• 1 Introduction
  • 2 Cybenko (1989): sigmoidal density
  • 3 Leshno–Lin–Pinkus–Schocken (1993): the polynomial dichotomy
  • 4 Monotone networks — Mikulincer–Reichman ▶
    • 4.1 The threshold-network model (Mikulincer–Reichman)
  • 5 Monotone networks — Sartor et al. ▶
    • 5.1 Beyond thresholds: saturating activations (Sartor et al. 2025)
  • 6 Deep constrained monotonic networks — Runje et al. ▶
    • 6.1 Constrained monotone dense layers
    • 6.2 Skip connections and deep monotone networks
    • 6.3 Deep monotone universal approximation
    • 6.4 Partial monotonicity (secondary) ▶
      • 6.4.1 Embedding non-monotone features
      • 6.4.2 Soundness and universal approximation
      • 6.4.3 Box-domain variant
      • 6.4.4 Deep-core variant
  • 7 Input-convex networks — Amos et al.
  • Dependency graph

Neural Network Universal Approximation — Blueprint

Davor Runje

  • 1 Introduction
  • 2 Cybenko (1989): sigmoidal density
  • 3 Leshno–Lin–Pinkus–Schocken (1993): the polynomial dichotomy
  • 4 Monotone networks — Mikulincer–Reichman
    • 4.1 The threshold-network model (Mikulincer–Reichman)
  • 5 Monotone networks — Sartor et al.
    • 5.1 Beyond thresholds: saturating activations (Sartor et al. 2025)
  • 6 Deep constrained monotonic networks — Runje et al.
    • 6.1 Constrained monotone dense layers
    • 6.2 Skip connections and deep monotone networks
    • 6.3 Deep monotone universal approximation
    • 6.4 Partial monotonicity (secondary)
      • 6.4.1 Embedding non-monotone features
      • 6.4.2 Soundness and universal approximation
      • 6.4.3 Box-domain variant
      • 6.4.4 Deep-core variant
  • 7 Input-convex networks — Amos et al.