Perturbed networks can learn to compensate for inactivation but the speed of recovery depends on the timescale of inactivation. a, Post-inactivation training can be much faster than the initial training. The lines show changes in the MSE error of the hierarchical network of Figure 1a during the initial training (gray) and during training after inactivation of 30% of P₂ neurons. b, Percent correct as a function of retraining trials. The gray dashed line indicates the average network performance across all stimulus strengths after initial training. c, The stability criterion α as a function of the number of retraining trials. Data points show 10 different networks before inactivation (gray) and after inactivation of 30% of P₂ neurons (black). d, Activity projected onto the first principal component for the network prior to inactivation. e, Activity projected onto the first principal component for the network after inactivation of 30% of P₂ neurons. f, Activity projected on the first principal component for the network after post-inactivation retraining. g, Fraction of explained variance as a function of the number of latent dimensions of the network activity after initial learning (black), after inactivation (purple), and after retraining (blue dashes). h, Mean retraining time to reach the pre-inactivation accuracy (<mml:math display="inline"><mml:mn>80</mml:mn><mml:mo>±</mml:mo><mml:mn>0.5</mml:mn><mml:mi mathvariant="normal">%</mml:mi></mml:math>80±0.5%) as a function of the percentage of unperturbed neurons in the network. i, Retraining slows down considerably if inactivation of neurons occurs on a fast timescale that allows mixing perturbed and unperturbed trials during retraining. In this simulation, inactivation was limited to a random half of trials. Integration error goes down slowly with the number of perturbed trials (orange), taking more trials than that required for the trial initial training (gray). For the unperturbed trials (black), integration error remains close to the levels following the initial training. Error bars indicate ±1 s.e.m. over 10 trained networks.