Active Online Learning in the Binary Perceptron Problem*

Supported by the National Natural Science Foundation of China under Grant Nos. 11421063 and 11747601 and the Chinese Academy of Sciences under Grant No. QYZDJ-SSW-SYS018

Zhou Hai-Jun1, 2, †
       

The performance of passive online learning. The P training patterns are fed to the student sequentially and they are independent random N-dimensional Ising vectors. The pattern density is α = P/N. The total number of simulated independent online learning trajectories is . (a) The mean inference error, i.e., the mean fraction of incorrectly inferred teacher weights. The inset shows the tail part of the numerical data in semi-logarithmic scale. (b) The success fraction, i.e., the fraction of simulation trajectories in which the inferred weight vector is identical to the teacher’s weight vector.