Table 1 Summary of the relation between zero error and kernel index sets SE, SK and the corresponding different types of QNN training dynamics
From: Quantum-data-driven dynamical transition in quantum learning
\({S}_{E}\cap {S}_{K}={{\emptyset}}\) | Exponential convergence class |
|---|---|
\({S}_{K}={{\emptyset}}\) | frozen-kernel dynamics |
\({S}_{E}={{\emptyset}}\) | frozen-error dynamics |
\({S}_{E},{S}_{K}\,\ne\, {{\emptyset}}\) | mixed-frozen dynamics |
\(\bf{ {S}_{E}\cap {S}_{K}\,\ne\, {{\emptyset}}}\) | Polynomial convergence class |
SE = SK = Ω | critical point |
SK ⊊ SE = Ω | critical-frozen-kernel dynamics |
SE ⊊ SK = Ω | critical-frozen-error dynamics |
SE ⊄ SK, SK ⊄ SE | critical-mixed-frozen dynamics |
