Prerequisites for Neural ODEs and Continuous-Depth Networks

Direct prerequisites (4)

1. Classical ODEs: Existence, Stability, and Numerical Methodslayer 1, tier 1
2. Skip Connections and ResNetslayer 2, tier 1
3. Gradient Flow and Vanishing Gradientslayer 2, tier 1
4. Automatic Differentiationlayer 1, tier 1

Reachable through the chain (14)

These topics are not directly cited as prerequisites but are reached transitively by following the chain upward. Working through the direct prerequisites pulls these in.

• Continuity in Rⁿlayer 0A, tier 1
• Metric Spaces, Convergence, and Completenesslayer 0A, tier 1
• The Jacobian Matrixlayer 0A, tier 1
• Feedforward Networks and Backpropagationlayer 2, tier 1
• Differentiation in Rnlayer 0A, tier 1
• Sets, Functions, and Relationslayer 0A, tier 1
• Basic Logic and Proof Techniqueslayer 0A, tier 2
• Vectors, Matrices, and Linear Mapslayer 0A, tier 1
• Matrix Calculuslayer 1, tier 1
• The Hessian Matrixlayer 0A, tier 1
• Matrix Operations and Propertieslayer 0A, tier 1
• Eigenvalues and Eigenvectorslayer 0A, tier 1
• Activation Functionslayer 1, tier 1
• Convex Optimization Basicslayer 1, tier 1