It has been shown by a number of people that the weights of such an element are assured of arriving at a set of values which produce the correct output-input relation after a sufficient number of errors, provided that such a set exists. An upper bound on the number of possible errors can be given which depends only on the initial weight values and the logical function to be learned. This does not, however, solve our network problem for two reasons. First, as the number, n, of inputs gets large, the number of errors to be expected for most functions which can be learned increases to unreasonable values. For example, for n = 6, most such functions result in 500 to 1000 errors compared to an average of 32 errors to be expected in a perfect learning device. Second, and more important, the fraction of those logical functions which can be generated in a single element becomes vanishingly small as n increases. For example, at n = 6 less than one in each three trillion logical functions is so obtainable. NETWORKS OF ELEMENTS It can be demonstrated that if a sufficiently large number of linear threshold elements is used, with the outputs of some being the inputs of others, then a final output can be produced which is any desired logical function of the inputs. The difficulty in such a network lies in the fact that we are no longer provided with a knowledge of the correct output for each element, but only for the final output. If the final output is incorrect there is no obvious way to determine which sets of weights should be altered. As a result of considerable study and experimentation at Aeronutronic, a network model has been evolved which, it is felt, will get around these difficulties. It consists of four basic features which will now be described. Positive Interconnecting Weights It is proposed that all weights in elements attached to inputs which come from other elements in the network be restricted to positive values. (Weights attached to the original inputs to the network, of course, must be allowed to be of either sign.) The reason for such a restriction is this. If element 1 is an input to element 2 with weight c₁₂, element 2 to element 3 with weight c₂₃, _etc._, then the sign of the product, c₁₂c₂₃ ..., gives the sense of the effect of a change in the output of element 1 on the final element in the chain (assuming this is the only such chain between the two elements). If these various weights were of either possible sign, then a decision as to whether or not to change the output in element 1 to help correct an error in the final element would involve all weights in the chain. Moreover, since there would in general be a multiplicity of such chains, the decision is rendered impossibly difficult. The above restriction removes this difficulty. If the output of any element in the network is changed, say, from -1 to +1, the effect on the final element, if it is affected at all, is in the same direction.