Wavelet-like receptive fields emerges by non-linear minimization of neuron error

Redundancy reduction as a form of neural coding has been since the early sixties a topic of large research interest. A number of strategies has been proposed, but the one which is attracting most attention recently assumes that this coding is carried out so that the output signals are mutually independent. In this work we go one step further and suggest an strategy to deal also with non-orthogonal signals (i.e., "dependent" signals). Moreover, instead of working with the usual squared error, we design a neuron where the non-linearity is operating on the error. It is computationally more economic and, importantly, the permutation/scaling problem is avoided. The framework is given with a biological background, as we avocate throughout the manuscript that the algorithm fits well the single neuron and redundancy reduction doctrine. Moreover, we show that wavelet-like receptive fields emerges from natural images processed by this algorithm.