Fig. 3.

Generalization and training error dynamics compared with simulations. Here we demonstrate that our theoretical predictions for generalization and training error dynamics at different measurement densities ($\alpha =1∕2,\alpha =1$, and $\alpha =2$) match with simulations. The simulations for generalization (blue) and training (green) errors have a width of $\pm 2$ standard deviations generated from 20 trials using $N=300$, $P=\alpha N$ and Gaussian input, noise, and parameters with ${\sigma }_{\overline{w}}=1,{\sigma }_w^0=0$, and $\text{SNR}=5$. The simulations show excellent agreement with our theoretical predictions for generalization and training error provided in (14), (26). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)