C = & 2, the number of errors made during training is bounded above by 2 !2 " 2 " $ 1 #2 + 8 " $ 4. Corollary 5 Suppose for a given ", B and C are such that C2 + 2(1 $ ")BC = 1; letting $ = (C!)#2, the [...] hyperplane. De- noting the normalization factor Nk on update k, we find: N2 k+1 $ ||wk + %k!||2 $ ||wk||2 + %2 k + 2%kwk $! $ 1 + %2 k + 2(1 # &)%k# (# is the mar- gin) by observing ! is bounded above by # since [...] 93.9 92.8 91.9 91.3 90.9 5 90.5 94.3 94.4 94.1 94.1 10 89.6 94.3 94.4 94.2 94.2 25 88.7 94.2 94.5 94.3 94.3 50 88.4 94.2 94.4 94.2 94.4 have suggested that learning and decoding should be done in the same …