【正文】 – in automatic systems, metaknowledge is supplied to the puter learner by the human teacher in the form of a criterion of performance assessment. Two questions then arise: – what connects the knowledge with the metaknowledge? – how is metaknowledge learnt in the first place? 4 Learning by Demonstration To answer the above questions, we get a clue from the second type of learning we mentioned earlier, namely learning by demonstration. The demonstrator here is the teacher. The next is a story I heard from my grandmother. Remember that the traditional way of teaching children has always been through stories and parables. This story offers the clue we are searching for. ?Once upon a time there was a potter who got an apprentice who wanted to learn the art of pottery. The potter made his clay pots and put them in the oven. After two hours, he turned the fire off, and sat down to rest and smoke, as he was an old man. Then he took the pots out of the oven. They were perfect. The apprentice later decided to do his own pots. He made them out of clay and put them in the oven. After two hours, he took them out. The pots broke. He repeated the task and he had the same results. He went back to the potter: “You did not teach me well. Such and such happened.” “Did you stop to smoke after you switched off the fire?” “No, I am not a smoker.” “So, you got the pots out of the oven too soon.”? I am sure the story was related to me in order to teach me to pay attention to the detail. Indeed, if the apprentice had seen the potter performing the act dozens of times with slight variation each time, but always with the pause before the pots were taken out of the oven, he might have worked out that that pose was crucial to the process. On the other hand, the teacher might have been a better teacher if he had made that information explicit. So, this story tells us that we learn fast, from very few examples, only when somebody explains to us why things are done the way they are done. A child asks lots of “why”s and that is how a child learns. This tells me that we cannot disassociate learning to recognise objects from learning why each object is the way it is. One may consider the following exchange between a teacher and a learner: “What is this?” “This is a window.” “Why?” “Because it lets the light in and allows the people to look out.” “How?” “By having an opening at eye level.” “Does it really?” This sequence of learning is shown in Fig. 1. This figure proposes that knowledge in our brain is represented by a series of works, forming a plex structure that I call the “tower of knowledge”. The work of nouns is a work of object names, labels, . “window”, “chimney”, “door”, etc. The work of verbs or actions, is a work of functionalities, . “to look out”, “to enter”, “to exit”, etc. The work of appearances is a work of basic shapes necessary for a functionality to be fulfilled, . “it is an opening of human size at floor level”. So, the flow of knowledge goes like the fragment of conversation given above. The loop closes when we confirm that the object we are looking at has the right characteristics for its functional purpose to be fulfilled. The task, therefore, for the artificial vision scientist, is to model these layers of works and their interconnections. We have various tools at our disposal: Markov Random Fields [8], grammars [19], inference rules [24], Bayesian works [16], Fuzzy inference [27], etc. I would exclude from the beginning any deterministic crisp approaches, either because things are genuinely random in nature (or at least have a significant random ponent), or because our models and our knowledge is far too gross and imperfect for creating crisp rules and dogmatic decisions. 5 Markov Random Fields Some recent work [17] showed evidence that the work of nouns (better described in psychophysical terms as work of “ideas”) is topologically a random work, while the work of relations, made up from pairs of ideas, is topologically scalefree. For example, pairs like “forkknife”, “doorwindow” e up much more frequently in trains of thought than “door” alone, or “window” alone. This indicates that the connections in these works are of varied strength, and actually are not always symmetric. For example, the idea “door” may trigger the idea “window” more frequently than the idea “window” triggers the idea “door”. This asymmetry in the interactions is a manifestation that Markov Random Fields (MRFs) are not applicable here in their usual form in which they are applied in image processing. An example of the interactions in a neighbourhood of an MRF, defined on a grid, is shown in Fig. 2b. This MRF, and the weights it gives for neighbouring interactions, cannot be expressed by a Gibbs joint probability density function. For example, the cell at the centre is influenced by its top left neighbour with weight ?1, but itself, being the bottom right neighbor of the cell at the top left, influences it with weight +1. This asymmetry leads to instability when one tries to relax such a random field, because local patterns created are not globally consistent (and therefore not expressible by global Gibbs distributions) [18]. According to Li [9,10,11], relaxations of such MRFs do not converge, but oscillate between several possible states. (Optimisations of Gibbs distributions either converge to the right interpretation, but more often than not, they hallucinate, . they settle on wrong interpretations.) So, one could model the work at each level of the tower of knowledge shown in Fig. 1, using a nonGibbsian MRF [5]. The interdependences between layers might also be modelled by such works, but perhaps it is more appropriate to use Bayesian models, as the interlayer dependencies are causal or diagnostic, rather than peertopeer.