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So far, the
states of the units in one layer have only been
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used to
determine the effective biases of the units in the
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layer below.
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It would be much
more powerful to modulate the pair-wise
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interactions in
the layer below. (A good way
to design a
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hierarchical
system is to allow each level to determine the
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objective
function of the level below.)
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For
example, a vertical edge represents a breakdown in
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the
usual correlational structure of the pixels: Horizontal
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interpolation
does not work, so it needs to be turned off,
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but
interpolation parallel to the edge is OK.
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To modulate
pair-wise interactions we need higher-order
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Boltzmann
machines.
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