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. 2019 Apr 23;116(19):9592–9597. doi: 10.1073/pnas.1815910116

Fig. 3.

Fig. 3.

Mechanisms underlying robustness. (A) Example initial and final W matrices after 105 iterations of learning with HVC index ordered by when the HVC cell bursts. (Top) Initial W for 0 and 50 HVC perturbations; (Middle) final W for 0 (Left) and 50 (Right) HVC perturbation events; (Bottom) learned motor trajectories for 0 (Left) and 50 (Right) HVC perturbations. Black line is the target. Light colored lines are learned trials after 105 iterations. (B) Average pairwise correlations after 105 iterations of learning between HVC cells’ synaptic projections to RA (columns of W) as a function of the time difference in firing onset. Averages are taken over HVC cells and learning trials. Correlations decrease with more HVC perturbation events. (C) Maximum pairwise correlations between HVC neurons’ synaptic projections to RA as a function of the number of HVC perturbation events. (Inset) Trajectory of maximum correlations over learning iterations. Drops in correlation occur at HVC perturbation events. (D) Schematic of the progression of W over the course of learning. Error first proceeds quickly to a minimum. Correlations in the LMAN inputs then slowly push the solution toward higher correlations if learning continues without perturbations. Solid white line shows region of approximately equal error. Purple trajectory shows W matrix undergoing learning from an initial position of low pairwise correlation. Gold trajectory shows W matrix undergoing learning from an initial position of high pairwise correlation. Blue and green dots show initial and final positions. The region near and at Wij = Wi,j+1 where error increases again is not shown in this schematic. (E) Average relearning trajectory (over 50 trials) for altered song target. (Inset) Maximum HVC pairwise correlation in W at the beginning and end of 3,000 song iterations for representative trials from E. The correlations of the initial weight matrix before learning strongly influences the correlations of the final weights after learning. Error bars represent standard error.