Learning symmetry groups with hidden units: Beyond the perceptron
Terrence J. Sejnowski, Paul K. Kienker, Geoffrey E. Hinton · Physica D Nonlinear Phenomena · 1986
Learning to recognize mirror, rotational and translational symmetries is a difficult problem for massively-parallel network models. These symmetries cannot be learned by first-order perceptrons or Hopfield networks, which have no means for incorporating additional adaptive units that are hidden from the input and output layers. We demonstrate that the Boltzmann learning algorithm is capable of finding sets of weights which turn hidden units into useful higher-order feature detectors capable of solving symmetry problems.