Outline of a Linear Neural Network

By utilizing a new definition of product, we develop a neural net model. The memorization and generalization capabilities are investigated in an Information Theory fashion. To show the memorization capabilities, we use it as a decoder, and prove the net reduces the error probability to zero in the range of the error correcting capacity of the used code. To show the generalization capabilities, we use it to infer a code from patterns received by a noisy channel. When the data are affected by independent random errors, this strategy is shown to require a small number of patterns to obtain a good identification with high probability of the code from the noisy data. We also address its use as an associative memory