### Neurally-plausible position-invariant flow field detectors

We previously demonstrated that it is possible to learn
position-independent responses to rotation and dilation by filtering
rotations and dilations with different centers through an input layer
with MT-like speed and direction tuning curves and connecting them to
an MST-like layer with simple Hebbian synapses (Sereno and Sereno
1991). By analyzing an idealized version of the network with broader,
sinusoidal direction-tuning and linear speed-tuning, Kechen Zhang
showed analytically that a Hebb rule trained with arbitrary rotation,
dilation/contraction, and translation velocity fields yields units
with weight fields that are a rotation plus a dilation or contraction
field, and whose responses to a rotating or dilating/contracting disk
are exactly position-independent. Differences between the performance
of this idealized model and our original model (and real MST neurons)
are discussed.

### Proof of position-invariant response to flow fields

Response elicited by a rotating (a) or dilating (b) ring in a
receptive field with circular or radial distribution of direction
selectivity is independent of the position of the ring (see Zhang,
Sereno, and Sereno, 1993).

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