2 papers
math.NA2026
Residual neural networks overcome the curse of dimensionality for semilinear heat equations
Ilkhom Mukhammadiev, Diyora Salimova
Rigorous results show that feedforward neural networks can overcome the curse of dimensionality in the numerical approximation of high-dimensional partial differential equations (P…
math.OC2026
Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions
Shokhrukh Ibragimov, Ilkhom Mukhammadiev, Diyora Salimova
In this paper, we study the optimization landscape induced by the true loss for shallow polynomial neural networks (PNNs) with neurons on the hidden l…