  Learning to detect content-independent transformations from data is one of
the central problems in biological and artificial intelligence. An example of
such problem is unsupervised learning of a visual motion detector from pairs of
consecutive video frames. Rao and Ruderman formulated this problem in terms of
learning infinitesimal transformation operators (Lie group generators) via
minimizing image reconstruction error. Unfortunately, it is difficult to map
their model onto a biologically plausible neural network (NN) with local
learning rules. Here we propose a biologically plausible model of motion
detection. We also adopt the transformation-operator approach but, instead of
reconstruction-error minimization, start with a similarity-preserving objective
function. An online algorithm that optimizes such an objective function
naturally maps onto an NN with biologically plausible learning rules. The
trained NN recapitulates major features of the well-studied motion detector in
the fly. In particular, it is consistent with the experimental observation that
local motion detectors combine information from at least three adjacent pixels,
something that contradicts the celebrated Hassenstein-Reichardt model.
