النقل والتجميد والتكييف المقيد

features = [[1.0, 2.0], [2.0, 1.0]]
targets = [3.0, 3.0]
head = [0.0, 0.0]
gradient = [sum((sum(w*x for w,x in zip(head,row))-y)*row[j]
                for row,y in zip(features,targets))/len(targets) for j in range(2)]
updated = [w-0.1*g for w,g in zip(head,gradient)]
print("gradient", gradient)
print("head", updated)
print("features unchanged", features == [[1.0,2.0],[2.0,1.0]])

gradient [-4.5, -4.5]
head [0.45, 0.45]
features unchanged True

يمثل جدول ثابت مستخرجاً مجمداً، ولا يحدث سوى معاملي الرأس الخطي.

W = [[1, 0], [0, 1]]
a = [1, -1]
b = [2, 3]
update = [[ai*bj for bj in b] for ai in a]
adapted = [[W[i][j]+update[i][j] for j in range(2)] for i in range(2)]
print("rank-one update", update)
print("adapted", adapted)

rank-one update [[2, 3], [-2, -3]]
adapted [[3, 3], [-2, -2]]

يعطي الضرب الخارجي تحديثاً جمعياً رتبته لا تتجاوز واحداً دون تدريب أو نموذج سابق.