view of feedforward ReLU neural networks, building all prerequisites from scratch and working up to the results of Bosca & Ghrist (2026).
Preface
Welcome to Neural Networks as Sheaves: A Local-to-Global Course.
This is a graduate-level web book that teaches the cellular-sheaf view of feedforward ReLU neural networks developed in Bosca & Ghrist, “Neural Networks as Local-to-Global Computations,” arXiv:2603.14831v3 (March 2026). The book is designed for readers comfortable with basic calculus, abstract algebra, topology, and deep learning, but not assumed to have prior exposure to cellular sheaves, sheaf cohomology, nonsmooth dynamics, or the specific Hansen–Ghrist / Curry / Gould literature.
0.1 How to read this book
[TO FILL: one-paragraph reading contract — who this book is for, what you'll learn, what you can skip.]
See Chapter 0 for notation, a dependency graph between chapters, and skip recipes for readers who already know some of the prerequisites.
0.2 Status
This is a living draft. Most chapters contain [TO FILL: ...] placeholders that will be expanded across multiple passes. See the changelog for versioned releases.
0.3 Companion materials
- Paper: arXiv:2603.14831v3
- Code:
github.com/vicenbosca/neural-sheaf - This book:
github.com/USER/neural-sheaves-book[TO FILL]
0.4 License
[TO FILL: CC-BY 4.0 recommended]