We consider the fundamental question: how a legacy ‘student’ Artificial Intelligent (AI) system could learn from a legacy ‘teacher’ AI system or a human expert without complete re-training and, most importantly, without requiring significant computational resources. Here ‘learning’ is understood as an ability of one system to mimic responses of the other and vice-versa. We call such learning an Artificial Intelligence knowledge transfer. We show that if internal variables of the ‘student’ Artificial Intelligent system have the structure of an $n$-dimensional topological vector space and $n$ is sufficiently high then, with probability close to one, the required knowledge transfer can be implemented by simple cascades of linear functionals. In particular, for $n$ sufficiently large, with probability close to one, the ‘student’ system can successfully and non-iteratively learn $k\ll n$ new examples from the ‘teacher’ (or correct the same number of mistakes) at the cost of two additional inner products. The concept is illustrated with an example of knowledge transfer from a pre-trained convolutional neural network to a simple linear classifier with HOG features. Knowledge Transfer Between Artificial Intelligence Systems